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17 pages, 58573 KiB  
Article
A 3D Estimation Method Using an Omnidirectional Camera and a Spherical Mirror
by Yuya Hiruta, Chun Xie, Hidehiko Shishido and Itaru Kitahara
Appl. Sci. 2023, 13(14), 8348; https://doi.org/10.3390/app13148348 - 19 Jul 2023
Cited by 1 | Viewed by 1514
Abstract
As the demand for 3D information continues to grow in various fields, technologies are rapidly being used to acquire such information. Laser-based estimation and multi-view images are popular methods for sensing 3D information, while deep learning techniques are also being developed. However, the [...] Read more.
As the demand for 3D information continues to grow in various fields, technologies are rapidly being used to acquire such information. Laser-based estimation and multi-view images are popular methods for sensing 3D information, while deep learning techniques are also being developed. However, the former method requires precise sensing equipment or large observation systems, while the latter relies on substantial prior information in the form of extensive learning datasets. Given these limitations, our research aims to develop a method that is independent of learning and makes it possible to capture a wide range of 3D information using a compact device. This paper introduces a novel approach for estimating the 3D information of an observed scene utilizing a monocular image based on a catadioptric imaging system employing an omnidirectional camera and a spherical mirror. By employing a curved mirror, it is possible to capture a large area in a single observation. At the same time, using an omnidirectional camera enables the creation of a simplified imaging system. The proposed method focuses on a spherical or spherical cap-shaped mirror in the scene. It estimates the mirror’s position from the captured images, allowing for the estimation of the scene with great flexibility. Simulation evaluations are conducted to validate the characteristics and effectiveness of our proposed method. Full article
(This article belongs to the Special Issue 3D Scene Understanding and Object Recognition)
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Figure 1
<p>Flow of 3D Estimation Using an Omnidirectional Camera and a Spherical Mirror: The capture of two images from different viewpoints using an omnidirectional camera and a spherical mirror, and the estimation of the 3D information of the scene using stereo vision.</p>
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<p>The Process of a 3D Estimation Based on a Catadioptric Imaging System with an Omnidirectional Camera and a Spherical Mirror: 1. Segmentation of the mirror image region in an omnidirectional image by network. Estimation of the 3D position of a spherical mirror from the shape of the mirror image (<a href="#sec4-applsci-13-08348" class="html-sec">Section 4</a>). 2. Estimation of the 3D information of the shooting scene based on the 3D position of the spherical mirror. Searching for the omnidirectional image part corresponding to the mirror image using the incident light rays from the object obtained by the 3D position information of the spherical mirror, using stereo matching (<a href="#sec5-applsci-13-08348" class="html-sec">Section 5</a>).</p>
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<p>Process of segmenting mirror image in omnidirectional image: The procedure begins with the segmenting of the omnidirectional image into perspective projection images via cube mapping. Subsequently, a deep learning model is applied to the perspective projection image containing the mirror image for further segmentation.</p>
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<p>Relationship between the Camera and the Spherical Mirror: The estimation of the 3D position of the spherical mirror involves identifying the supporting plane (normal <math display="inline"><semantics><mi mathvariant="bold-italic">n</mi></semantics></math>, distance <math display="inline"><semantics><msub><mi>h</mi><mi>p</mi></msub></semantics></math> from the camera) using the ellipse shape of the mirror image (matrix <math display="inline"><semantics><mi mathvariant="bold">Q</mi></semantics></math>). This process employs prior knowledge of the spherical mirror’s shape, including the radius <span class="html-italic">R</span> of the mirror sphere and the radius r of the 3D circle.</p>
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<p>The shape of a spherical mirror that allows for the estimation of its 3D position. When the radius of the 3D circle is unknown: On the <b>left</b> and in the <b>middle</b>, tangent lines can be drawn, allowing for estimation of the mirror’s position. On the <b>right</b>, tangent lines cannot possibly be drawn, making estimation impossible.</p>
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<p>Backward Projection (projection from 2D to 3D): Estimation of the light path from an object to the omnidrectional camera via reflection point on the spherical mirror.</p>
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<p>Search for Matching Point by Color Histogram: Calculate the color histograms of the mirrored image at the reflection point and the corresponding omnidirectional image. Then, search for corresponding points based on their similarity.</p>
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<p>Effect of 3D Position Estimation Errors of the Spherical Mirror on 3D Estimation: The effect of the error in the 3D position estimation of the spherical mirror on the 3D estimation is shown by expressing the distance <math display="inline"><semantics><mrow><mo stretchy="false">∥</mo><mi mathvariant="bold-italic">P</mi><mo stretchy="false">∥</mo></mrow></semantics></math> from the camera center to the 3D point with the imaging position of the 3D point (the direct image <math display="inline"><semantics><msub><mi>θ</mi><mi>i</mi></msub></semantics></math>, the mirror image <math display="inline"><semantics><mi>ϕ</mi></semantics></math>) and the radius <span class="html-italic">R</span> of the spherical mirror.</p>
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<p>Input Images in Comparetion Simulation in Room Model: (<b>a</b>) The shooting omnidirectional image. The mirror image is in the center. (<b>b</b>) The GT image of the shooting image.</p>
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<p>Estimation Result Images of Position of Sherical Mirror: (<b>a</b>) The image of the mirror image region from the shooting image. (<b>b</b>) The image of the segmented mirror region from the image of (<b>a</b>). (<b>c</b>) The image of the estimated elliptical shape based on (<b>b</b>).</p>
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<p>Distance and error estimation from the simulated scene: (<b>a</b>) The estimation map by the proposed method. The map is visualized by changing the hue linearly. (<b>b</b>) The error map. The map is visualized by varying the brightness linearly. The map is obtained by the difference between the ground truth at each pixel and the result estimated by the proposed method. The errors are larger at the edge and the center of the mirror image region.</p>
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<p>Change in Estimation Accuracy against Change in Angle between Optical Axis and Camera Ray in the Spherical Mirror: MAE increases as the angle <math display="inline"><semantics><mi>ϕ</mi></semantics></math> of incidence at the reflection point <math display="inline"><semantics><msub><mi mathvariant="bold-italic">X</mi><mi mathvariant="bold-italic">s</mi></msub></semantics></math> decreases or increases. On the other hand, MAE decreases and accuracy is stable in the central area.</p>
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<p>Definition of Parameter <span class="html-italic">h</span>: The parameter <span class="html-italic">h</span> is defined as the size of the line segment perpendicular from the camera to the incident ray <math display="inline"><semantics><msub><mi mathvariant="bold-italic">v</mi><mi mathvariant="bold-italic">r</mi></msub></semantics></math> from the object to the reflection point <math display="inline"><semantics><msub><mi mathvariant="bold-italic">X</mi><mi mathvariant="bold-italic">s</mi></msub></semantics></math> in 3D space.</p>
