[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 

Computer Graphics, Image Processing and Artificial Intelligence

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: closed (28 February 2022) | Viewed by 68563

Special Issue Editors


E-Mail Website
Guest Editor
1. Department of Applied Mathematics and Computational Sciences, University of Cantabria, C.P. 39005 Santander, Spain
2. Department of Information Science, Faculty of Sciences, Toho University, 2-2-1 Miyama, Funabashi 274-8510, Japan
Interests: artificial Intelligence; soft computing for optimization; evolutionary computation; computational intelligence
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
National Centre for Computer Animation, Bournemouth University, Bournemouth BH12 5BB, UK
Interests: geometric modeling; computer animation; computer graphics; image and point cloud-based shape reconstruction; machine learning; applications of ODEs and PDEs in geometric modeling and computer animation
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Centre for Visual Computing, University of Bradford, Bradford BD7 1DP, UK
Interests: geometric design; computer graphics; machine learning; visualisation; mathematical modelling
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
1. Department of Applied Mathematics and Computational Sciences, University of Cantabria, C.P. 39005 Santander, Spain
2. Department of Information Science, Faculty of Sciences, Toho University, 2-2-1 Miyama, 274-8510 Funabashi, Japan
Interests: swarm intelligence and swarm robotics; bio-inspired optimisation; computer graphics; geometric modelling
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Mathematics, University of Bergen, PB 7803, 5020 Bergen, Norway
Interests: numerical methods; image processing

Special Issue Information

Dear Colleagues,

Computer graphics, image processing and artificial intelligence are three of the most popular, exciting, and hot domains in the intersection of mathematics and computer science. These three areas share a broad range of applications in many different fields, and new impressive developments are arising every year. This Special Issue is aimed at providing a forum for discussion of new techniques, algorithms, methods, and technologies in any such areas, as well as their applications to science, engineering, industry, education, health, and entertainment. The interplay between any two of these areas is also of interest for this Special Issue.

This Special Issue will be mainly based on the selected papers from the 2nd International Workshop on Computer Graphics, Image Processing and Artificial Intelligence, CGIPAI-2021, held in Krakow (Poland), as a part of the International Conference on Computational Sciences (ICCS-2021). However, it is also open to researchers and practitioners working in these areas and submitting papers from outside this workshop.

We invite prospective authors to submit their contributions for fruitful interdisciplinary cooperation and exchange of new ideas and experiences, as well as to identify new issues and challenges and to shape future directions and trends for research in computer graphics, image processing, and/or artificial intelligence.

Potential topics include but are not limited to:

  • Geometric and solid modelling and processing;
  • CAD/CAM/CAE;
  • Curve/surface reconstruction;
  • Computer graphic techniques, algorithms, software, and hardware;
  • Computer animation, video games;
  • Virtual/augmented reality, virtual environments, autonomous agents;
  • Computer graphics applications (science, engineering, education, health, industry, entertainment);
  • Image processing techniques;
  • Image processing processes (e.g., image denoising, image deblurring, image segmentation, image reconstruction, depth estimation, 3D surface restoration);
  • Image processing applications;
  • Evolutionary and nature-inspired algorithms (evolutionary programming, genetic algorithms);
  • Neural networks, machine learning, deep learning, and data mining;
  • Swarm intelligence and swarm robotics;
  • Bio-informatics and bio-engineering;
  • Natural computing, soft computing, and evolutionary computing;
  • Artificial intelligence applications;

Interplay among some of the previous areas.

Prof. Dr. Akemi Galvez Tomida
Dr. Lihua You
Prof. Dr. Hassan Ugail
Prof. Dr. Andres Iglesias Prieto
Prof. Dr. Alexander Malyshev
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Computer graphics 
  • Geometric modelling 
  • Curves and surfaces
  • Image processing 
  • Image reconstruction 
  • Visualisation 
  • Artificial intelligence
  • Machine learning 
  • Deep learning 
  • Bio-inspired computation 
  • Swarm intelligence

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (20 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Jump to: Review