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<p>Change in Parameter <span class="html-italic">h</span> against Change in Angle <math display="inline"><semantics><mi>ϕ</mi></semantics></math>: The parameters <span class="html-italic">h</span> increase as angle <math display="inline"><semantics><mi>ϕ</mi></semantics></math> increases or decreases. This feature is similar to the change in MAE against the angle of incidence.</p>
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<p>Estimation Result Images when Mirror Position is Ground Truth: (<b>a</b>) The estimation map using the proposed method, with mirror position as GT. The map is visualized by changing the hue linearly. (<b>b</b>) The error map. The map is visualized by varying the brightness linearly. The map is obtained from the difference between the ground truth at each pixel and the result estimated by the proposed method. The overall errors are smaller than when the mirror position is estimated, although the errors are still larger at the edges and in the center of the mirror image.</p>
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<p>Application Result of Equation (<a href="#FD13-applsci-13-08348" class="html-disp-formula">13</a>): The result shows that adding the effect of the spherical mirror position estimation to the result in the <a href="#applsci-13-08348-f011" class="html-fig">Figure 11</a>a is similar to the result in <a href="#applsci-13-08348-f015" class="html-fig">Figure 15</a>a.</p>
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<p>Change in 3D Information of the poster against Change in 3D Position of the Spherical Mirror along the Z-axis: Changes in 3D information are indicated by the solid blue line. The green vertical dashed line represents the ground truth of the 3D information, and the red horizontal dashed line represents the ground truth of the spherical mirror position. Since the poster is located at the edge of the mirror surface, if the position of the sphere is estimated to be large in the depth direction, the distance error rapidly increases.</p>
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<p>Input Images in Real-world Simulation: The shooting omnidirectional image. The mirror image is on the center.</p>
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<p>Estimation Result Images of Position of Spherical Mirror: (<b>a</b>) The image of the mirror image region from the shooting image. (<b>b</b>) The image of the segmented mirror region from the image of (<b>a</b>). (<b>c</b>) The image of the estimated elliptical shape based on (<b>b</b>).</p>
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<p>Estimation Result Image on Real-World Simulation: The estimation map using the proposed method, with mirror position as GT. The map is visualized by changing the hue linearly.</p>
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25 pages, 6279 KiB  
Article
Optimizing Appearance-Based Localization with Catadioptric Cameras: Small-Footprint Models for Real-Time Inference on Edge Devices
by Marta Rostkowska and Piotr Skrzypczyński
Sensors 2023, 23(14), 6485; https://doi.org/10.3390/s23146485 - 18 Jul 2023
Cited by 3 | Viewed by 1271
Abstract
This paper considers the task of appearance-based localization: visual place recognition from omnidirectional images obtained from catadioptric cameras. The focus is on designing an efficient neural network architecture that accurately and reliably recognizes indoor scenes on distorted images from a catadioptric camera, even [...] Read more.
This paper considers the task of appearance-based localization: visual place recognition from omnidirectional images obtained from catadioptric cameras. The focus is on designing an efficient neural network architecture that accurately and reliably recognizes indoor scenes on distorted images from a catadioptric camera, even in self-similar environments with few discernible features. As the target application is the global localization of a low-cost service mobile robot, the proposed solutions are optimized toward being small-footprint models that provide real-time inference on edge devices, such as Nvidia Jetson. We compare several design choices for the neural network-based architecture of the localization system and then demonstrate that the best results are achieved with embeddings (global descriptors) yielded by exploiting transfer learning and fine tuning on a limited number of catadioptric images. We test our solutions on two small-scale datasets collected using different catadioptric cameras in the same office building. Next, we compare the performance of our system to state-of-the-art visual place recognition systems on the publicly available COLD Freiburg and Saarbrücken datasets that contain images collected under different lighting conditions. Our system compares favourably to the competitors both in terms of the accuracy of place recognition and the inference time, providing a cost- and energy-efficient means of appearance-based localization for an indoor service robot. Full article
(This article belongs to the Special Issue Sensors for Robots II)
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<p>Overview of the proposed method—a flowchart of the appearance-based localization system. The service robot is shown with the latest, larger-field-of-view catadioptric camera, but without the perspective camera, which is not used in this research.</p>
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<p>Diagram of the CNN-based image description blocks that produce embeddings used as global descriptors in the localization system. The global map is built from <math display="inline"><semantics><msub><mi>n</mi><mi>i</mi></msub></semantics></math> images (<math display="inline"><semantics><mrow><msub><mi>i</mi><mn>1</mn></msub><mo>…</mo><msub><mi>i</mi><msub><mi>n</mi><mi>i</mi></msub></msub></mrow></semantics></math>) converted to embedding vectors <math display="inline"><semantics><msub><mover accent="true"><mi mathvariant="bold">d</mi><mo>→</mo></mover><mi>i</mi></msub></semantics></math> that are stored in the map <math display="inline"><semantics><msub><mi mathvariant="bold">D</mi><mi>embeddings</mi></msub></semantics></math> of <math display="inline"><semantics><msub><mi>n</mi><mi>i</mi></msub></semantics></math> embeddings (global descriptors). Note that panoramic images can be used as well instead of the omnidirectional ones.</p>
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<p>Labbot mobile robot with the integrated sensor with a catadioptric camera (<b>a</b>); robot paths during image collection—different colours indicate different paths (<b>b</b>).</p>
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<p>Omnidirectional images of different locations (<b>a</b>,<b>b</b>) in the Mechatronics Centre and an example image after masking (<b>c</b>).</p>
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<p>Blueprint of the first floor (<b>a</b>) and third floor (<b>b</b>) of the Mechatronics Centre building, with marked places (blue crosses) where images were taken.</p>
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<p>Example of omnidirectional image augmentation: (<b>a</b>)—original picture; (<b>b</b>,<b>c</b>)—augmented images.</p>
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<p>Maps of the two parts of the laboratory in Freiburg with approximate paths followed by the robot during data acquisition (map and trajectories data adopted from the COLD dataset web page <a href="https://www.cas.kth.se/COLD/cold-freiburg.html" target="_blank">https://www.cas.kth.se/COLD/cold-freiburg.html</a>).</p>
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<p>Example images from the COLD Freiburg dataset: (<b>a</b>) one-person office (1PO-A); (<b>b</b>) kitchen (KT-A); (<b>c</b>) stairs area (ST-A); (<b>d</b>) printer area (PA-A).</p>
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<p>Model training results in Experiment 1.</p>
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<p>Confusion matrix for 17 sections.</p>
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<p>Results of sample section predictions. The image in the first column is a query; the other columns are the four closest neighbours. In square brackets, there is the section number (i.e. [12], [02]), and next to it, the L2 distances between the query and the presented image are given. An example of (<b>a</b>) correct place recognition and (<b>b</b>) mismatched sections having slightly overlapping ranges.</p>
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<p>Quantitative results for Configuration A: (<b>a</b>)—a percentage of matches that are within a range of distance from the actual distance (the units on the x-axis are the ranges of distances); (<b>b</b>)—average distance measurement error.</p>
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<p>Quantitative results for Configuration B. (<b>a</b>)—the percentage of matches that are within a range of distance from the actual distance (the units on the x-axis are the ranges of distances); (<b>b</b>)—the average distance measurement error.</p>
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<p>Quantitative results for Configuration C: (<b>a</b>)—the percentage of matches that are within a range of distance from the actual distance (the units on the x-axis are the ranges of distances); (<b>b</b>)—the average distance measurement error.</p>
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<p>Success ratio for EfficientNetV2L and the set of embeddings acquired from the training set for the room search task for the COLD Freiburg dataset. The result obtained under cloudy (blue), night (black), and sunny (yellow) conditions for the model learned on the training set, namely, a set of images on cloudy days (<b>a</b>), a set of images on cloudy days extended by missing acquisition locations found in images for sunny days and night (<b>b</b>), and a balanced set of images obtained on cloudy and sunny days and at night (<b>c</b>). Average location error in meters for a set of images on cloudy days (<b>d</b>), a set of images on cloudy days extended by missing acquisition locations found in images for sunny days and at night (<b>e</b>), and a balanced set of images obtained on cloudy and sunny days and at night (<b>f</b>).</p>
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<p>Success ratio for EfficientNetV2L and the set of embeddings acquired from the training set for the room search task for COLD Saarbrücken dataset for part B. Results obtained under cloudy (blue), night (black), and sunny (yellow) conditions for the model learned on the training set are a balanced set of images obtained on cloudy and sunny days and night (<b>a</b>). Average location error in meters for a balanced set of images obtained on cloudy and sunny days and night (<b>b</b>).</p>
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20 pages, 8961 KiB  
Article
Noniterative Generalized Camera Model for Near-Central Camera System
by Taehyeon Choi, Seongwook Yoon, Jaehyun Kim and Sanghoon Sull
Sensors 2023, 23(11), 5294; https://doi.org/10.3390/s23115294 - 2 Jun 2023
Cited by 1 | Viewed by 1738
Abstract
This paper proposes a near-central camera model and its solution approach. ’Near-central’ refers to cases in which the rays do not converge to a point and do not have severely arbitrary directions (non-central cases). Conventional calibration methods are difficult to apply in such [...] Read more.
This paper proposes a near-central camera model and its solution approach. ’Near-central’ refers to cases in which the rays do not converge to a point and do not have severely arbitrary directions (non-central cases). Conventional calibration methods are difficult to apply in such cases. Although the generalized camera model can be applied, dense observation points are required for accurate calibration. Moreover, this approach is computationally expensive in the iterative projection framework. We developed a noniterative ray correction method based on sparse observation points to address this problem. First, we established a smoothed three-dimensional (3D) residual framework using a backbone to avoid using the iterative framework. Second, we interpolated the residual by applying local inverse distance weighting on the nearest neighbor of a given point. Specifically, we prevented excessive computation and the deterioration in accuracy that may occur in inverse projection through the 3D smoothed residual vectors. Moreover, the 3D vectors can represent the ray directions more accurately than the 2D entities. Synthetic experiments show that the proposed method can achieve prompt and accurate calibration. The depth error is reduced by approximately 63% in the bumpy shield dataset, and the proposed approach is noted to be two digits faster than the iterative methods. Full article
(This article belongs to the Section Optical Sensors)
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<p>Process flow of the proposed camera model.</p>
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<p>Differences in the existing and proposed camera models.</p>
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<p>Generating the smoothed 3D vectors field.</p>
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<p>Our ray calibration method.</p>
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<p>The acquisition process of calibration data. The laser scanner shoots the laser to the patterned panel, and then the position of 3D points can be obtained by the laser scanner. Two-dimensional image points corresponding to the three-dimensional points in the panel can be obtained by the image of the near-central camera system. When the panel is positioned far away from the camera, using a non-patterned panel may cause the laser point to become invisible to the near central camera system. To overcome this issue, a patterned panel can be used instead. By directing the laser to the corner point of the patterned panel, it becomes possible to obtain the 2D image point corresponding to the 3D laser point.</p>
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<p>Three cases involving a transparent shield.</p>
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<p>Results of distance for planar, spherical, and bumpy shields [<a href="#B21-sensors-23-05294" class="html-bibr">21</a>,<a href="#B22-sensors-23-05294" class="html-bibr">22</a>].</p>
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<p>Comparison of the reprojection error by increasing the number of training points [<a href="#B22-sensors-23-05294" class="html-bibr">22</a>].</p>
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<p>Results of the depth for planar, spherical, and bumpy shields [<a href="#B21-sensors-23-05294" class="html-bibr">21</a>,<a href="#B22-sensors-23-05294" class="html-bibr">22</a>].</p>
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<p>Reference fisheye lens model [<a href="#B24-sensors-23-05294" class="html-bibr">24</a>].</p>
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<p>Statistical results (min, max, and standard deviation) for the fisheye case #1 dataset [<a href="#B22-sensors-23-05294" class="html-bibr">22</a>].</p>
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<p>Statistical results (min, max, and standard deviation) for the fisheye case #2 dataset [<a href="#B22-sensors-23-05294" class="html-bibr">22</a>].</p>
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<p>Configuration of catadioptric stereo camera system.</p>
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14 pages, 6466 KiB  
Article
A Tailor-Made, Mirror-Based Infrared Scanner for the Reflectography of Paintings: Development, Features, and Applications
by Marco Gargano, Daniele Viganò, Tiziana Cavaleri, Francesco Cavaliere, Nicola Ludwig and Federica Pozzi
Sensors 2023, 23(9), 4322; https://doi.org/10.3390/s23094322 - 27 Apr 2023
Cited by 1 | Viewed by 1827
Abstract
Since infrared reflectography was first applied in the 1960s to visualize the underdrawings of ancient paintings, several devices and scanning techniques were successfully proposed both as prototypes and commercial instruments. In fact, because of the sensors’ small dimension, typically ranging from 0.1 to [...] Read more.