26 pages, 15315 KiB  
Article
IFS-Based Image Reconstruction of Binary Images with Functional Networks
by Akemi Gálvez, Iztok Fister, Andrés Iglesias, Iztok Fister, Jr., Valentín Gómez-Jauregui, Cristina Manchado and César Otero
Mathematics 2022, 10(7), 1107; https://doi.org/10.3390/math10071107 - 29 Mar 2022
Cited by 1 | Viewed by 1748
Abstract
This work addresses the IFS-based image reconstruction problem for binary images. Given a binary image as the input, the goal is to obtain all the parameters of an iterated function system whose attractor approximates the input image accurately; the quality of this approximation [...] Read more.
This work addresses the IFS-based image reconstruction problem for binary images. Given a binary image as the input, the goal is to obtain all the parameters of an iterated function system whose attractor approximates the input image accurately; the quality of this approximation is measured according to a similarity function between the original and the reconstructed images. This paper introduces a new method to tackle this issue. The method is based on functional networks, a powerful extension of neural networks that uses functions instead of the scalar weights typically found in standard neural networks. The method relies on an artificial network comprised of several functional networks, one for each of the contractive affine maps forming the IFS. The method is applied to an illustrative and challenging example of a fractal binary image exhibiting a complicated shape. The graphical and numerical results show that the method performs very well and is able to reconstruct the input image using IFS with high accuracy. The results also show that the method is not yet optimal and offers room for further improvement. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Functional network of the contractive affine map in Equation (<a href="#FD5-mathematics-10-01107" class="html-disp-formula">5</a>).</p>
Full article ">Figure 2
<p>General scheme of the network computing the IFS code of the input image.</p>
Full article ">Figure 3
<p>Fractal image used in this paper: (<b>left</b>) in black and white; (<b>right</b>) in different colors for each contractive map.</p>
Full article ">Figure 4
<p>(<b>left</b>–<b>right</b>, <b>top</b>–<b>bottom</b>): Evolution of the reconstructed image for 0–380 iterations (step size, 20 iterations).</p>
Full article ">Figure 5
<p>(<b>left</b>–<b>right</b>, <b>top</b>–<b>bottom</b>): Evolution of the reconstructed image for 400–780 iterations (step size, 20 iterations).</p>
Full article ">Figure 6
<p>(<b>left</b>–<b>right</b>, <b>top</b>–<b>bottom</b>): Evolution of the reconstructed image for 800–1180 iterations (step size, 20 iterations).</p>
Full article ">Figure 7
<p>(<b>left</b>–<b>right</b>, <b>top</b>–<b>bottom</b>): Evolution of the intersection between the original and the reconstructed images for 0–380 iterations (step size, 20 iterations).</p>
Full article ">Figure 8
<p>(<b>left</b>–<b>right</b>, <b>top</b>–<b>bottom</b>): Evolution of the intersection between the original and the reconstructed images for 400–780 iterations (step size, 20 iterations).</p>
Full article ">Figure 9
<p>(<b>left</b>–<b>right</b>, <b>top</b>–<b>bottom</b>): Evolution of the intersection between the original and the reconstructed images for 800–1180 iterations (step size, 20 iterations).</p>
Full article ">Figure 10
<p>(<b>left</b>–<b>right</b>, <b>top</b>–<b>bottom</b>): Evolution of the union between the original and the reconstructed images for 0–380 iterations (step size, 20 iterations).</p>
Full article ">Figure 11
<p>(<b>left</b>–<b>right</b>, <b>top</b>–<b>bottom</b>): Evolution of the union between the original and the reconstructed images for 400–780 iterations (step size, 20 iterations).</p>
Full article ">Figure 12
<p>(<b>left</b>–<b>right</b>, <b>top</b>–<b>bottom</b>): Evolution of the union between the original and the reconstructed images for 800–1180 iterations (step size, 20 iterations).</p>
Full article ">
30 pages, 14633 KiB  
Article
Reversible Data Hiding with a New Local Contrast Enhancement Approach
by Eduardo Fragoso-Navarro, Manuel Cedillo-Hernandez, Francisco Garcia-Ugalde and Robert Morelos-Zaragoza
Mathematics 2022, 10(5), 841; https://doi.org/10.3390/math10050841 - 7 Mar 2022
Cited by 5 | Viewed by 2531
Abstract
Reversible data hiding schemes hide information into a digital image and simultaneously increase its contrast. The improvements of the different approaches aim to increase the capacity, contrast, and quality of the image. However, recent proposals contrast the image globally and lose local details [...] Read more.
Reversible data hiding schemes hide information into a digital image and simultaneously increase its contrast. The improvements of the different approaches aim to increase the capacity, contrast, and quality of the image. However, recent proposals contrast the image globally and lose local details since they use two common methodologies that may not contribute to obtaining better results. Firstly, to generate vacancies for hiding information, most schemes start with a preprocessing applied to the histogram that may introduce visual distortions and set the maximum hiding rate in advance. Secondly, just a few hiding ranges are selected in the histogram, which means that just limited contrast and capacity may be achieved. To solve these problems, in this paper, a novel approach without preprocessing performs an automatic selection of multiple hiding ranges into the histograms. The selection stage is based on an optimization process, and the iterative-based algorithm increases capacity at embedding execution. Results show that quality and capacity values overcome previous approaches. Additionally, visual results show how greyscale values are better differentiated in the image, revealing details globally and locally. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Histogram embedding in histogram shifting scheme; (<b>a</b>) original histogram; (<b>b</b>) shifted histogram; (<b>c</b>) histogram with concealed data.</p>
Full article ">Figure 2
<p>Representation of the (<b>a</b>) original, (<b>b</b>) preprocessed, (<b>c</b>) final histograms. (<b>d</b>) Original, and (<b>e</b>) contrasted images [<a href="#B25-mathematics-10-00841" class="html-bibr">25</a>].</p>
Full article ">Figure 3
<p>Embedding and removal stages based on MRLHS.</p>
Full article ">Figure 4
<p>Detailed MRLHS process: (<b>a</b>) embedding and (<b>b</b>) removal.</p>
Full article ">Figure 5
<p>(<b>a</b>) Original image, (<b>b</b>) enhanced image without block shifting, and (<b>c</b>) enhanced image with block shifting.</p>
Full article ">Figure 6
<p>Proposed embedding procedure with a minimum bin: (<b>a</b>) original histogram; (<b>b</b>) shifted histogram; (<b>c</b>) histogram with concealed data.</p>
Full article ">Figure 7
<p>(<b>a</b>) Example of a histogram; (<b>b</b>) one range selected with capacity equal to 14 bits; (<b>c</b>) three ranges selected with total capacity equal to 20 bits; (<b>d</b>) Histogram with concealed information in the range of (<b>b</b>); (<b>e</b>) Histogram with concealed information in the three ranges of (<b>c</b>).</p>
Full article ">Figure 8
<p>Optimization process based on iterative updating of vectors <math display="inline"><semantics> <mi mathvariant="bold-italic">a</mi> </semantics></math> and <math display="inline"><semantics> <mi mathvariant="bold-italic">b</mi> </semantics></math>.</p>
Full article ">Figure 9
<p>PSNR visual quality according to hiding rate.</p>
Full article ">Figure 10
<p>Original images: (<b>a</b>) F-16; (<b>b</b>) Lena; (<b>c</b>) Baboon with a selected block (red square); (<b>d</b>–<b>f</b>) original histogram (black line) and enhanced histogram (red line) of the selected block.</p>
Full article ">Figure 11
<p>Assessment metrics with different hiding rates for F-16, Lena, and Baboon images: RCE (<b>a</b>–<b>c</b>); BRISQUE (<b>d</b>–<b>f</b>); PSNR (<b>g</b>–<b>i</b>); SSIM (<b>j</b>–<b>l</b>).</p>
Full article ">Figure 12
<p>(<b>a</b>,<b>d</b>,<b>g</b>) Original images; (<b>b</b>,<b>e</b>,<b>h</b>) enhanced images with internal removal sequence <math display="inline"><semantics> <mrow> <mi>k</mi> <mi>i</mi> </mrow> </semantics></math> embedded; (<b>c</b>,<b>f</b>,<b>i</b>) enhanced images with internal removal sequence <math display="inline"><semantics> <mrow> <mi>k</mi> <mi>i</mi> </mrow> </semantics></math> and binary string <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>S</mi> </mrow> </semantics></math> embedded.</p>
Full article ">Figure 13
<p>Embedding time according to (<b>a</b>) hiding rate with <math display="inline"><semantics> <mrow> <mi>F</mi> <mo>=</mo> <mi>C</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, (<b>b</b>) number of blocks (<math display="inline"><semantics> <mrow> <mi>F</mi> <mo>×</mo> <mi>C</mi> </mrow> </semantics></math>) for a hiding rate equal to 0.2 bpp, and (<b>c</b>) image size with a hiding rate of 0.5 bpp and <math display="inline"><semantics> <mrow> <mi>F</mi> <mo>=</mo> <mi>C</mi> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 14
<p>Relation between embedding time and removal time using <a href="#mathematics-10-00841-f013" class="html-fig">Figure 13</a>a information.</p>
Full article ">Figure 15
<p>Test images used in the experimental results of <a href="#mathematics-10-00841-t007" class="html-table">Table 7</a> and <a href="#mathematics-10-00841-t008" class="html-table">Table 8</a>.</p>
Full article ">Figure 16
<p>Two original images of USC-SIP dataset (<b>a</b>) Baboon and (<b>e</b>) F-16. Enhanced images obtained by algorithms in (<b>b</b>,<b>f</b>) [<a href="#B21-mathematics-10-00841" class="html-bibr">21</a>], (<b>c</b>,<b>g</b>) [<a href="#B31-mathematics-10-00841" class="html-bibr">31</a>], and (<b>d</b>,<b>h</b>) the present proposal.</p>
Full article ">Figure 17
<p>Two original images of USC-SIP dataset: (<b>a</b>) parrots and (<b>e</b>) house. Enhanced images obtained by algorithms in (<b>b</b>,<b>f</b>) [<a href="#B21-mathematics-10-00841" class="html-bibr">21</a>], (<b>c</b>,<b>g</b>) [<a href="#B31-mathematics-10-00841" class="html-bibr">31</a>], and (<b>d</b>,<b>h</b>) the present proposal.</p>
Full article ">Figure 17 Cont.
<p>Two original images of USC-SIP dataset: (<b>a</b>) parrots and (<b>e</b>) house. Enhanced images obtained by algorithms in (<b>b</b>,<b>f</b>) [<a href="#B21-mathematics-10-00841" class="html-bibr">21</a>], (<b>c</b>,<b>g</b>) [<a href="#B31-mathematics-10-00841" class="html-bibr">31</a>], and (<b>d</b>,<b>h</b>) the present proposal.</p>
Full article ">Figure 18
<p>Zoomed parts of some original images (<b>left column</b>), enhanced images obtained by algorithm in [<a href="#B31-mathematics-10-00841" class="html-bibr">31</a>] (<b>centered column</b>), and by our proposal (<b>right column</b>).</p>
Full article ">
26 pages, 35233 KiB  
Article
Deep Red Lesion Classification for Early Screening of Diabetic Retinopathy
by Muhammad Nadeem Ashraf, Muhammad Hussain and Zulfiqar Habib
Mathematics 2022, 10(5), 686; https://doi.org/10.3390/math10050686 - 23 Feb 2022
Cited by 4 | Viewed by 2520
Abstract
Diabetic retinopathy (DR) is an asymptotic and vision-threatening complication among working-age adults. To prevent blindness, a deep convolutional neural network (CNN) based diagnosis can help to classify less-discriminative and small-sized red lesions in early screening of DR patients. However, training deep models with [...] Read more.
Diabetic retinopathy (DR) is an asymptotic and vision-threatening complication among working-age adults. To prevent blindness, a deep convolutional neural network (CNN) based diagnosis can help to classify less-discriminative and small-sized red lesions in early screening of DR patients. However, training deep models with minimal data is a challenging task. Fine-tuning through transfer learning is a useful alternative, but performance degradation, overfitting, and domain adaptation issues further demand architectural amendments to effectively train deep models. Various pre-trained CNNs are fine-tuned on an augmented set of image patches. The best-performing ResNet50 model is modified by introducing reinforced skip connections, a global max-pooling layer, and the sum-of-squared-error loss function. The performance of the modified model (DR-ResNet50) on five public datasets is found to be better than state-of-the-art methods in terms of well-known metrics. The highest scores (0.9851, 0.991, 0.991, 0.991, 0.991, 0.9939, 0.0029, 0.9879, and 0.9879) for sensitivity, specificity, AUC, accuracy, precision, F1-score, false-positive rate, Matthews’s correlation coefficient, and kappa coefficient are obtained within a 95% confidence interval for unseen test instances from e-Ophtha_MA. This high sensitivity and low false-positive rate demonstrate the worth of a proposed framework. It is suitable for early screening due to its performance, simplicity, and robustness. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>(<b>a</b>) DR lesions along with healthy landmarks (blood vessels and optic discs). (<b>b</b>) Extracted region of interest (ROI) containing red lesions.</p>
Full article ">Figure 2
<p>An overview of a proposed deep CNN-based red lesion classification technique for early DR screening.</p>
Full article ">Figure 3
<p>(<b>a</b>) A 200 × 200 patch extraction from fundus image. (<b>b</b>) A few generated patches are shown with their specific naming conventions for reference in the future.</p>
Full article ">Figure 4
<p>A schematic diagram of the proposed method, showing the DR-ResNet50 architecture to classify red lesions of DR using small image patches.</p>
Full article ">Figure 5
<p>Training progress of a proposed DR-ResNet50 model on the e-Ophtha_MA dataset.</p>
Full article ">Figure 6
<p>Confusion matrix results were obtained using the 3460 test instances by splitting the data using Scheme-2. (<b>a</b>) Percentage of two-class predictions, and (<b>b</b>) a total number of true and false classified instances from both classes.</p>
Full article ">Figure 7
<p>Per-image evaluation on the e-Ophtha MA for DR screening.</p>
Full article ">Figure 8
<p>Successfully classified cases of small patches from e-Ophtha_MA images along their Grad-CAMs. (<b>a</b>) True positive cases, (<b>b</b>) true negative cases.</p>
Full article ">Figure 9
<p>Unsuccessfully classified cases of small patches from e-Ophtha_MA images along their Grad-CAMs. (<b>a</b>) False negative cases, (<b>b</b>) false positive cases.</p>
Full article ">Figure 10
<p>Back association of extracted patches on a fundus image for region marking according to classification decisions. The blue box depicts unhealthy while the white box represents healthy regions classified by the system.</p>
Full article ">
17 pages, 5224 KiB  
Article
PDE-Based 3D Surface Reconstruction from Multi-View 2D Images
by Zaiping Zhu, Andres Iglesias, Liqi Zhou, Lihua You and Jianjun Zhang
Mathematics 2022, 10(4), 542; https://doi.org/10.3390/math10040542 - 9 Feb 2022
Cited by 5 | Viewed by 4122
Abstract
Partial differential equation (PDE) based surfaces own a lot of advantages, compared to other types of 3D representation. For instance, fewer variables are required to represent the same 3D shape; the position, tangent, and even curvature continuity between PDE surface patches can be [...] Read more.
Partial differential equation (PDE) based surfaces own a lot of advantages, compared to other types of 3D representation. For instance, fewer variables are required to represent the same 3D shape; the position, tangent, and even curvature continuity between PDE surface patches can be naturally maintained when certain conditions are satisfied, and the physics-based nature is also kept. Although some works applied implicit PDEs to 3D surface reconstruction from images, there is little work on exploiting the explicit solutions of PDE to this topic, which is more efficient and accurate. In this paper, we propose a new method to apply the explicit solutions of a fourth-order partial differential equation to surface reconstruction from multi-view images. The method includes two stages: point clouds data are extracted from multi-view images in the first stage, which is followed by PDE-based surface reconstruction from the obtained point clouds data. Our computational experiments show that the reconstructed PDE surfaces exhibit good quality and can recover the ground truth with high accuracy. A comparison between various solutions with different complexity to the fourth-order PDE is also made to demonstrate the power and flexibility of our proposed explicit PDE for surface reconstruction from images. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>The pipeline of the proposed PDE-based 3D surface reconstruction method from multi-view images.</p>
Full article ">Figure 2
<p>(<b>a</b>) Scene setting; (<b>b</b>) rendered multi-view 2D images.</p>
Full article ">Figure 3
<p>(<b>a</b>) Reconstructed cylinder point cloud with the Meshroom algorithm; (<b>b</b>) magnified view of the reconstructed point cloud in (<b>a</b>); (<b>c</b>) magnified view of the reconstructed point cloud in <a href="#mathematics-10-00542-f004" class="html-fig">Figure 4</a>c with Colmap algorithm.</p>
Full article ">Figure 4
<p>(<b>a</b>) Input to Colmap: multi-view 2D images; (<b>b</b>) 3D point cloud reconstruction from multi-view 2D images; (<b>c</b>) reconstructed 3D point cloud.</p>
Full article ">Figure 5
<p>(<b>a</b>) Cylinder in the cylindrical coordinate system; (<b>b</b>) parameterizing point cloud of cylinder shape.</p>
Full article ">Figure 6
<p>(<b>a</b>) Fitting plane to the point clouds; (<b>b</b>) projecting points to the projecting plane (u, v plane).</p>
Full article ">Figure 7
<p>(<b>a</b>) Reconstructed 3D point cloud of a cylinder shape from multi-view 2D images; (<b>b</b>) reconstructed PDE surface using a single PDE model with 16 variables; (<b>c</b>) reconstructed PDE surface using a single PDE model with 64 variables; (<b>d</b>) reconstructed PDE surface using two PDE models with 16 variables; (<b>e</b>) segmented point cloud.</p>
Full article ">Figure 8
<p>(<b>a</b>) Point set of a bowl; (<b>b</b>) surface reconstructed using Poisson; (<b>c</b>) PDE-based surface using single 16-variables PDE model; (<b>d</b>) PDE-based surface using single 64-variables PDE model.</p>
Full article ">Figure 9
<p>(<b>a</b>) The ground truth of a bench surface; (<b>b</b>) point set of a bench surface; (<b>c</b>) surface reconstructed using Poisson; (<b>d</b>) PDE-based surface using a single 16-variables PDE model; and (<b>e</b>) PDE-based surface using a single 64-variables PDE model.</p>
Full article ">Figure 10
<p>(<b>a</b>) The ground truth of a slide surface; (<b>b</b>) point set of a slide surface; (<b>c</b>) surface reconstructed using Poisson after segmentation; (<b>d</b>) PDE-based surface using a single 16-variable PDE model; (<b>e</b>) PDE-based surface using a single 64-variable PDE model.</p>
Full article ">Figure 11
<p>(<b>a</b>) The point cloud of a hat; (<b>b</b>) segmented 2 subsets; (<b>c</b>) reconstructed PDE-based surface using 2 PDE patches defined by the 64-variables PDE model; (<b>d</b>) segmented 3 subsets; (<b>e</b>) reconstructed PDE-based surface using 3 PDE patches defined by the 64-variable PDE mode.</p>
Full article ">Figure 12
<p>(<b>a</b>) The point cloud of a truck; (<b>b</b>) segmented subsets; (<b>c</b>) reconstructed PDE-based surface.</p>
Full article ">
14 pages, 3187 KiB  
Article
GeoStamp: Detail Transfer Based on Mean Curvature Field
by Jung-Ho Park, Ji-Hye Moon, Sanghun Park and Seung-Hyun Yoon
Mathematics 2022, 10(3), 500; https://doi.org/10.3390/math10030500 - 4 Feb 2022
Cited by 2 | Viewed by 1641
Abstract
A shape detail transfer is the process of extracting the geometric details of a source region and transferring it onto a target region. In this paper, we present a simple and effective method, called GeoStamp, for transferring shape details using a Poisson [...] Read more.
A shape detail transfer is the process of extracting the geometric details of a source region and transferring it onto a target region. In this paper, we present a simple and effective method, called GeoStamp, for transferring shape details using a Poisson equation. First, the mean curvature field on a source region is computed by using the Laplace–Beltrami operator and is defined as the shape details of the source region. Subsequently, the source and target regions are parameterized on a common 2D domain, and a mean curvature field on the target region is interpolated by the correspondence between two regions. Finally, we solve the Poisson equation using the interpolated mean curvature field and the Laplacian matrix of the target region. Consequently, the mean curvature field of the target region is replaced with that of the source region, which results in the transfer of shape details from the source region to the target region. We demonstrate the effectiveness of our technique by showing several examples and also show that our method is quite useful for adding shape details to a surface patch filling a hole in a triangular mesh. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Overview of the proposed method: (<b>a</b>) Color-coded mean curvature field of a source region <span class="html-italic">S</span>; (<b>b</b>) 2D parameterization of a source and a target region over a common unit square; (<b>c</b>) interpolated mean curvature field on a target region <span class="html-italic">T</span>; and (<b>d</b>) target region <span class="html-italic">T</span> reconstructed from the interpolated mean curvature field.</p>
Full article ">Figure 2
<p>Local area <math display="inline"><semantics> <msub> <mi>A</mi> <mi>i</mi> </msub> </semantics></math> of <math display="inline"><semantics> <msub> <mi mathvariant="bold">v</mi> <mi>i</mi> </msub> </semantics></math> is defined as a mixed Voronoi cell [<a href="#B8-mathematics-10-00500" class="html-bibr">8</a>], and <math display="inline"><semantics> <msub> <mi>α</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>β</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </semantics></math> are the opposite angles of an edge incident to <math display="inline"><semantics> <msub> <mi mathvariant="bold">v</mi> <mi>i</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="bold">v</mi> <mi>j</mi> </msub> </semantics></math>.</p>
Full article ">Figure 3
<p>Visualization of the mean curvature normal vectors pointing to the (<b>a</b>) front and (<b>b</b>) back faces. (<b>c</b>) Color-coded mean curvature values. The curvature becomes positive in the concave region and negative in the convex region.</p>
Full article ">Figure 4
<p>A source region <span class="html-italic">S</span> (<b>left</b>) is parameterized in the unit square (<b>right</b>). The starting vertex and the boundary vertices are first fixed, and the interior vertices are then determined through a convex combination of the neighboring vertices.</p>
Full article ">Figure 5
<p>A triangle <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>∈</mo> <mi>S</mi> </mrow> </semantics></math> and a vertex <math display="inline"><semantics> <mrow> <mi mathvariant="bold">v</mi> <mo>∈</mo> <mi>T</mi> </mrow> </semantics></math> are mapped to the triangle <math display="inline"><semantics> <msup> <mi>τ</mi> <mo>′</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mrow> <mi mathvariant="bold">v</mi> </mrow> <mo>′</mo> </msup> </semantics></math> in the common unit square <math display="inline"><semantics> <mi mathvariant="double-struck">D</mi> </semantics></math>.</p>
Full article ">Figure 6
<p>Reconstruction of a target region <span class="html-italic">T</span> (in purple) by transferring the shape details from a source region <span class="html-italic">S</span> (in yellow). Depending on the starting vertex in 2D parameterization, the orientation of the shape details changes.</p>
Full article ">Figure 7
<p>Depending on user-specified parameter <math display="inline"><semantics> <mi>α</mi> </semantics></math>, the shape of the details transferred from <span class="html-italic">S</span> to <span class="html-italic">T</span> varies.</p>
Full article ">Figure 8
<p>We subdivide a target region to increase its resolution: (<b>a</b>) source region <span class="html-italic">S</span> with high resolution, (<b>b</b>) target region <span class="html-italic">T</span> with low resolution (<b>left</b>) and shape details transferred to <span class="html-italic">T</span> (<b>right</b>), and (<b>c</b>) remeshed target region <span class="html-italic">T</span> (<b>left</b>) and shape details transferred to <span class="html-italic">T</span> (<b>right</b>).</p>
Full article ">Figure 9
<p>Editing shape details within frequency domain: (<b>a</b>) The grayscale image <math display="inline"><semantics> <msub> <mi>I</mi> <mi>S</mi> </msub> </semantics></math> is generated from <math display="inline"><semantics> <msub> <mi>H</mi> <mi>S</mi> </msub> </semantics></math> and transformed into the frequency domain; (<b>b</b>) the shape details are edited by applying a filtering technique to the grayscale image <math display="inline"><semantics> <msub> <mi>I</mi> <mi>S</mi> </msub> </semantics></math>.</p>
Full article ">Figure 10
<p>As the user controls the detail transfer function <math display="inline"><semantics> <mrow> <mi>F</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math> within the frequency domain, different shape details are transferred to the target region.</p>
Full article ">Figure 11
<p>Various blending effects of the source and target shape details.</p>
Full article ">Figure 12
<p>Detail transfer with increasing <math display="inline"><semantics> <mi>α</mi> </semantics></math>. As <math display="inline"><semantics> <mi>α</mi> </semantics></math> increases, the overall mean curvature of the target region continuously increases.</p>
Full article ">Figure 13
<p>Detail transfer with various curvature field filtering. Defining <math display="inline"><semantics> <mrow> <mi>F</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math> by the user, the transferred curvature field can be interactively constructed.</p>
Full article ">Figure 14
<p>Four examples of a detail transfer. The third columns show the results of transferring shape details inside the yellow boundaries of <span class="html-italic">S</span> to <span class="html-italic">T</span>: (<b>a</b>) The pattern detail from the pouf is transferred onto the cushion. (<b>b</b>) From the damaliscus’s horn onto the Bunny’s head. (<b>c</b>) From the starfish skin onto the Armadillo’s shell. (<b>d</b>) From the coin onto the wallet.</p>
Full article ">Figure 15
<p>Hole-filling results of five models with holes. By adding shape details, our detail transfer method can be used to reconstruct a surface patch filling a hole.</p>
Full article ">
26 pages, 17007 KiB  
Article
CellsDeepNet: A Novel Deep Learning-Based Web Application for the Automated Morphometric Analysis of Corneal Endothelial Cells
by Alaa S. Al-Waisy, Abdulrahman Alruban, Shumoos Al-Fahdawi, Rami Qahwaji, Georgios Ponirakis, Rayaz A. Malik, Mazin Abed Mohammed and Seifedine Kadry
Mathematics 2022, 10(3), 320; https://doi.org/10.3390/math10030320 - 20 Jan 2022
Cited by 8 | Viewed by 2733
Abstract
The quantification of corneal endothelial cell (CEC) morphology using manual and semi-automatic software enables an objective assessment of corneal endothelial pathology. However, the procedure is tedious, subjective, and not widely applied in clinical practice. We have developed the CellsDeepNet system to automatically segment [...] Read more.
The quantification of corneal endothelial cell (CEC) morphology using manual and semi-automatic software enables an objective assessment of corneal endothelial pathology. However, the procedure is tedious, subjective, and not widely applied in clinical practice. We have developed the CellsDeepNet system to automatically segment and analyse the CEC morphology. The CellsDeepNet system uses Contrast-Limited Adaptive Histogram Equalization (CLAHE) to improve the contrast of the CEC images and reduce the effects of non-uniform image illumination, 2D Double-Density Dual-Tree Complex Wavelet Transform (2DDD-TCWT) to reduce noise, Butterworth Bandpass filter to enhance the CEC edges, and moving average filter to adjust for brightness level. An improved version of U-Net was used to detect the boundaries of the CECs, regardless of the CEC size. CEC morphology was measured as mean cell density (MCD, cell/mm2), mean cell area (MCA, μm2), mean cell perimeter (MCP, μm), polymegathism (coefficient of CEC size variation), and pleomorphism (percentage of hexagonality coefficient). The CellsDeepNet system correlated highly significantly with the manual estimations for MCD (r = 0.94), MCA (r = 0.99), MCP (r = 0.99), polymegathism (r = 0.92), and pleomorphism (r = 0.86), with p < 0.0001 for all the extracted clinical features. The Bland–Altman plots showed excellent agreement. The percentage difference between the manual and automated estimations was superior for the CellsDeepNet system compared to the CEAS system and other state-of-the-art CEC segmentation systems on three large and challenging corneal endothelium image datasets captured using two different ophthalmic devices. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>The block diagram of the proposed CellsDeepNet web application: (<b>a</b>) client-side and (<b>b</b>) server-side.</p>
Full article ">Figure 2
<p>Examples of corneal endothelium images: (<b>a</b>) a healthy subject, (<b>b</b>) an obese patient, and (<b>c</b>) a diabetic patient displaying a high difference in the size and shape of CECs.</p>
Full article ">Figure 3
<p>The main steps of the proposed CEC image enhancement procedure.</p>
Full article ">Figure 4
<p>The outputs of the CellsDeepNet system: (<b>a</b>) the original corneal image, (<b>b</b>) output of the CLAHE approach, (<b>c</b>) output of the 2DDD-TCWT approach, (<b>d</b>) output of the Butterworth Bandpass filter, (<b>e</b>) applying the brightness level adjustment step, (<b>f</b>) final endothelial cells segmented image, (<b>g</b>) labelling of endothelial cells, and (<b>h</b>) imposed traced endothelial cells boundaries on the original image.</p>