Since infrared reflectography was first applied in the 1960s to visualize the underdrawings of ancient paintings, several devices and scanning techniques were successfully proposed both as prototypes and commercial instruments. In fact, because of the sensors’ small dimension, typically ranging from 0.1 to 0.3 megapixels, scanning is always required. Point, line, and image scanners are all viable options to obtain an infrared image of the painting with adequate spatial resolution. This paper presents a newly developed, tailormade scanning system based on an InGaAs camera equipped with a catadioptric long-focus lens in a fixed position, enabling all movements to occur by means of a rotating mirror and precision step motors. Given the specific design of this system, as the mirror rotates, refocus of the lens is necessary and it is made possible by an autofocus system involving a laser distance meter and a motorized lens. The system proved to be lightweight, low cost, easily portable, and suitable for the examination of large-scale painting surfaces by providing high-resolution reflectograms. Furthermore, high-resolution images at different wavelengths can be obtained using band-pass filters. The in-situ analysis of a 16th-century panel painting is also discussed as a representative case study to demonstrate the effectiveness and reliability of the system described herein. Full article
(This article belongs to the Special Issue Sensor Techniques for Artworks Analysis and Investigations)
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<p>Components and modules of the scanning system.</p>
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<p>Graphical scheme showing the assembling of the individual components into the operating scanning system.</p>
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<p>Control module of the scanning system based on the Arduino Uno board.</p>
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<p>Front panel view of the application developed in the LabVIEW™ environment.</p>
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<p>(<b>a</b>) Scheme of the system’s optical design showing the path of the laser beam used to measure the camera–painting working distance (red lines) and the path of the infrared radiation focused on the camera plane for image acquisition (green solid lines for the path outside the lens and green dashed lines for the path inside the lens). (<b>b</b>) USAF resolution target as captured by the scanning system.</p>
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<p>Rotation of the camera coordinates (<span class="html-italic">x</span>, <span class="html-italic">y</span>, <span class="html-italic">z</span>) of an angle <span class="html-italic">α</span> and to the equivalent reference frame (<span class="html-italic">x</span>′, <span class="html-italic">y</span>′, <span class="html-italic">z</span>′) for camera (<b>a</b>) and mirror (<b>c</b>) movement. If we add a rotation <span class="html-italic">β</span>, the new reference frames (<span class="html-italic">x</span>″, <span class="html-italic">y</span>″, <span class="html-italic">z</span>″) for the camera (<b>b</b>) and mirror (<b>d</b>) are different since the reference frame for the mirror undergoes an additional rotation <span class="html-italic">β</span> around the <span class="html-italic">z</span>″ axis with respect to the camera.</p>
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<p>Gandolfino da Roreto (attributed), <span class="html-italic">Genealogy of the Virgin</span>, ca. 1510–1520, painting on wooden panel, 173 × 83 cm. Church of Santa Maria Assunta, Grignasco (Novara), Italy.</p>
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<p>Instrumental setup for IRR of the panel painting in the CCR “La Venaria Reale” conservation laboratories. Scanning was performed by placing the work in horizontal position on an easel.</p>
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<p>(<b>a</b>) All individual infrared images captured from the top and bottom sections of the panel painting are placed side by side in preparation for the merging process. (<b>b</b>) Stitching of the individual 2000 + 2000 image sets. (<b>c</b>) Final recomposition with flat field correction, image registration, and gray levels optimization.</p>
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<p>Detail of the painting’s lower right quadrant, depicting the Virgin’s sister, Salome, with her two sons, James the Greater and John the Evangelist. Compared to the visible light photograph (<b>left</b>), the IRR image (<b>right</b>) shows compositional changes such as the shading on John the Evangelist’s chest and an overall modified position for James the Greater, highlighted with green and red arrows.</p>
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<p>Detail of Salome’s proper left hand holding the baby. Compared to the visible light photograph (<b>top</b>), the IRR image (<b>bottom</b>) shows compositional changes such as the figure’s middle finger in bent position.</p>
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<p>Detail of the painting’s upper right quadrant, depicting a landscape scene beyond a curtain. Compared to the visible light photograph (<b>a</b>), the IRR image (<b>b</b>) shows compositional changes such as a house with roof, walls, and windows.</p>
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<p>Detail of the painting’s lower left quadrant, depicting two children. Compared to the visible light photograph (<b>left</b>), the IRR image (<b>right</b>) shows compositional changes such as a subsequent addition of a sleeve in Joseph’s robe.</p>
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19 pages, 6280 KiB  
Article
Achromatic and Athermal Design of Aerial Catadioptric Optical Systems by Efficient Optimization of Materials
by Jing Li, Yalin Ding, Xueji Liu, Guoqin Yuan and Yiming Cai
Sensors 2023, 23(4), 1754; https://doi.org/10.3390/s23041754 - 4 Feb 2023
Cited by 4 | Viewed by 1788
Abstract
The remote sensing imaging requirements of aerial cameras require their optical system to have wide temperature adaptability. Based on the optical passive athermal technology, the expression of thermal power offset of a single lens in the catadioptric optical system is first derived, and [...] Read more.
The remote sensing imaging requirements of aerial cameras require their optical system to have wide temperature adaptability. Based on the optical passive athermal technology, the expression of thermal power offset of a single lens in the catadioptric optical system is first derived, and then a mathematical model for efficient optimization of materials is established; finally, the mechanical material combination (mirror and housing material) is optimized according to the comprehensive weight of offset with temperature change and the position change of the equivalent single lens, and achieve optimization of the lens material on an athermal map. In order to verify the effectiveness of the method, an example of a catadioptric aerial optical system with a focal length of 350 mm is designed. The results show that in the temperature range of −40 °C to 60 °C, the diffraction-limited MTF of the designed optical system is 0.59 (at 68 lp/mm), the MTF of each field of view is greater than 0.39, and the thermal defocus is less than 0.004 mm, which is within one time of the focal depth, indicating that the imaging quality of the optical system basically does not change with temperature, meeting the stringent application requirements of the aerial camera. Full article
(This article belongs to the Section Optical Sensors)
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<p>Flow chart of athermal design for catadioptric optical systems.</p>
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<p>Achromatic and athermal conditions on an athermal map of (<b>a</b>) refractive optical system and (<b>b</b>) catadioptric optical system.</p>
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<p>Achromatic and athermal conditions on an athermal map when the offset changes with temperature.</p>
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<p>Evaluation method of mirror and housing material combinations.</p>
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<p>Evaluation method of lens materials.</p>
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<p>Layout of the initial optical system.</p>
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<p>MTF performance of the initial optical system at temperatures of (<b>a</b>) 20 °C, (<b>b</b>) −40 °C, and (<b>c</b>) 60 °C.</p>
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<p>Chengdu Guangming glass (<b>a</b>) material catalog, (<b>b</b>) n<sub>d</sub>/v<sub>d</sub> map.</p>
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<p>Athermal glass map of the Chengdu Guangming catalog calculated by equations.</p>
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<p>Athermal glass map of different material combinations.</p>
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<p>Weight map for different material combinations.</p>
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<p>Athermal map of the combination of mirror and housing material as FS + CF.</p>
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<p>Athermal glass optimization map.</p>
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<p>Final athermal map.</p>
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<p>Thermal defocus curves (<b>a</b>) initial system (<b>b</b>) athermal system.</p>
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<p>MTF performance of the final athermal optical system at temperatures of (<b>a</b>) 20 °C, (<b>b</b>) −40 °C, and (<b>c</b>) 60 °C.</p>
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16 pages, 4833 KiB  
Article
Precision Calibration of Omnidirectional Camera Using a Statistical Approach
by Vasilii P. Lazarenko, Valery V. Korotaev, Sergey N. Yaryshev, Marin B. Marinov and Todor S. Djamiykov
Computation 2022, 10(12), 209; https://doi.org/10.3390/computation10120209 - 30 Nov 2022
Viewed by 2493
Abstract
Omnidirectional optoelectronic systems (OOES) find applications in many areas where a wide viewing angle is crucial. The disadvantage of these systems is the large distortion of the images, which makes it difficult to make wide use of them. The purpose of this study [...] Read more.
Omnidirectional optoelectronic systems (OOES) find applications in many areas where a wide viewing angle is crucial. The disadvantage of these systems is the large distortion of the images, which makes it difficult to make wide use of them. The purpose of this study is the development an algorithm for the precision calibration of an omnidirectional camera using a statistical approach. The calibration approach comprises three basic stages. The first stage is the formation of a cloud of points characterizing the view field of the virtual perspective camera. In the second stage, a calibration procedure that provides the projection function for the camera calibration is performed. The projection functions of traditional perspective lenses and omnidirectional wide-angle fisheye lenses with a viewing angle of no less than 180° are compared. The construction of the corrected image is performed in the third stage. The developed algorithm makes it possible to obtain an image for part of the field of view of an OOES by correcting the distortion from the original omnidirectional image.Using the developed algorithm, a non-mechanical pivoting camera based on an omnidirectional camera is implemented. The achieved mean squared error of the reproducing points from the original omnidirectional image onto the image with corrected distortion is less than the size of a very few pixels. Full article
(This article belongs to the Section Computational Engineering)
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<p>Perspective geometric models: (<b>a</b>) of the lens and (<b>b</b>) of an extra wide-angle fisheye lens.</p>
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<p>Geyer and Daniilidis Unified Imaging Model (adapted from [<a href="#B7-computation-10-00209" class="html-bibr">7</a>], p. 344).</p>
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<p>Geometric projection models: (<b>a</b>) catadioptric omnidirectional camera, (<b>b</b>) camera with a fisheye lens, and (<b>c</b>) coordinates on the plane of the camera receiver.</p>
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<p>Distortions caused by the discretization process (using rectangular pixels) and the displacement of the camera and mirror (lens) axes.</p>
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<p>The three main steps of the algorithm.</p>
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<p>Virtual camera field of view with <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
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<p>Field of view slope of the virtual camera at an angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math>.</p>
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<p>Field of view rotation of the virtual camera at an angle <math display="inline"><semantics> <mi>φ</mi> </semantics></math> relative to the <math display="inline"><semantics> <mi>Z</mi> </semantics></math> axis.</p>
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<p>Calibration results using the OCamCalib toolkit. (<b>a</b>) An example of the wrong determination of the calibration parameters [<a href="#B32-computation-10-00209" class="html-bibr">32</a>]; (<b>b</b>) the result of the experimental calibration is the position where calibration points and re-projected points coincide, which confirms the correct determination of calibration parameters. Yellow crosses denote the determined calibration points of the test object, and red crosses—the result of projecting the calibration points with three-dimensional coordinates, calculated during the calibration process, back to the image. The size of each square of the test object is 20 mm estimated center coordinates of the circular image.</p>
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<p>The implementation of the algorithm in the “Typhoon” system: (<b>a</b>) the original image; (<b>b</b>) virtual PTZ camera, guided by a motion detector.</p>
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<p>Initial image with the test object for calibration.</p>
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<p>Images obtained after applying the algorithm to a field of view of (<b>a</b>) 90 degrees and (<b>b</b>) 120 degrees.</p>
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15 pages, 3609 KiB  
Article
Calibration of a Catadioptric System and 3D Reconstruction Based on Surface Structured Light
by Zhenghai Lu, Yaowen Lv, Zhiqing Ai, Ke Suo, Xuanrui Gong and Yuxuan Wang
Sensors 2022, 22(19), 7385; https://doi.org/10.3390/s22197385 - 28 Sep 2022
Cited by 1 | Viewed by 2055
Abstract
In response to the problem of the small field of vision in 3D reconstruction, a 3D reconstruction system based on a catadioptric camera and projector was built by introducing a traditional camera to calibrate the catadioptric camera and projector system. Firstly, the intrinsic [...] Read more.