Full article ">Figure 5
<p>The architecture of the proposed U-Net model developed for the segmentation of the CECs.</p>
Full article ">Figure 6
<p>An illustration of the suggested training methodology to obtain the best network architecture.</p>
Full article ">Figure 7
<p>The loss and accuracy plots during the training process on training and validation set: (<b>a</b>) the MCCM dataset and (<b>b</b>) the ECA dataset.</p>
Full article ">Figure 8
<p>The data augmentation procedure: (<b>a</b>) the original CEC image, (<b>b</b>) horizontal flipped image, (<b>c</b>) vertical flipped image, and (<b>d</b>) the eight random image patches.</p>
Full article ">Figure 9
<p>Examples of the generated figures in the clinical features quantification stage: (<b>a</b>) Colour-coded cell pleomorphism map where the orange colour is referring to six neighbours’ cells and (<b>b</b>) the histogram distribution plot of the pleomorphism parameter.</p>
Full article ">Figure 10
<p>The GIMP software yields: (<b>a</b>) The input image, (<b>b</b>) a typical sample of manually detected CEC boundaries, (<b>c</b>) a produced binarized image employed as a ground-truth segmented image.</p>
Full article ">Figure 11
<p>Comparison of the segmentation performance between the original U-Net, CellsDeepNet, and CEAS system using the MCCM dataset. The performance is better with higher values of SSIM and PRI and lower values of VoI, GMSD, GCE, MSE, and NAE.</p>
Full article ">Figure 12
<p>Correlation plots between manual and automated endothelial cell parameters for the MCCM dataset. (<b>a</b>) MCD, (<b>b</b>) MCA, (<b>c</b>) MCP, (<b>d</b>) polymegathism, and (<b>e</b>) pleomorphism.</p>
Full article ">Figure 13
<p>Bland-Altman plots present the difference against the mean for each pair of manual compared to automated endothelial cell parameters. (<b>a</b>) MCD, (<b>b</b>) MCA, (<b>c</b>) MCP, (<b>d</b>) polymegathism, and (<b>e</b>) pleomorphism from the MCCM dataset. The dashed lines refer to the (95%) lines of agreement, and solid lines represent the mean differences.</p>
Full article ">Figure 14
<p>Comparison of the segmentation performance between the original U-Net, CellsDeepNet, and CEAS systems using the ECA dataset. The performance is better with higher values of SSIM and PRI, and lower values of VoI, GMSD, GCE, MSE, and NAE.</p>
Full article ">Figure 15
<p>Correlation plots of the manual and automated CEC parameters from the ECA dataset. (<b>a</b>) MCD, (<b>b</b>) MCA, (<b>c</b>) MCP, (<b>d</b>) polymegathism, and (<b>e</b>) pleomorphism.</p>
Full article ">Figure 16
<p>Bland–Altman plots present the difference against the mean for each pair of manual compared to automated endothelial cell parameters. (<b>a</b>) MCD, (<b>b</b>) MCA, (<b>c</b>) MCP, (<b>d</b>) polymegathism, and (<b>e</b>) pleomorphism from ECA dataset. The dashed lines refer to the (95%) lines of agreement, and solid lines represent the mean differences.</p>
Full article ">Figure 17
<p>Differences between the manual and CellsDeepNet system segmentation: (<b>a</b>) ground-truth manual segmented image, (<b>b</b>) CellsDeepNet system segmented image, and (<b>c</b>) overlapped CEC borders that the manual and CellsDeepNet system had.</p>
Full article ">Figure 18
<p>Comparison of the segmentation performance between CellsDeepNet and Selig et al. [<a href="#B21-mathematics-10-00320" class="html-bibr">21</a>] using the ECA dataset. The performance is better with higher values of SSIM and PRI and lower values of VoI, GMSD, GCE, MSE, and NAE.</p>
Full article ">Figure 19
<p>Comparison between the automated segmentation outputs: (<b>a</b>) original image, (<b>b</b>) Selig et al. [<a href="#B21-mathematics-10-00320" class="html-bibr">21</a>] system, (<b>c</b>) the proposed CellsDeepNet system.</p>
Full article ">
20 pages, 5541 KiB  
Article
3D Modelling with C2 Continuous PDE Surface Patches
by Haibin Fu, Shaojun Bian, Ouwen Li, Jon Macey, Andres Iglesias, Ehtzaz Chaudhry, Lihua You and Jian Jun Zhang
Mathematics 2022, 10(3), 319; https://doi.org/10.3390/math10030319 - 20 Jan 2022
Cited by 1 | Viewed by 2043
Abstract
In this paper, we present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Then, a vector-valued sixth-order partial differential equation is proposed, and its closed form solution is derived to [...] Read more.
In this paper, we present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Then, a vector-valued sixth-order partial differential equation is proposed, and its closed form solution is derived to create PDE surface patches from cross section curves where two adjacent PDE-surface patches are automatically stitched together. With the approach presented in this paper, C2 continuity between adjacent surface patches is well-maintained. Since surface creation of the model is transformed into the generation of cross sectional curves and few undetermined constants are required to describe cross sectional curves accurately, the proposed approach can save manual operations, reduce information storage, and generate 3D models quickly. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Comparison of different digital 3D modeling methods.</p>
Full article ">Figure 2
<p>Overall proposed algorithm.</p>
Full article ">Figure 3
<p>Curve fitting example. The ground truth curves are shown in blue and fitted generalized elliptic curves are in red.</p>
Full article ">Figure 4
<p>Surface creation example. The six curves <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">C</mi> <mn>4</mn> </msub> </mrow> </semantics></math> − <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">C</mi> <mn>9</mn> </msub> </mrow> </semantics></math> (red) are used to construct the PDE surface patch 1.</p>
Full article ">Figure 5
<p>The cross section curves and created human body parts.</p>
Full article ">Figure 6
<p>The cross section curves of the human body and the created human body model in front and side views using <math display="inline"><semantics> <mrow> <msup> <mi>C</mi> <mn>2</mn> </msup> </mrow> </semantics></math> continues PDE method.</p>
Full article ">Figure 7
<p>Surface shape generation from cross section curves by using the method proposed in this paper. (<b>a</b>) a smooth vase model, (<b>b</b>) a horse belly model, (<b>c</b>) front leg and nose models of an elephant.</p>
Full article ">
15 pages, 20739 KiB  
Article
Melanoma Classification from Dermoscopy Images Using Ensemble of Convolutional Neural Networks
by Rehan Raza, Fatima Zulfiqar, Shehroz Tariq, Gull Bano Anwar, Allah Bux Sargano and Zulfiqar Habib
Mathematics 2022, 10(1), 26; https://doi.org/10.3390/math10010026 - 22 Dec 2021
Cited by 29 | Viewed by 5041
Abstract
Human skin is the most exposed part of the human body that needs constant protection and care from heat, light, dust, and direct exposure to other harmful radiation, such as UV rays. Skin cancer is one of the dangerous diseases found in humans. [...] Read more.
Human skin is the most exposed part of the human body that needs constant protection and care from heat, light, dust, and direct exposure to other harmful radiation, such as UV rays. Skin cancer is one of the dangerous diseases found in humans. Melanoma is a form of skin cancer that begins in the cells (melanocytes) that control the pigment in human skin. Early detection and diagnosis of skin cancer, such as melanoma, is necessary to reduce the death rate due to skin cancer. In this paper, the classification of acral lentiginous melanoma, a type of melanoma with benign nevi, is being carried out. The proposed stacked ensemble method for melanoma classification uses different pre-trained models, such as Xception, Inceptionv3, InceptionResNet-V2, DenseNet121, and DenseNet201, by employing the concept of transfer learning and fine-tuning. The selection of pre-trained CNN architectures for transfer learning is based on models having the highest top-1 and top-5 accuracies on ImageNet. A novel stacked ensemble-based framework is presented to improve the generalizability and increase robustness by fusing fine-tuned pre-trained CNN models for acral lentiginous melanoma classification. The performance of the proposed method is evaluated by experimenting on a Figshare benchmark dataset. The impact of applying different augmentation techniques has also been analyzed through extensive experimentations. The results confirm that the proposed method outperforms state-of-the-art techniques and achieves an accuracy of 97.93%. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Concept of transfer learning.</p>
Full article ">Figure 2
<p>Illustration of modified depthwise separable convolution in Xception network.</p>
Full article ">Figure 3
<p>The fine-tuning of proposed method of pre-trained Xception architecture.</p>
Full article ">Figure 4
<p>The fine-tuning of proposed method of pre-trained Inception-ResNet-V2 architecture.</p>
Full article ">Figure 5
<p>The fine-tuning of proposed method of pre-trained DenseNet121 and DenseNet201 architecture.</p>
Full article ">Figure 6
<p>Block diagram of the proposed methodology.</p>
Full article ">Figure 7
<p>Block diagram of proposed stacked ensemble model.</p>
Full article ">Figure 8
<p>Acral melanoma and benign nevi sample images.</p>
Full article ">Figure 9
<p>Sample classification results of pre-trained model.</p>
Full article ">Figure 10
<p>Stacked ensemble model confusion matrix.</p>
Full article ">
19 pages, 27092 KiB  
Article
PDE Surface-Represented Facial Blendshapes
by Haibin Fu, Shaojun Bian, Ehtzaz Chaudhry, Shuangbu Wang, Lihua You and Jian Jun Zhang
Mathematics 2021, 9(22), 2905; https://doi.org/10.3390/math9222905 - 15 Nov 2021
Cited by 1 | Viewed by 2491
Abstract
Partial differential equation (PDE)-based geometric modelling and computer animation has been extensively investigated in the last three decades. However, the PDE surface-represented facial blendshapes have not been investigated. In this paper, we propose a new method of facial blendshapes by using curve-defined and [...] Read more.
Partial differential equation (PDE)-based geometric modelling and computer animation has been extensively investigated in the last three decades. However, the PDE surface-represented facial blendshapes have not been investigated. In this paper, we propose a new method of facial blendshapes by using curve-defined and Fourier series-represented PDE surfaces. In order to develop this new method, first, we design a curve template and use it to extract curves from polygon facial models. Then, we propose a second-order partial differential equation and combine it with the constraints of the extracted curves as boundary curves to develop a mathematical model of curve-defined PDE surfaces. After that, we introduce a generalized Fourier series representation to solve the second-order partial differential equation subjected to the constraints of the extracted boundary curves and obtain an analytical mathematical expression of curve-defined and Fourier series-represented PDE surfaces. The mathematical expression is used to develop a new PDE surface-based interpolation method of creating new facial models from one source facial model and one target facial model and a new PDE surface-based blending method of creating more new facial models from one source facial model and many target facial models. Some examples are presented to demonstrate the effectiveness and applications of the proposed method in 3D facial blendshapes. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>An example of input model and target models with different topologies and vertices.</p>
Full article ">Figure 2
<p>Algorithm overview.</p>
Full article ">Figure 3
<p>The curves designed to divide a canonical 3D face model into patches, (<b>a</b>) face photo with 68 landmark points, (<b>b</b>) anatomical diagram of facial muscles, (<b>c</b>) a concept sketch of face curves designed using landmark points and the anatomical diagram as references.</p>
Full article ">Figure 4
<p>Front and side view of the design of the curves dividing a canonical 3D face model into patches, (<b>a</b>,<b>c</b>) are a source male face model, (<b>b</b>,<b>d</b>) are a target female face model.</p>
Full article ">Figure 5
<p>Extracting correspondent curves from 3D models. (<b>a</b>) Male model (mesh), (<b>b</b>) male model (with wireframe), (<b>c</b>) face model (with extracted curves), (<b>d</b>) local view of the extracted curves in the left eye area.</p>
Full article ">Figure 6
<p>New created PDE surface patch <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="bold-italic">w</mi> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> </msup> <mfenced> <mrow> <mi>u</mi> <mo>,</mo> <mo> </mo> <mi>v</mi> </mrow> </mfenced> </mrow> </semantics></math> depicted in (<b>b</b>), which was obtained by using Equation (25) to interpolate the source PDE surface patch <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="bold-italic">w</mi> <mn>0</mn> </msup> <mfenced> <mrow> <mi>u</mi> <mo>,</mo> <mo> </mo> <mi>v</mi> </mrow> </mfenced> </mrow> </semantics></math> in (<b>d</b>) and the target PDE surface patch <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="bold-italic">w</mi> <mn>1</mn> </msup> <mfenced> <mrow> <mi>u</mi> <mo>,</mo> <mo> </mo> <mi>v</mi> </mrow> </mfenced> </mrow> </semantics></math> in (<b>e</b>), where (<b>a</b>) shows the boundary curves of the source PDE surface patch in (<b>d</b>), and (<b>c</b>) depicts the boundary curves of the target PDE surface patch in (<b>e</b>).</p>
Full article ">Figure 7
<p>Facial models created by using Equation (25) to interpolate source facial models and target facial models, where the left column shows four source facial models, the right column depicts four target facial models, and the four middle facial models on each of the four rows are new created facial models by setting <span class="html-italic">t</span> = 0.2, 0.4, 0.6, and 0.8 in Equation (25).</p>
Full article ">Figure 8
<p>Facial blendshapes by using Equation (29) to blend PDE surface patches on one source facial model and three target facial models with <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0.34</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 9
<p>Facial blendshapes created by using Equation (29) with <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 10
<p>Facial blendshapes created by using Equation (29) with <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p>Facial blendshapes created by using Equation (29) with <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.35</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">w</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0.35</mn> </mrow> </semantics></math>.</p>
Full article ">
15 pages, 854 KiB  
Article
DSTnet: Deformable Spatio-Temporal Convolutional Residual Network for Video Super-Resolution
by Anusha Khan, Allah Bux Sargano and Zulfiqar Habib
Mathematics 2021, 9(22), 2873; https://doi.org/10.3390/math9222873 - 12 Nov 2021
Cited by 1 | Viewed by 2500
Abstract
Video super-resolution (VSR) aims at generating high-resolution (HR) video frames with plausible and temporally consistent details using their low-resolution (LR) counterparts, and neighboring frames. The key challenge for VSR lies in the effective exploitation of intra-frame spatial relation and temporal dependency between consecutive [...] Read more.
Video super-resolution (VSR) aims at generating high-resolution (HR) video frames with plausible and temporally consistent details using their low-resolution (LR) counterparts, and neighboring frames. The key challenge for VSR lies in the effective exploitation of intra-frame spatial relation and temporal dependency between consecutive frames. Many existing techniques utilize spatial and temporal information separately and compensate motion via alignment. These methods cannot fully exploit the spatio-temporal information that significantly affects the quality of resultant HR videos. In this work, a novel deformable spatio-temporal convolutional residual network (DSTnet) is proposed to overcome the issues of separate motion estimation and compensation methods for VSR. The proposed framework consists of 3D convolutional residual blocks decomposed into spatial and temporal (2+1) D streams. This decomposition can simultaneously utilize input video’s spatial and temporal features without a separate motion estimation and compensation module. Furthermore, the deformable convolution layers have been used in the proposed model that enhances its motion-awareness capability. Our contribution is twofold; firstly, the proposed approach can overcome the challenges in modeling complex motions by efficiently using spatio-temporal information. Secondly, the proposed model has fewer parameters to learn than state-of-the-art methods, making it a computationally lean and efficient framework for VSR. Experiments are conducted on a benchmark Vid4 dataset to evaluate the efficacy of the proposed approach. The results demonstrate that the proposed approach achieves superior quantitative and qualitative performance compared to the state-of-the-art methods. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Proposed DSTnet architecture, the structure of a residual blocks is shown on left, and temporal fusion and reconstruction module shown on the right side of the figure.</p>
Full article ">Figure 2
<p>Comparison of (<b>a</b>) FSTRN [<a href="#B11-mathematics-09-02873" class="html-bibr">11</a>] 3D residual block, (<b>b</b>) EDSR [<a href="#B21-mathematics-09-02873" class="html-bibr">21</a>] 2D residual block, and (<b>c</b>) the proposed spatio-temporal convolutional residual block.</p>
Full article ">Figure 3
<p>Qualitative comparison between VSR results obtained by (<b>a</b>) Bicubic, (<b>b</b>) VSRNET [<a href="#B24-mathematics-09-02873" class="html-bibr">24</a>], (<b>c</b>) SRCNN [<a href="#B16-mathematics-09-02873" class="html-bibr">16</a>], (<b>d</b>) VESPCN [<a href="#B27-mathematics-09-02873" class="html-bibr">27</a>], (<b>e</b>) Proposed and (<b>f</b>) Ground-Truth on “<span class="html-italic">calendar</span>” from Vid4 with scaling factor of x4.</p>
Full article ">Figure 4
<p>Qualitative comparison between VSR results obtained by (<b>a</b>) Bicubic, (<b>b</b>) VSRNET [<a href="#B24-mathematics-09-02873" class="html-bibr">24</a>], (<b>c</b>) SRCNN [<a href="#B16-mathematics-09-02873" class="html-bibr">16</a>], (<b>d</b>) VESPCN [<a href="#B27-mathematics-09-02873" class="html-bibr">27</a>], (<b>e</b>) Proposed and (<b>f</b>) Ground-Truth on “<span class="html-italic">city</span>” from Vid4 with scaling factor of x4.</p>
Full article ">Figure 5
<p>Qualitative comparison between VSR results obtained by (<b>a</b>) Bicubic, (<b>b</b>) VSRNET [<a href="#B24-mathematics-09-02873" class="html-bibr">24</a>], (<b>c</b>) SRCNN [<a href="#B16-mathematics-09-02873" class="html-bibr">16</a>], (<b>d</b>) VESPCN [<a href="#B27-mathematics-09-02873" class="html-bibr">27</a>], (<b>e</b>) Proposed and (<b>f</b>) Ground-Truth on “<span class="html-italic">foliage</span>” from Vid4 with scaling factor of x4.</p>
Full article ">Figure 6
<p>Qualitative comparison between VSR results obtained by (<b>a</b>) Bicubic, (<b>b</b>) VSRNET [<a href="#B24-mathematics-09-02873" class="html-bibr">24</a>], (<b>c</b>) SRCNN [<a href="#B16-mathematics-09-02873" class="html-bibr">16</a>], (<b>d</b>) VESPCN [<a href="#B27-mathematics-09-02873" class="html-bibr">27</a>], (<b>e</b>) Proposed and (<b>f</b>) Ground-Truth on “<span class="html-italic">walk</span>” from Vid4 with scaling factor of x4.</p>
Full article ">
15 pages, 3985 KiB  
Article
Optimized Unidirectional and Bidirectional Stiffened Objects for Minimum Material Consumption of 3D Printing
by Anzong Zheng, Zaiping Zhu, Shaojun Bian, Jian Chang, Habibollah Haron, Andres Iglesias, Lihua You and Jianjun Zhang
Mathematics 2021, 9(21), 2835; https://doi.org/10.3390/math9212835 - 8 Nov 2021
Cited by 1 | Viewed by 2283
Abstract
3D printing, regarded as the most popular additive manufacturing technology, is finding many applications in various industrial sectors. Along with the increasing number of its industrial applications, reducing its material consumption and increasing the strength of 3D printed objects have become an important [...] Read more.
3D printing, regarded as the most popular additive manufacturing technology, is finding many applications in various industrial sectors. Along with the increasing number of its industrial applications, reducing its material consumption and increasing the strength of 3D printed objects have become an important topic. In this paper, we introduce unidirectionally and bidirectionally stiffened structures into 3D printing to increase the strength and stiffness of 3D printed objects and reduce their material consumption. To maximize the advantages of such stiffened structures, we investigated finite element analysis, especially for general cases of stiffeners in arbitrary positions and directions, and performed optimization design to minimize the total volume of stiffened structures. Many examples are presented to demonstrate the effectiveness of the proposed finite element analysis and optimization design as well as significant reductions in the material costs and stresses in 3D printed objects stiffened with unidirectional and bidirectional stiffeners. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>(<b>a</b>) Rib–skin structures in a plant leaf (Photo by Daniel Hodgkins on Unsplash (<a href="https://unsplash.com/photos/I7sNoicir_I" target="_blank">https://unsplash.com/photos/I7sNoicir_I</a>, accessed on 7 September 2021)), (<b>b</b>) fly wing (Photo by Martin Hauser Phycus (<a href="https://commons.wikimedia.org/wiki/File:Wing_D_suzukii_female.jpg" target="_blank">https://commons.wikimedia.org/wiki/File:Wing_D_suzukii_female.jpg</a>, accessed 27 October 2021)), and (<b>c</b>) the human body (Photo by Bernhard Ungerer (<a href="https://commons.wikimedia.org/wiki/File:3D_Female_Skeleton_Anatomy.png" target="_blank">https://commons.wikimedia.org/wiki/File:3D_Female_Skeleton_Anatomy.png</a>, accessed on 10 September 2021)).</p>
Full article ">Figure 2
<p>(<b>a</b>) Stiffened structures in the Salisbury cathedral (Photo by Tony Hisgett on Flickr (<a href="https://www.flickr.com/photos/hisgett/5690722283/" target="_blank">https://www.flickr.com/photos/hisgett/5690722283/</a>, accessed on 8 September 2021)), (<b>b</b>) Yamanashi fruit museum (Photo by scarletgreen on Flickr (<a href="https://www.flickr.com/photos/9160678@N06/620307455/" target="_blank">https://www.flickr.com/photos/9160678@N06/620307455/</a>, accessed on 8 September 2021)), (<b>c</b>) garden at Marina South (Photo from eVolo (<a href="https://www.evolo.us/worlds-largest-climate-controlled-glasshouse-wilkinson-eyre-architects/" target="_blank">https://www.evolo.us/worlds-largest-climate-controlled-glasshouse-wilkinson-eyre-architects/</a>, accessed on 8 September 2021)), and (<b>d</b>) gas holder (Photo by Richard Rogerson (<a href="https://commons.wikimedia.org/wiki/File:Gas_Holder_by_Battersea_Railway_Station_-_geograph.org.uk_-_1820717.jpg" target="_blank">https://commons.wikimedia.org/wiki/File:Gas_Holder_by_Battersea_Railway_Station_-_geograph.org.uk_-_1820717.jpg</a>, accessed on 10 September 2021)).</p>
Full article ">Figure 3
<p>(<b>a</b>) Single-sided structures in an F-16 (Photo from (<a href="https://commons.m.wikimedia.org/wiki/File:Cutaway_drawing_of_an_F-16.jpg" target="_blank">https://commons.m.wikimedia.org/wiki/File:Cutaway_drawing_of_an_F-16.jpg</a>, accessed on 27 October 2021)) and (<b>b</b>) double-sided stiffened structures.</p>
Full article ">Figure 4
<p>Local coordinate system of a stiffener within a flat shell element.</p>
Full article ">Figure 5
<p>Two ways of slicing of geometries: (<b>a</b>) unidirectional slicing; (<b>b</b>) bidirectional slicing.</p>
Full article ">Figure 6
<p>Optimized unidirectional stiffeners from the algorithm: (<b>a</b>) 4 stiffeners; (<b>b</b>) 9 stiffeners; (<b>c</b>) 10 stiffeners.</p>
Full article ">Figure 7
<p>Optimized bidirectional stiffeners from the algorithm: (<b>a</b>) 6 stiffeners; (<b>b</b>) 12 stiffeners and (<b>c</b>) 14 stiffeners.</p>
Full article ">Figure 8
<p>All of the 3D printed models.</p>
Full article ">Figure 9
<p>Unidirectionally stiffened flat plate, from left to right: (<b>a</b>) initial stress without stiffeners; (<b>b</b>) optimized stiffeners; (<b>c</b>) final stress with stiffeners; (<b>d</b>) 3D print.</p>
Full article ">Figure 10
<p>Bidirectionally stiffened square plate, from left to right: (<b>a</b>) initial stress without stiffeners; (<b>b</b>) optimized stiffeners; (<b>c</b>) final stress with stiffeners; (<b>d</b>) 3D print.</p>
Full article ">Figure 11
<p>Unidirectionally stiffened snail, from left to right: (<b>a</b>) initial stress without stiffeners; (<b>b</b>) optimized stiffeners; (<b>c</b>) final stress with stiffeners; (<b>d</b>) 3D print.</p>
Full article ">Figure 12
<p>Bidirectionally stiffened botanic, from left to right: (<b>a</b>) initial stress without stiffeners, (<b>b</b>) optimized stiffeners, (<b>c</b>) final stress with stiffeners, (<b>d</b>) 3D print.</p>
Full article ">Figure 13
<p>Unidirectionally stiffened arch bridge, from left to right: (<b>a</b>) initial stress without stiffeners; (<b>b</b>) optimized stiffeners; (<b>c</b>) final stress with stiffeners; (<b>d</b>) 3D print.</p>
Full article ">Figure 14
<p>Bidirectionally stiffened dome, from left to right: (<b>a</b>) initial stress without stiffeners; (<b>b</b>) optimized stiffeners; (<b>c</b>) final stress with stiffeners; (<b>d</b>) 3D print.</p>
Full article ">Figure 15
<p>Bidirectionally stiffened hemisphere, from left to right: (<b>a</b>) initial stress without stiffeners; (<b>b</b>) optimized stiffeners; (<b>c</b>) final stress with stiffeners; (<b>d</b>) 3D print.</p>
Full article ">
23 pages, 108354 KiB  
Article
Imperceptible–Visible Watermarking to Information Security Tasks in Color Imaging
by Oswaldo Ulises Juarez-Sandoval, Francisco Javier Garcia-Ugalde, Manuel Cedillo-Hernandez, Jazmin Ramirez-Hernandez and Leobardo Hernandez-Gonzalez
Mathematics 2021, 9(19), 2374; https://doi.org/10.3390/math9192374 - 24 Sep 2021
Cited by 7 | Viewed by 3048
Abstract
Digital image watermarking algorithms have been designed for intellectual property, copyright protection, medical data management, and other related fields; furthermore, in real-world applications such as official documents, banknotes, etc., they are used to deliver additional information about the documents’ authenticity. In this context, [...] Read more.
Digital image watermarking algorithms have been designed for intellectual property, copyright protection, medical data management, and other related fields; furthermore, in real-world applications such as official documents, banknotes, etc., they are used to deliver additional information about the documents’ authenticity. In this context, the imperceptible–visible watermarking (IVW) algorithm has been designed as a digital reproduction of the real-world watermarks. This paper presents a new improved IVW algorithm for copyright protection that can deliver additional information to the image content. The proposed algorithm is divided into two stages: in the embedding stage, a human visual system-based strategy is used to embed an owner logotype or a 2D quick response (QR) code as a watermark into a color image, maintaining a high watermark imperceptibility and low image-quality degradation. In the exhibition, a new histogram binarization function approach is introduced to exhibit any watermark with enough quality to be recognized or decoded by any application, which is focused on reading QR codes. The experimental results show that the proposed algorithm can embed one or more watermark patterns, maintaining the high imperceptibility and visual quality of the embedded and the exhibited watermark. The performance evaluation shows that the method overcomes several drawbacks reported in previous algorithms, including geometric and image processing attacks such as JPEG and JPEG2000. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Invisible–visible watermarking classification.</p>
Full article ">Figure 2
<p>General diagram of the IVW.</p>
Full article ">Figure 3
<p>General diagram of the IIVW.</p>
Full article ">Figure 4
<p>Histogram of the watermarked region. (<b>a</b>) Histogram of the watermarked region by Equation (2), (<b>b</b>) histogram of the watermarked region by Equation (3).</p>
Full article ">Figure 5
<p>Histogram of the watermarked region by Equation (5).</p>
Full article ">Figure 6
<p>General diagram of the embedding stage.</p>
Full article ">Figure 7
<p>Histogram distortion of the watermarked region, (<b>a</b>) Histogram distortion induced by Equation (13), (<b>b</b>) Histogram distortion induced by Equation (14).</p>
Full article ">Figure 8
<p>General diagram of the exhibition stage.</p>
Full article ">Figure 9
<p>Binary watermark patterns: (<b>a</b>) Owner logotype FI, (<b>b</b>) QR code level L, and (<b>c</b>) Owner logotype UNAM.</p>
Full article ">Figure 10
<p>Watermarked UCID graphical quality degradation and imperceptibility. (<b>a</b>–<b>c</b>) are the corresponding PSNR, SSIM, and NCD for the FI watermark; (<b>d</b>–<b>f</b>) are the corresponding PSNR, SSIM, and NCD for the QR watermark; (<b>g</b>–<b>i</b>) are the corresponding PSNR, SSIM, and NCD for the UNAM watermark.</p>
Full article ">Figure 11
<p>Performance comparison in terms of compression. (<b>a</b>) BER vs. JPEG, (<b>b</b>) BER vs. JPEG2000.</p>
Full article ">Figure 12
<p>Multi-Watermarked image, (<b>a</b>) Watermarked image PSNR = 48.63 dB, SSIM = 0.9964, NDC = 0.0055, (<b>b</b>) Exhibited FI watermark, (<b>c</b>) Exhibited QR watermark, (<b>d</b>) Exhibited UNAM watermark.</p>
Full article ">Figure 13
<p>Histogram modulation-based exhibition strategy applied to the proposed algorithm, (<b>a</b>) Multi-Watermarked image, (<b>b</b>) Exhibited FI watermark, (<b>c</b>) Exhibited QR watermark, (<b>d</b>) Exhibited UNAM watermark.</p>
Full article ">
11 pages, 2680 KiB  
Article
Voxel-Based 3D Object Reconstruction from Single 2D Image Using Variational Autoencoders
by Rohan Tahir, Allah Bux Sargano and Zulfiqar Habib
Mathematics 2021, 9(18), 2288; https://doi.org/10.3390/math9182288 - 17 Sep 2021
Cited by 23 | Viewed by 8910