In response to the problem of the small field of vision in 3D reconstruction, a 3D reconstruction system based on a catadioptric camera and projector was built by introducing a traditional camera to calibrate the catadioptric camera and projector system. Firstly, the intrinsic parameters of the camera and the traditional camera are calibrated separately. Then, the calibration of the projection system is accomplished by the traditional camera. Secondly, the coordinate system is introduced to calculate, respectively, the position of the catadioptric camera and projector in the coordinate system, and the position relationship between the coordinate systems of the catadioptric camera and the projector is obtained. Finally, the projector is used to project the structured light fringe to realize the reconstruction using a catadioptric camera. The experimental results show that the reconstruction error is 0.75 mm and the relative error is 0.0068 for a target of about 1 m. The calibration method and reconstruction method proposed in this paper can guarantee the ideal geometric reconstruction accuracy. Full article
(This article belongs to the Collection 3D Imaging and Sensing System)
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<p>The schematic diagram of the unified sphere model.</p>
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<p>The schematic diagram of the pinhole imaging model.</p>
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<p>Calibration flow chart of ordinary camera and projector.</p>
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<p>Calibration process of the catadioptric camera. (<b>a</b>) The catadioptric camera consists of a reflector and a camera; (<b>b</b>) some pictures of the calibration plate were used to calibrate the catadioptric camera; (<b>c</b>) principal point estimation; (<b>d</b>) the focal length is estimated from three points horizontally; (<b>e</b>) framing out the feature point area and establishing the coordinate system; (<b>f</b>) detection of all feature points.</p>
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<p>Reprojection error of calibrating the catadioptric camera.</p>
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<p>Calibration and 3D reconstruction flow chart of catadioptric system.</p>
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<p>The hardware design of the catadioptric system is based on structured light.</p>
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<p>Diagram of structured light decoding. (<b>a</b>) The decoding results of the direct decoding of object reflection effects; (<b>b</b>) the decoding results of adding median filtering and a background pickle operation to remove the background and reflections.</p>
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<p>Three-dimensional reconstruction of the geometry. (<b>a</b>) Depth map of the projected area; (<b>b</b>) using Meshlab software to display the point cloud map of the geometry.</p>
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15 pages, 22318 KiB  
Communication
Optical System Design of Oblique Airborne-Mapping Camera with Focusing Function
by Hongwei Zhang, Weining Chen, Yalin Ding, Rui Qu and Sansan Chang
Photonics 2022, 9(8), 537; https://doi.org/10.3390/photonics9080537 - 31 Jul 2022
Cited by 3 | Viewed by 1834
Abstract
The use of airborne-mapping technology plays a key role in the acquisition of large-scale basic geographic data information, especially in various important civil/military-mapping missions. However, most airborne-mapping cameras are limited by parameters, such as the flight altitude, working-environment temperature, and so on. To [...] Read more.
The use of airborne-mapping technology plays a key role in the acquisition of large-scale basic geographic data information, especially in various important civil/military-mapping missions. However, most airborne-mapping cameras are limited by parameters, such as the flight altitude, working-environment temperature, and so on. To solve this problem, in this paper, we designed a panchromatic wide-spectrum optical system with a focusing function. Based on the catadioptric optical structure, the optical system approached a telecentric optical structure. Sharp images at different object distances could be acquired by micro-moving the focusing lens. At the same time, an optical passive compensation method was adopted to realize an athermalization design in the range of −40–60 °C. According to the design parameters of the optical system, we analyzed the influence of system focusing on mapping accuracy during the focusing process of the airborne-mapping camera. In the laboratory, the camera calibration and imaging experiments were performed at different focusing positions. The results show that the experimental data are consistent with the analysis results. Due to the limited experiment conditions, only a single flight experiment was performed. The results show that the airborne-mapping camera can achieve 1:5000 scale-imaging accuracy. Flight experiments for different flight altitudes are being planned, and the relevant experimental data will be released in the future. In conclusion, the airborne-mapping camera is expected to be applied in various high-precision scale-mapping fields. Full article
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<p>Schematic diagram of the main working modes of the oblique airborne mapping camera: (<b>a</b>) vertical downward view/oblique view; (<b>b</b>) ±60° full-amplitude/interval scanning.</p>
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<p>Schematic of the focal length calculation.</p>
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<p>Schematic of the optical system for the oblique airborne-mapping camera.</p>
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<p>Corresponding MTF performance of the oblique airborne-mapping camera at different temperatures: (<b>a</b>) −40 °C; (<b>b</b>) +20 °C; (<b>c</b>) +60 °C.</p>
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<p>The calibrated principal distance error at different temperatures.</p>
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<p>MTF-defocus amount curves of the optical system (80 lp/mm).</p>
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<p>MTF curves of the optical system at different object distances after focusing on 1 km object distance: (<b>a</b>) 0.8 km object distance; (<b>b</b>) 1.3 km object distance.</p>
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<p>Calibrated principal distance variation (error) curves of the optical system at different conditions: (<b>a</b>) different focusing position; (<b>b</b>) different repeated focusing-positioning accuracy.</p>
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<p>Principal point location error at different decenters and tilt errors.</p>
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<p>Pixel resolution experiment platform of the mapping camera.</p>
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<p>The images of the pixel resolution experiment: (<b>a</b>) the real scene; (<b>b</b>) the experiment result.</p>
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<p>Interior orientation element calibration experiment platform of the mapping camera.</p>
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<p>The images of the interior orientation element calibration experiment: (<b>a</b>) the real scene; (<b>b</b>) the star-point image.</p>
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<p>The images of the flight experiment: (<b>a</b><b>,</b><b>b</b>) the real scene; (<b>c</b>) the mapping image.</p>
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<p>The experiment results of the flight experiment: (<b>a</b>) the distribution of the tie points and measuring points; (<b>b</b>) the comparison of the experiment results.</p>
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18 pages, 3259 KiB  
Article
Optimization Method for Low Tilt Sensitivity of Secondary Mirror Based on the Nodal Aberration Theory
by Jing Li, Yalin Ding, Yiming Cai, Guoqin Yuan and Mingqiang Zhang
Appl. Sci. 2022, 12(13), 6514; https://doi.org/10.3390/app12136514 - 27 Jun 2022
Cited by 1 | Viewed by 1702
Abstract
The optical system that combines imaging and image motion compensation is conducive to the miniaturization of aerial mapping cameras, but the movement of optical element for image motion compensation will cause a decrease in image quality. To solve this problem, reducing the sensitivity [...] Read more.