Abstract
In recent years, learning-based approaches for 3D reconstruction have gained much popularity due to their encouraging results. However, unlike 2D images, 3D cannot be represented in its canonical form to make it computationally lean and memory-efficient. Moreover, the generation of a 3D model [...] Read more.
In recent years, learning-based approaches for 3D reconstruction have gained much popularity due to their encouraging results. However, unlike 2D images, 3D cannot be represented in its canonical form to make it computationally lean and memory-efficient. Moreover, the generation of a 3D model directly from a single 2D image is even more challenging due to the limited details available from the image for 3D reconstruction. Existing learning-based techniques still lack the desired resolution, efficiency, and smoothness of the 3D models required for many practical applications. In this paper, we propose voxel-based 3D object reconstruction (V3DOR) from a single 2D image for better accuracy, one using autoencoders (AE) and another using variational autoencoders (VAE). The encoder part of both models is used to learn suitable compressed latent representation from a single 2D image, and a decoder generates a corresponding 3D model. Our contribution is twofold. First, to the best of the authors’ knowledge, it is the first time that variational autoencoders (VAE) have been employed for the 3D reconstruction problem. Second, the proposed models extract a discriminative set of features and generate a smoother and high-resolution 3D model. To evaluate the efficacy of the proposed method, experiments have been conducted on a benchmark ShapeNet data set. The results confirm that the proposed method outperforms state-of-the-art methods. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>2D image and its corresponding 3D model.</p>
Full article ">Figure 2
<p>Detailed Architecture of the Proposed Autoencoder Approach.</p>
Full article ">Figure 3
<p>Detailed Architecture of the Proposed Variational Autoencoder Approach.</p>
Full article ">
43 pages, 20071 KiB  
Article
Multimodal Human Recognition in Significantly Low Illumination Environment Using Modified EnlightenGAN
by Ja Hyung Koo, Se Woon Cho, Na Rae Baek and Kang Ryoung Park
Mathematics 2021, 9(16), 1934; https://doi.org/10.3390/math9161934 - 13 Aug 2021
Cited by 7 | Viewed by 2511
Abstract
Human recognition in indoor environments occurs both during the day and at night. During the day, human recognition encounters performance degradation owing to a blur generated when a camera captures a person’s image. However, when images are captured at night with a camera, [...] Read more.
Human recognition in indoor environments occurs both during the day and at night. During the day, human recognition encounters performance degradation owing to a blur generated when a camera captures a person’s image. However, when images are captured at night with a camera, it is difficult to obtain perfect images of a person without light, and the input images are very noisy owing to the properties of camera sensors in low-illumination environments. Studies have been conducted in the past on face recognition in low-illumination environments; however, there is lack of research on face- and body-based human recognition in very low illumination environments. To solve these problems, this study proposes a modified enlighten generative adversarial network (modified EnlightenGAN) in which a very low illumination image is converted to a normal illumination image, and the matching scores of deep convolutional neural network (CNN) features of the face and body in the converted image are combined with a score-level fusion for recognition. The two types of databases used in this study are the Dongguk face and body database version 3 (DFB-DB3) and the ChokePoint open dataset. The results of the experiment conducted using the two databases show that the human verification accuracy (equal error rate (ERR)) and identification accuracy (rank 1 genuine acceptance rate (GAR)) of the proposed method were 7.291% and 92.67% for DFB-DB3 and 10.59% and 87.78% for the ChokePoint dataset, respectively. Accordingly, the performance of the proposed method was better than the previous methods. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Overall procedure of proposed method.</p>
Full article ">Figure 2
<p>Architecture of modified EnlightenGAN: (<b>a</b>) generator and (<b>b</b>) discriminator.</p>
Full article ">Figure 2 Cont.
<p>Architecture of modified EnlightenGAN: (<b>a</b>) generator and (<b>b</b>) discriminator.</p>
Full article ">Figure 3
<p>Example of DFB-DB3 figures obtained from (<b>a</b>) the Logitech C920 camera and (<b>b</b>) the Logitech BCC950 camera. (<b>c</b>) Converted low-illumination figure of DFB-DB3.</p>
Full article ">Figure 4
<p>Example images for ChokePoint dataset. (<b>a</b>) Original images of ChokePoint dataset [<a href="#B34-mathematics-09-01934" class="html-bibr">34</a>]. (<b>b</b>) Converted low-illumination image of ChokePoint dataset.</p>
Full article ">Figure 4 Cont.
<p>Example images for ChokePoint dataset. (<b>a</b>) Original images of ChokePoint dataset [<a href="#B34-mathematics-09-01934" class="html-bibr">34</a>]. (<b>b</b>) Converted low-illumination image of ChokePoint dataset.</p>
Full article ">Figure 5
<p>Method for data augmentation including (<b>a</b>) cropping and image translation, and (<b>b</b>) horizontal flipping.</p>
Full article ">Figure 6
<p>Graphs illustrating training accuracy and loss of DFB-DB3 (<b>a</b>–<b>d</b>) result and ChokePoint dataset (<b>e</b>–<b>h</b>) result. VGG face net-16 with respect to (<b>a</b>,<b>e</b>) the first fold and (<b>b</b>,<b>f</b>) the second fold. ResNet-50 with respect to (<b>c</b>,<b>g</b>) the first fold and (<b>d</b>,<b>h</b>) the second fold.</p>
Full article ">Figure 6 Cont.
<p>Graphs illustrating training accuracy and loss of DFB-DB3 (<b>a</b>–<b>d</b>) result and ChokePoint dataset (<b>e</b>–<b>h</b>) result. VGG face net-16 with respect to (<b>a</b>,<b>e</b>) the first fold and (<b>b</b>,<b>f</b>) the second fold. ResNet-50 with respect to (<b>c</b>,<b>g</b>) the first fold and (<b>d</b>,<b>h</b>) the second fold.</p>
Full article ">Figure 7
<p>Comparisons of output images by original EnlightenGAN and modified EnlightenGAN. (<b>a</b>) Original normal illumination image. (<b>b</b>) Low-illumination image. Output images by (<b>c</b>) original EnlightenGAN, and (<b>d</b>) modified EnlightenGAN.</p>
Full article ">Figure 7 Cont.
<p>Comparisons of output images by original EnlightenGAN and modified EnlightenGAN. (<b>a</b>) Original normal illumination image. (<b>b</b>) Low-illumination image. Output images by (<b>c</b>) original EnlightenGAN, and (<b>d</b>) modified EnlightenGAN.</p>
Full article ">Figure 8
<p>ROC curves of recognition accuracies with or without modified EnlightenGAN. Results of (<b>a</b>) face and body recognition, and (<b>b</b>) various score-level fusions.</p>
Full article ">Figure 9
<p>Graph for ROC curves acquired using our method and the previous GAN-based techniques. (<b>a</b>,<b>b</b>) Recognition results for face and body images, and (<b>c</b>) score-level fusion result.</p>
Full article ">Figure 9 Cont.
<p>Graph for ROC curves acquired using our method and the previous GAN-based techniques. (<b>a</b>,<b>b</b>) Recognition results for face and body images, and (<b>c</b>) score-level fusion result.</p>
Full article ">Figure 10
<p>ROC curves acquired by the previous methods and proposed method. (<b>a</b>) Recognition results for face image, and (<b>b</b>) recognition results for body and face image.</p>
Full article ">Figure 11
<p>CMC curves of the proposed and state-of-the-art methods. (<b>a</b>) Face recognition results obtained by the proposed and state-of-the-art methods, and (<b>b</b>) face and body recognition results obtained by the proposed and state-of-the-art methods.</p>
Full article ">Figure 12
<p>Graphs for <span class="html-italic">t</span>-test result between the second best model and our proposed method with respect to accuracy of average recognition. (<b>a</b>) Comparison between ResNet-50 and the proposed method, and (<b>b</b>) comparison between ResNet IDE + LIME and the proposed method.</p>
Full article ">Figure 13
<p>Cases of FA, FR, and correction recognition. (<b>a</b>) Cases of FA, (<b>b</b>) cases of FR, and (<b>c</b>) correct cases. In (<b>a</b>–<b>c</b>), left and right images are enrolled and recognized images, respectively.</p>
Full article ">Figure 13 Cont.
<p>Cases of FA, FR, and correction recognition. (<b>a</b>) Cases of FA, (<b>b</b>) cases of FR, and (<b>c</b>) correct cases. In (<b>a</b>–<b>c</b>), left and right images are enrolled and recognized images, respectively.</p>
Full article ">Figure 14
<p>Results on class activation feature map of DFB-DB3. (<b>a</b>,<b>b</b>) are the activation map results from face images. From the left image to the right image: original image, low-illumination image, enhancement image from modified EnlightenGAN, result from 7th ReLU layer, result from 12th ReLU layer, and result from 13th ReLU layer of VGG face-net 16. (<b>c</b>,<b>d</b>) are the activation map results from body images. From the left image to the right image: original image, low-illumination image, enhancement image from modified EnlightenGAN, result from 3rd batch-normalized layer, result from conv5 2nd block, and result from conv5 3rd block of ResNet-50.</p>
Full article ">Figure 15
<p>ROC curves of recognition accuracies with and without modified EnlightenGAN. Results of (<b>a</b>) face and body recognition, and (<b>b</b>) various score-level fusions.</p>
Full article ">Figure 15 Cont.
<p>ROC curves of recognition accuracies with and without modified EnlightenGAN. Results of (<b>a</b>) face and body recognition, and (<b>b</b>) various score-level fusions.</p>
Full article ">Figure 16
<p>ROC curves acquired by our proposed method and previous GAN-based methods. (<b>a</b>,<b>b</b>) Recognition results for face and body images, and (<b>c</b>) score-level fusion result.</p>
Full article ">Figure 16 Cont.
<p>ROC curves acquired by our proposed method and previous GAN-based methods. (<b>a</b>,<b>b</b>) Recognition results for face and body images, and (<b>c</b>) score-level fusion result.</p>
Full article ">Figure 17
<p>ROC curves acquired using the proposed method and the previous methods. (<b>a</b>) Results for face recognition, and (<b>b</b>) results for body and face recognition.</p>
Full article ">Figure 18
<p>CMC curves of the proposed and state-of-the-art methods. (<b>a</b>) Face recognition results obtained by the proposed and state-of-the-art methods, and (<b>b</b>) face and body recognition results obtained by the proposed and state-of-the-art methods.</p>
Full article ">Figure 19
<p>Graphs for <span class="html-italic">t</span>-test result of the second best model and our proposed method with regard to average recognition accuracy. (<b>a</b>) Comparison of VGG face net-16 [<a href="#B44-mathematics-09-01934" class="html-bibr">44</a>] and the proposed method, and (<b>b</b>) comparison of the proposed method and ELF [<a href="#B48-mathematics-09-01934" class="html-bibr">48</a>].</p>
Full article ">Figure 20
<p>Cases of FA, FR, and correction recognition on ChokePoint database [<a href="#B34-mathematics-09-01934" class="html-bibr">34</a>]. (<b>a</b>) Cases of FA, (<b>b</b>) cases of FR, and (<b>c</b>) correct cases. In (<b>a</b>–<b>c</b>), the left and right images are enrolled and recognized images, respectively.</p>
Full article ">Figure 20 Cont.
<p>Cases of FA, FR, and correction recognition on ChokePoint database [<a href="#B34-mathematics-09-01934" class="html-bibr">34</a>]. (<b>a</b>) Cases of FA, (<b>b</b>) cases of FR, and (<b>c</b>) correct cases. In (<b>a</b>–<b>c</b>), the left and right images are enrolled and recognized images, respectively.</p>
Full article ">Figure 21
<p>Results on class activation feature map on ChokePoint dataset [<a href="#B34-mathematics-09-01934" class="html-bibr">34</a>]. (<b>a</b>,<b>b</b>) are activation map results from face images. From the left image to the right image: original image, low-illumination image, enhancement image from modified EnlightenGAN, result from 7th ReLU layer, result from 12th ReLU layer, and result from 13th ReLU layer of VGG face-net 16. (<b>c</b>,<b>d</b>) are activation map results from body images. From the left image to the right image: original image, low-illumination image, enhancement image from modified EnlightenGAN, result from 3rd batch-normalized layer, result from conv5 2nd block, and result from conv5 3rd block of ResNet-50.</p>
Full article ">Figure 22
<p>Examples of original images captured in real low-light environments.</p>
Full article ">Figure 23
<p>Comparisons of (<b>a</b>) ROC and (<b>b</b>) CMC curves obtained by proposed method and state-of-the-art-methods.</p>
Full article ">Figure 24
<p>Example of an original image from an open database captured in a real low-light environment.</p>
Full article ">Figure 25
<p>Comparisons of (<b>a</b>) ROC and (<b>b</b>) CMC curves obtained by the proposed method and state-of-the-art-methods with an open database.</p>
Full article ">Figure 25 Cont.
<p>Comparisons of (<b>a</b>) ROC and (<b>b</b>) CMC curves obtained by the proposed method and state-of-the-art-methods with an open database.</p>
Full article ">Figure 26
<p>Jetson TX2 embedded system.</p>
Full article ">
12 pages, 5900 KiB  
Article
The Development of Long-Distance Viewing Direction Analysis and Recognition of Observed Objects Using Head Image and Deep Learning
by Yu-Shiuan Tsai, Nai-Chi Chen, Yi-Zeng Hsieh and Shih-Syun Lin
Mathematics 2021, 9(16), 1880; https://doi.org/10.3390/math9161880 - 7 Aug 2021
Cited by 1 | Viewed by 2512
Abstract
In this study, we use OpenPose to capture many facial feature nodes, create a data set and label it, and finally bring in the neural network model we created. The purpose is to predict the direction of the person’s line of sight from [...] Read more.
In this study, we use OpenPose to capture many facial feature nodes, create a data set and label it, and finally bring in the neural network model we created. The purpose is to predict the direction of the person’s line of sight from the face and facial feature nodes and finally add object detection technology to calculate the object that the person is observing. After implementing this method, we found that this method can correctly estimate the human body’s form. Furthermore, if multiple lenses can get more information, the effect will be better than a single lens, evaluating the observed objects more accurately. Furthermore, we found that the head in the image can judge the direction of view. In addition, we found that in the case of the test face tilt, approximately at a tilt angle of 60 degrees, the face nodes can still be captured. Similarly, when the inclination angle is greater than 60 degrees, the facing node cannot be used. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Flowchart of long-distance viewing direction recognition.</p>
Full article ">Figure 2
<p>(<b>a</b>) OpenPose face node numbers [<a href="#B24-mathematics-09-01880" class="html-bibr">24</a>]; (<b>b</b>) face node test.</p>
Full article ">Figure 3
<p>Taking the nose node as the center node.</p>
Full article ">Figure 4
<p>The line from the nose node and the red paper center.</p>
Full article ">Figure 5
<p>Direction class.</p>
Full article ">Figure 6
<p>Value of training times for the combination with the highest accuracy. (<b>a</b>) accuracy’s change to each epoch; (<b>b</b>) loss’s change to each epoch.</p>
Full article ">Figure 7
<p>Predicting the direction of the person’s viewing direction. (<b>a</b>) The human body is at the center of the screen; (<b>b</b>) the human body is at the edge of the screen.</p>
Full article ">Figure 7 Cont.
<p>Predicting the direction of the person’s viewing direction. (<b>a</b>) The human body is at the center of the screen; (<b>b</b>) the human body is at the edge of the screen.</p>
Full article ">Figure 8
<p>Comparison of normalized face nodes for two persons. The <span class="html-italic">X</span>-axis is the distance from the camera, and the <span class="html-italic">Y</span>-axis is the average value for each face point to the nose vector after normalization on (<b>a</b>) person 1; (<b>b</b>) person 2.</p>
Full article ">Figure 9
<p>Average node weights for two persons. The <span class="html-italic">X</span>-axis is the distance from the camera, and the <span class="html-italic">Y</span>-axis is the average weight of all face nodes on (<b>a</b>) person 1; (<b>b</b>) person 2.</p>
Full article ">Figure 10
<p>Comparison of face nodes after normalization. The <span class="html-italic">Y</span>-axis is the average value of the normalized vectors from face points to nose.</p>
Full article ">Figure 11
<p>Average graph of face node weights.</p>
Full article ">Figure 12
<p>Average weight vertical inclination.</p>
Full article ">Figure 13
<p>Viewing object detection.</p>
Full article ">Figure 13 Cont.
<p>Viewing object detection.</p>
Full article ">
20 pages, 5767 KiB  
Article
Image Region Prediction from Thermal Videos Based on Image Prediction Generative Adversarial Network
by Ganbayar Batchuluun, Ja Hyung Koo, Yu Hwan Kim and Kang Ryoung Park
Mathematics 2021, 9(9), 1053; https://doi.org/10.3390/math9091053 - 7 May 2021
Cited by 6 | Viewed by 2386
Abstract
Various studies have been conducted on object detection, tracking, and action recognition based on thermal images. However, errors occur during object detection, tracking, and action recognition when a moving object leaves the field of view (FOV) of a camera and part of the [...] Read more.
Various studies have been conducted on object detection, tracking, and action recognition based on thermal images. However, errors occur during object detection, tracking, and action recognition when a moving object leaves the field of view (FOV) of a camera and part of the object becomes invisible. However, no studies have examined this issue so far. Therefore, this article proposes a method for widening the FOV of the current image by predicting images outside the FOV of the camera using the current image and previous sequential images. In the proposed method, the original one-channel thermal image is converted into a three-channel thermal image to perform image prediction using an image prediction generative adversarial network. When image prediction and object detection experiments were conducted using the marathon sub-dataset of the Boston University-thermal infrared video (BU-TIV) benchmark open dataset, we confirmed that the proposed method showed the higher accuracies of image prediction (structural similarity index measure (SSIM) of 0.9839) and object detection (F1 score (F1) of 0.882, accuracy (ACC) of 0.983, and intersection over union (IoU) of 0.791) than the state-of-the-art methods. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Example of thermal image prediction.</p>
Full article ">Figure 2
<p>Overall flowchart of the proposed method.</p>
Full article ">Figure 3
<p>Procedure of preprocessing.</p>
Full article ">Figure 4
<p>Example of the structure of the proposed IPGAN.</p>
Full article ">Figure 5
<p>Example of the postprocessing.</p>
Full article ">Figure 6
<p>Examples of dataset preparation. In (<b>a</b>–<b>c</b>), on the left: from top to bottom, an original thermal image and an ROI image. In (<b>a</b>–<b>c</b>), on the right: from top to bottom, a ground-truth image and an input image.</p>
Full article ">Figure 6 Cont.
<p>Examples of dataset preparation. In (<b>a</b>–<b>c</b>), on the left: from top to bottom, an original thermal image and an ROI image. In (<b>a</b>–<b>c</b>), on the right: from top to bottom, a ground-truth image and an input image.</p>
Full article ">Figure 7
<p>Training loss curves of GAN.</p>
Full article ">Figure 8
<p>Examples of result images obtained using Methods 1 and 2. From left to right, the input, output, and ground-truth images, respectively, obtained using (<b>a</b>) Method 1 and (<b>b</b>) Method 2. The size of the input, output, and ground-truth images is 80 × 170 pixels.</p>
Full article ">Figure 9
<p>Examples of result images obtained using Methods 3 and 4. From left to right, the input, output, and ground-truth images, respectively, obtained using (<b>a</b>) Method 3 and (<b>b</b>) Method 4.</p>
Full article ">Figure 10
<p>Examples of result images obtained using Methods 5–7. From left to right, the input, output, and ground-truth images, respectively, obtained using (<b>a</b>) Method 5, (<b>b</b>) Method 6, and (<b>c</b>) Method 7.</p>
Full article ">Figure 11
<p>Examples of result images obtained using Methods 4 and 7. From left to right, the input, output, and ground-truth images, respectively, obtained using (<b>a</b>) Method 4 and (<b>b</b>) Method 7.</p>
Full article ">Figure 12
<p>Examples of result images obtained using the proposed method. In (<b>a</b>–<b>d</b>), from left to right, the original, ground-truth, and predicted (output) images, respectively.</p>
Full article ">Figure 13
<p>Examples of detection results before and after image prediction. In (<b>a</b>–<b>d</b>), from left to right, the original input images, results with original input images, ground-truth images, results with ground-truth images, images predicted using our method, and results with predicted images, respectively.</p>
Full article ">Figure 14
<p>Comparisons of the original images, ground-truth images, and prediction results obtained using the state-of-the-art methods and our method: (<b>a</b>) original images; (<b>b</b>) ground-truth images. Images predicted using: (<b>c</b>) Haziq et al.’s method; (<b>d</b>) Liu et al.’s method; (<b>e</b>) Shin et al.’s method; (<b>f</b>) Nazeri et al.’s method; (<b>g</b>) the proposed method.</p>
Full article ">Figure 15
<p>Comparisons of detection results using the original images, ground-truth images, and the predicted images obtained using the state-of-the-art methods and our method. (<b>a</b>) Original images. Detection results using the (<b>b</b>) original images, (<b>c</b>) ground-truth images, (<b>d</b>) images predicted using Haziq et al.’s method, (<b>e</b>) images predicted using Liu et al.’s method, (<b>f</b>) images predicted using Shin et al.’s method, (<b>g</b>) images predicted using Nazeri et al.’s method, and (<b>h</b>) images predicted using our method.</p>
Full article ">
18 pages, 4585 KiB  
Article
Semantic Segmentation by Multi-Scale Feature Extraction Based on Grouped Dilated Convolution Module
by Dong Seop Kim, Yu Hwan Kim and Kang Ryoung Park
Mathematics 2021, 9(9), 947; https://doi.org/10.3390/math9090947 - 23 Apr 2021
Cited by 7 | Viewed by 3160
Abstract
Existing studies have shown that effective extraction of multi-scale information is a crucial factor directly related to the increase in performance of semantic segmentation. Accordingly, various methods for extracting multi-scale information have been developed. However, these methods face problems in that they require [...] Read more.
Existing studies have shown that effective extraction of multi-scale information is a crucial factor directly related to the increase in performance of semantic segmentation. Accordingly, various methods for extracting multi-scale information have been developed. However, these methods face problems in that they require additional calculations and vast computing resources. To address these problems, this study proposes a grouped dilated convolution module that combines existing grouped convolutions and atrous spatial pyramid pooling techniques. The proposed method can learn multi-scale features more simply and effectively than existing methods. Because each convolution group has different dilations in the proposed model, they have receptive fields of different sizes and can learn features corresponding to these receptive fields. As a result, multi-scale context can be easily extracted. Moreover, optimal hyper-parameters are obtained from an in-depth analysis, and excellent segmentation performance is derived. To evaluate the proposed method, open databases of the Cambridge Driving Labeled Video Database (CamVid) and the Stanford Background Dataset (SBD) are utilized. The experimental results indicate that the proposed method shows a mean intersection over union of 73.15% based on the CamVid dataset and 72.81% based on the SBD, thereby exhibiting excellent performance compared to other state-of-the-art methods. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Examples of semantic segmentation applying pixel-wise classification, with the left column showing input images and the right column showing ground truth in which challenging factors, such as various classes and multi-scale objects, exist.</p>
Full article ">Figure 2
<p>Examples of each method: (<b>a</b>) grouped convolutions when G is two; (<b>b</b>) atrous pyramid pooling based on dilated convolutions among spatial pyramid pooling techniques; (<b>c</b>) structure of the proposed GDCM. * means convolution operation.</p>
Full article ">Figure 3
<p>Proposed GDCM in which all 32 grouped convolutions are applied in a convolution layer. All are divided into four subgroups that apply different dilation convolutions. The value of a dilation parameter is established to be 1, 2, 3 or 4 according to the group, and the final output is derived via concatenation.</p>
Full article ">Figure 4
<p>Examples of experimental databases: (<b>a</b>,<b>b</b>) CamVid; (<b>c</b>,<b>d</b>) SBD; In (<b>a</b>–<b>d</b>), the left and right images show the input and ground-truth images, respectively.</p>
Full article ">Figure 4 Cont.
<p>Examples of experimental databases: (<b>a</b>,<b>b</b>) CamVid; (<b>c</b>,<b>d</b>) SBD; In (<b>a</b>–<b>d</b>), the left and right images show the input and ground-truth images, respectively.</p>
Full article ">Figure 5
<p>Training loss graphs.</p>
Full article ">Figure 6
<p>Detected results by proposed method. The images in the 1st and 2nd rows are from CamVid and those in the 3rd row are from SBD. In each row, input, ground-truth, and detected result are respectively shown from the left. Class information is shown in <a href="#mathematics-09-00947-f004" class="html-fig">Figure 4</a>.</p>
Full article ">Figure 7
<p>Jetson TX2 embedded system.</p>
Full article ">
14 pages, 8447 KiB  
Article
Underwater Image Enhancement Based on Multi-Scale Fusion and Global Stretching of Dual-Model
by Huajun Song and Rui Wang
Mathematics 2021, 9(6), 595; https://doi.org/10.3390/math9060595 - 10 Mar 2021
Cited by 18 | Viewed by 3783
Abstract
Aimed at the two problems of color deviation and poor visibility of the underwater image, this paper proposes an underwater image enhancement method based on the multi-scale fusion and global stretching of dual-model (MFGS), which does not rely on the underwater optical imaging [...] Read more.
Aimed at the two problems of color deviation and poor visibility of the underwater image, this paper proposes an underwater image enhancement method based on the multi-scale fusion and global stretching of dual-model (MFGS), which does not rely on the underwater optical imaging model. The proposed method consists of three stages: Compared with other color correction algorithms, white-balancing can effectively eliminate the undesirable color deviation caused by medium attenuation, so it is selected to correct the color deviation in the first stage. Then, aimed at the problem of the poor performance of the saliency weight map in the traditional fusion processing, this paper proposed an updated strategy of saliency weight coefficient combining contrast and spatial cues to achieve high-quality fusion. Finally, by analyzing the characteristics of the results of the above steps, it is found that the brightness and clarity need to be further improved. The global stretching of the full channel in the red, green, blue (RGB) model is applied to enhance the color contrast, and the selective stretching of the L channel in the Commission International Eclairage-Lab (CIE-Lab) model is implemented to achieve a better de-hazing effect. Quantitative and qualitative assessments on the underwater image enhancement benchmark dataset (UIEBD) show that the enhanced images of the proposed approach achieve significant and sufficient improvements in color and visibility. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>The results of each stage.</p>
Full article ">Figure 2
<p>Method overview.</p>
Full article ">Figure 3
<p>The processing results of different white balance algorithms. (<b>a</b>) is the original input image. (<b>b</b>–<b>e</b>) represent the processing results of principal component analysis (PCA), the white patch retinex method, the grey world method, and our method, respectively.</p>
Full article ">Figure 4
<p>The two inputs are derived from the white-balancing image. Input 1 is the sharpened version of the white-balancing image and Input 2 is the gamma-corrected version of the white-balancing image. The rest of the pictures are three corresponding normalized weight maps and the merged weight maps for two inputs. The last one is the multi-scale fusion result.</p>
Full article ">Figure 5
<p>The saliency weight maps of two methods. In the first column, two images of the same scene are the sharpened version and the gamma corrected version of white-balancing images, respectively. The images in the second and third columns represent the saliency weight maps obtained by Ancuti et al. [<a href="#B12-mathematics-09-00595" class="html-bibr">12</a>] and our method, respectively.</p>
Full article ">Figure 6
<p>The stretching process in the RGB color model. (<b>a</b>) is the entire histogram distribution of three channels (RGB). (<b>b</b>–<b>d</b>) is the histogram distribution of a single channel in RGB color model, respectively.</p>
Full article ">Figure 7
<p>The stretching process in the Lab color model. Line (<b>b</b>) is the histogram distribution of the L component of the corresponding image in line (<b>a</b>), respectively.</p>
Full article ">Figure 8
<p>The qualitative evaluation result of 7 selected images from Data A.</p>
Full article ">Figure 9
<p>The qualitative evaluation result of 7 selected images from Data B/C.</p>
Full article ">