The optical system that combines imaging and image motion compensation is conducive to the miniaturization of aerial mapping cameras, but the movement of optical element for image motion compensation will cause a decrease in image quality. To solve this problem, reducing the sensitivity of moving optical element is one of the effective ways to ensure the imaging quality of aerial mapping cameras. Therefore, this paper proposes an optimization method for the low tilt sensitivity of the secondary mirror based on the Nodal aberration theory. In this method, the analytical expressions of the tilt sensitivity of the secondary mirror in different tilt directions are given in the form of zernike polynomial coefficients, and the influence of the field of view on the sensitivity is expressed in the mathematical model. The desensitization optimization function and desensitization optimization method are proposed. The catadioptric optical system with a focal length of 350 mm is used for desensitization optimization. The results show that the desensitization function proposed in this paper is linearly related to the decrease of sensitivity within a certain range, and the standard deviation of the system after desensitization is 0.020, which is 59% of the system without desensitization. Compared with the traditional method, the method in this paper widens the range of angle reduction sensitivity and has a better desensitization effect. The research results show that the optimization method for low tilt sensitivity of the secondary mirror based on the Nodal aberration theory proposed in this paper reduces the tilt sensitivity of the secondary mirror, revealing that the reduction of the sensitivity depends on the reduction of the aberration coefficient related to the misalignment in the field of view, which is critical for the development of an optical system for aerial mapping cameras that combines imaging and image motion compensation. Full article
(This article belongs to the Collection Optical Design and Engineering)
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<p>The changes of camera position and field of view during exposure time.</p>
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<p>Image motion compensation model of secondary mirror tilt motion.</p>
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<p>Flow diagram of catadioptric optical system with low tilt sensitivity of secondary mirror.</p>
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<p>The MTF of the optical system when the secondary mirror is tilted by 0.1° around the x-axis (<b>a</b>) without desensitization, (<b>b</b>) after final desensitization.</p>
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<p>Desensitization optimization process diagram.</p>
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<p>Variation of MTF when the secondary mirror is tilted by 0.1° around the x-axis and standard deviation of system (<b>a</b>) traditional method (<b>b</b>) this method.</p>
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<p>Layout of the optical system of (<b>a</b>) the solution of NO. 0, (<b>b</b>) the solution of NO. 1 and (<b>c</b>) the solution of NO. 6.</p>
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<p>The variation of the sensitivity of the aberration term with the field of view when the secondary mirror is tilted by (<b>a</b>) 0.1° around the x-axis, (<b>b</b>) −0.1° around the xaxis, (<b>c</b>) 0.1° around the y-axis and (<b>d</b>) −0.1° around the y-axis.</p>
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<p>Monte-Carlo tolerance analysis results of the optical system A without desensitization and C after final desensitization.</p>
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11 pages, 3568 KiB  
Article
A Semantic SLAM System for Catadioptric Panoramic Cameras in Dynamic Environments
by Yu Zhang, Xiping Xu, Ning Zhang and Yaowen Lv
Sensors 2021, 21(17), 5889; https://doi.org/10.3390/s21175889 - 1 Sep 2021
Cited by 5 | Viewed by 2886
Abstract
When a traditional visual SLAM system works in a dynamic environment, it will be disturbed by dynamic objects and perform poorly. In order to overcome the interference of dynamic objects, we propose a semantic SLAM system for catadioptric panoramic cameras in dynamic environments. [...] Read more.
When a traditional visual SLAM system works in a dynamic environment, it will be disturbed by dynamic objects and perform poorly. In order to overcome the interference of dynamic objects, we propose a semantic SLAM system for catadioptric panoramic cameras in dynamic environments. A real-time instance segmentation network is used to detect potential moving targets in the panoramic image. In order to find the real dynamic targets, potential moving targets are verified according to the sphere’s epipolar constraints. Then, when extracting feature points, the dynamic objects in the panoramic image are masked. Only static feature points are used to estimate the pose of the panoramic camera, so as to improve the accuracy of pose estimation. In order to verify the performance of our system, experiments were conducted on public data sets. The experiments showed that in a highly dynamic environment, the accuracy of our system is significantly better than traditional algorithms. By calculating the RMSE of the absolute trajectory error, we found that our system performed up to 96.3% better than traditional SLAM. Our catadioptric panoramic camera semantic SLAM system has higher accuracy and robustness in complex dynamic environments. Full article
(This article belongs to the Collection Positioning and Navigation)
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<p>Semantic segmentation results.</p>
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<p>Sphere epipolar geometry.</p>
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<p>Overall framework of dynamic point elimination.</p>
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<p>Dynamic point elimination results (<b>a</b>) Raw ORB feature points extract method and (<b>b</b>) ORB feature points extracted by our Method.</p>
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<p>Average relative translation error between our method and groundtruth: (<b>a</b>) result of low dynamic sequence, (<b>b</b>) result of high dynamic sequence, (<b>c</b>) result of sequences containing high dynamic and low dynamic objects.</p>
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<p>Comparison of absolute trajectory error (ATE) on public dataset (<b>a</b>) result of low dynamic sequence (<b>b</b>) result of high dynamic sequence (<b>c</b>) result of sequences containing high dynamic and low dynamic objects.</p>
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<p>Experimental platform.</p>
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<p>Comparison of experiment trajectories.</p>
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18 pages, 11166 KiB  
Article
Self-Localization of Mobile Robots Using a Single Catadioptric Camera with Line Feature Extraction
by Huei-Yung Lin, Yuan-Chi Chung and Ming-Liang Wang
Sensors 2021, 21(14), 4719; https://doi.org/10.3390/s21144719 - 9 Jul 2021
Cited by 6 | Viewed by 2422
Abstract
This paper presents a novel self-localization technique for mobile robots using a central catadioptric camera. A unified sphere model for the image projection is derived by the catadioptric camera calibration. The geometric property of the camera projection model is utilized to obtain the [...] Read more.