Review

Jump to: Research

38 pages, 2144 KiB  
Review
Digital Video Tampering Detection and Localization: Review, Representations, Challenges and Algorithm
by Naheed Akhtar, Mubbashar Saddique, Khurshid Asghar, Usama Ijaz Bajwa, Muhammad Hussain and Zulfiqar Habib
Mathematics 2022, 10(2), 168; https://doi.org/10.3390/math10020168 - 6 Jan 2022
Cited by 27 | Viewed by 6653
Abstract
Digital videos are now low-cost, easy to capture and easy to share on social media due to the common feature of video recording in smart phones and digital devices. However, with the advancement of video editing tools, videos can be tampered (forged) easily [...] Read more.
Digital videos are now low-cost, easy to capture and easy to share on social media due to the common feature of video recording in smart phones and digital devices. However, with the advancement of video editing tools, videos can be tampered (forged) easily for propaganda or to gain illegal advantages—ultimately, the authenticity of videos shared on social media cannot be taken for granted. Over the years, significant research has been devoted to developing new techniques for detecting different types of video tampering. In this paper, we offer a detailed review of existing passive video tampering detection techniques in a systematic way. The answers to research questions prepared for this study are also elaborated. The state-of-the-art research work is analyzed extensively, highlighting the pros and cons and commonly used datasets. Limitations of existing video forensic algorithms are discussed, and we conclude with research challenges and future directions. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Survey protocol plan.</p>
Full article ">Figure 2
<p>Motion detail of year-wise publications in conferences, journals and others.</p>
Full article ">Figure 3
<p>Engineering of video tampering (forgery). (<b>a</b>) Actual video, (<b>b</b>) spatially tampered video, (<b>c</b>) temporally tampered video, (<b>d</b>) spatio-temporal tampered video.</p>
Full article ">Figure 4
<p>Categories of video tampering detection techniques.</p>
Full article ">Figure 5
<p>Categories of spatial tampering detection methods.</p>
Full article ">Figure 6
<p>Categories of temporal tampering detection methods.</p>
Full article ">Figure 7
<p>Process of video tampering detection and localization.</p>
Full article ">
20 pages, 9520 KiB  
Review
Mathematical Principles of Object 3D Reconstruction by Shape-from-Focus Methods
by Dalibor Martišek and Karel Mikulášek
Mathematics 2021, 9(18), 2253; https://doi.org/10.3390/math9182253 - 14 Sep 2021
Cited by 3 | Viewed by 2671
Abstract
Shape-from-Focus (SFF) methods have been developed for about twenty years. They able to obtain the shape of 3D objects from a series of partially focused images. The plane to which the microscope or camera is focused intersects the 3D object in a contour [...] Read more.
Shape-from-Focus (SFF) methods have been developed for about twenty years. They able to obtain the shape of 3D objects from a series of partially focused images. The plane to which the microscope or camera is focused intersects the 3D object in a contour line. Due to wave properties of light and due to finite resolution of the output device, the image can be considered as sharp not only on this contour line, but also in a certain interval of height—the zone of sharpness. SSFs are able to identify these focused parts to compose a fully focused 2D image and to reconstruct a 3D profile of the surface to be observed. Full article
(This article belongs to the Special Issue Computer Graphics, Image Processing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p>Optical cut of fracture surface of hydrated cement paste acquired by confocal microscope Olympus LEXT 1000. Confocal mode (<b>a</b>), standard mode (<b>b</b>). Taken from [<a href="#B24-mathematics-09-02253" class="html-bibr">24</a>].</p>
Full article ">Figure 2
<p>Different scaling and different sharp and non-sharp regions in images acquired by the classic camera positioned at different distances from the 3D relief of the first (<b>a</b>) and the sixteenth (<b>b</b>) image of a series of sixteen images, blue marble, locality (Nedvedice, Czech Republic, photo Pavel Starha). Taken from [<a href="#B26-mathematics-09-02253" class="html-bibr">26</a>].</p>
Full article ">Figure 3
<p>Different scaling and different sharp and non-sharp regions in images acquired by the classic camera positioned at different distances from the 3D relief—the first (<b>a</b>) and the fourth (<b>b</b>) image of a series of eight images, limestone, locality Brno (Hady, Czech Republic, photo Tomas Ficker). Taken from [<a href="#B26-mathematics-09-02253" class="html-bibr">26</a>].</p>
Full article ">Figure 4
<p>The central projection of a large sample—ideal case (<b>a</b>) can be solved by elementary mathematics, real case (<b>b</b>) necessitates sophisticated mathematical tools. Taken from [<a href="#B26-mathematics-09-02253" class="html-bibr">26</a>].</p>
Full article ">Figure 5
<p>3D reconstruction of the data from <a href="#mathematics-09-02253-f003" class="html-fig">Figure 3</a> after elementary registration by <a href="#mathematics-09-02253-f004" class="html-fig">Figure 4</a>a. Reconstruction taken from [<a href="#B27-mathematics-09-02253" class="html-bibr">27</a>]. Software developed by the author.</p>
Full article ">Figure 6
<p>Fourier transforms of the fifth term of the series of expanding rectangular signals. The series <math display="inline"><semantics> <mrow> <msubsup> <mi>δ</mi> <mi>n</mi> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>ξ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> converges to the <math display="inline"><semantics> <mi>δ</mi> </semantics></math>-distribution. Taken from [<a href="#B26-mathematics-09-02253" class="html-bibr">26</a>].</p>
Full article ">Figure 7
<p>Even extension of the <math display="inline"><semantics> <mrow> <mn>32</mn> <mo>×</mo> <mn>32</mn> </mrow> </semantics></math> neighborhood (framed) of the pixel processed (cross). Taken from [<a href="#B27-mathematics-09-02253" class="html-bibr">27</a>].</p>
Full article ">Figure 8
<p>Graphical representation of sharpness detectors <math display="inline"><semantics> <mrow> <mmultiscripts> <mi>P</mi> <none/> <none/> <mprescripts/> <mi>a</mi> <none/> </mmultiscripts> </mrow> </semantics></math> (<b>a</b>); <math display="inline"><semantics> <mrow> <mmultiscripts> <mi>P</mi> <none/> <none/> <mprescripts/> <mi>b</mi> <none/> </mmultiscripts> </mrow> </semantics></math> (<b>b</b>); <math display="inline"><semantics> <mrow> <mmultiscripts> <mi>P</mi> <none/> <none/> <mprescripts/> <mi>c</mi> <none/> </mmultiscripts> </mrow> </semantics></math> (<b>c</b>). Taken from [<a href="#B26-mathematics-09-02253" class="html-bibr">26</a>].</p>
Full article ">Figure 9
<p>The first (<b>a</b>) and the fifteenth (<b>b</b>) image of a series of fifteen images of blue marble (see <a href="#mathematics-09-02253-f003" class="html-fig">Figure 3</a>) displayed in supplementary pseudo-colours. The software used has been written by the author. Taken from [<a href="#B26-mathematics-09-02253" class="html-bibr">26</a>].</p>
Full article ">Figure 10
<p>The arithmetic mean of the images of <a href="#mathematics-09-02253-f010" class="html-fig">Figure 10</a>: before registration (<b>a</b>), after registration (<b>b</b>). The software used has been written by the author. Taken from [<a href="#B26-mathematics-09-02253" class="html-bibr">26</a>].</p>
Full article ">Figure 11
<p>Optical cuts detected on multifocal image of limestone (two images in the series—see <a href="#mathematics-09-02253-f003" class="html-fig">Figure 3</a>). The software was written by the first author of this paper. Taken from [<a href="#B45-mathematics-09-02253" class="html-bibr">45</a>].</p>
Full article ">Figure 12
<p>A 2D reconstruction of the limestone image by the optical cuts used in <a href="#mathematics-09-02253-f011" class="html-fig">Figure 11</a>. The software was written by the first author. Taken from [<a href="#B45-mathematics-09-02253" class="html-bibr">45</a>].</p>
Full article ">Figure 13
<p>A 3D echelon approximation of the limestone sample by the optical cuts used in <a href="#mathematics-09-02253-f011" class="html-fig">Figure 11</a>. The software was written by the first author. Taken from [<a href="#B45-mathematics-09-02253" class="html-bibr">45</a>].</p>
Full article ">Figure 14
<p>A 3D echelon approximation of the limestone sample by the optical cuts used in <a href="#mathematics-09-02253-f013" class="html-fig">Figure 13</a> smoothed by 3D low-pass filters. The software was written by the first author. Taken from [<a href="#B45-mathematics-09-02253" class="html-bibr">45</a>].</p>
Full article ">Figure 15
<p>A 3D reconstruction of the limestone sample by data registration according to <a href="#sec4-mathematics-09-02253" class="html-sec">Section 4</a>, with focusing criterion 28 and profile height calculations 29 and 30 (compare with <a href="#mathematics-09-02253-f005" class="html-fig">Figure 5</a>). The software was written by the first author. Taken from [<a href="#B45-mathematics-09-02253" class="html-bibr">45</a>].</p>
Full article ">Figure 16
<p>A 3D reconstruction of the blue marble sample by data registration according to <a href="#sec4-mathematics-09-02253" class="html-sec">Section 4</a>, with focusing criterion (28) and profile height calculations (29) and (30). The software was written by the first author. Taken from [<a href="#B45-mathematics-09-02253" class="html-bibr">45</a>].</p>
Full article ">Figure 17
<p>A confocal 3D relief of a single pore of hydrated Portland cement paste; 47 optical cuts with a vertical stepping of 1.2 μm. Olympus LEXT 1000, confocal mode, Olympus factory software. Taken from [<a href="#B27-mathematics-09-02253" class="html-bibr">27</a>].</p>
Full article ">Figure 18
<p>The same single pore of hydrated Portland cement paste as in <a href="#mathematics-09-02253-f017" class="html-fig">Figure 17</a>; 47 optical cuts with a vertical stepping of 1.2 μm. Olympus LEXT 1000 again. Non−confocal mode. A 3D reconstruction by data registration according to <a href="#sec4-mathematics-09-02253" class="html-sec">Section 4</a>, focusing criterion (28), and profile height calculations (29) and (30). The software was written by the first author. Taken from [<a href="#B27-mathematics-09-02253" class="html-bibr">27</a>].</p>
Full article ">
Back to TopTop