This paper presents a novel self-localization technique for mobile robots using a central catadioptric camera. A unified sphere model for the image projection is derived by the catadioptric camera calibration. The geometric property of the camera projection model is utilized to obtain the intersections of the vertical lines and ground plane in the scene. Different from the conventional stereo vision techniques, the feature points are projected onto a known planar surface, and the plane equation is used for depth computation. The 3D coordinates of the base points on the ground are calculated using the consecutive image frames. The derivation of motion trajectory is then carried out based on the computation of rotation and translation between the robot positions. We develop an algorithm for feature correspondence matching based on the invariability of the structure in the 3D space. The experimental results obtained using the real scene images have demonstrated the feasibility of the proposed method for mobile robot localization applications. Full article
(This article belongs to the Section Sensors and Robotics)
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<p>The mobile robot platform used in the experiments. The catadioptric camera mounted on the top of the robot is used for robot self-localization and pose estimation.</p>
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<p>The unified sphere projection model for the catadioptric camera. Given a 3D point <math display="inline"><semantics> <mi mathvariant="bold">X</mi> </semantics></math>, it is projected to a point on the unified sphere at <math display="inline"><semantics> <msub> <mi>χ</mi> <mi>s</mi> </msub> </semantics></math>. This point is then projected to another point <span class="html-italic">m</span> on the image plane <math display="inline"><semantics> <mi>π</mi> </semantics></math> via the new projection center at <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mi>ζ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>The coordinate frame of the catadioptric camera system used to represent the robot motion.</p>
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<p>The image projection for the detection of the intersection (base point) from the corresponding vertical line.</p>
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<p>The detection of the ground plane region from the omnidirectional image using edge detection and the rays radiated from the image center.</p>
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<p>The vertical 3D line in the space is projected to a curve on the unified sphere model via the sphere center at <math display="inline"><semantics> <msub> <mi mathvariant="bold">C</mi> <mi>m</mi> </msub> </semantics></math>.</p>
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<p>The detection of vertical 3D lines in the space. The red lines in <a href="#sensors-21-04719-f007" class="html-fig">Figure 7</a>a,b indicate the detected vertical 3D lines. The images in which a mirror is placed perpendicular to the ground and tilted with a small angle are shown in <a href="#sensors-21-04719-f007" class="html-fig">Figure 7</a>c,d.</p>
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<p>The detection of line segments before and after filtering by the ground plane region.</p>
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<p>The situations considered to facilitate the line matching between the image frames by tracking. Their orders are always the same since the detected lines are space invariant with respect to the environment.</p>
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<p>The mobile robot moves from the “View 1” position to the “View 2” with the same set of base points observed. It adopts a catadioptric camera to detect the vertical lines in this structured environment. The base points are used to estimate the 3D information for mobile robot localization.</p>
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<p>The indoor environment for robot navigation and image acquisition in our experiments.</p>
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<p>The ground plane segmentation and vertical line identification from an acquired omnidirectional image sequence. It can be seen that the ground region extraction is relatively stable compared to the line segment detection.</p>
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<p>The trajectory of the mobile robot navigation in the indoor environment. It is derived from the proposed self-localization technique using the vertical lines in the space and the corresponding base points on the ground plane.</p>
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<p>The examination of the localization process. It consists of the vertical line identification, edge detection, ground region segmentation, and trajectory computation for various locations.</p>
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14 pages, 4157 KiB  
Article
Mobile Robot Self-Localization Using Omnidirectional Vision with Feature Matching from Real and Virtual Spaces
by Huei-Yung Lin and Chien-Hsing He
Appl. Sci. 2021, 11(8), 3360; https://doi.org/10.3390/app11083360 - 8 Apr 2021
Cited by 8 | Viewed by 2627
Abstract
This paper presents a novel self-localization technique for mobile robots based on image feature matching from omnidirectional vision. The proposed method first constructs a virtual space with synthetic omnidirectional imaging to simulate a mobile robot equipped with an omnidirectional vision system in the [...] Read more.
This paper presents a novel self-localization technique for mobile robots based on image feature matching from omnidirectional vision. The proposed method first constructs a virtual space with synthetic omnidirectional imaging to simulate a mobile robot equipped with an omnidirectional vision system in the real world. In the virtual space, a number of vertical and horizontal lines are generated according to the structure of the environment. They are imaged by the virtual omnidirectional camera using the catadioptric projection model. The omnidirectional images derived from the virtual and real environments are then used to match the synthetic lines and real scene edges. Finally, the pose and trajectory of the mobile robot in the real world are estimated by the efficient perspective-n-point (EPnP) algorithm based on the line feature matching. In our experiments, the effectiveness of the proposed self-localization technique was validated by the navigation of a mobile robot in a real world environment. Full article
(This article belongs to the Special Issue Control and Motion Planning in Industrial Applications)
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<p>The catadioptric projection model of an omnidirectional camera. It consists of a hyperbolic mirror for reflection and a pinhole model for perspective projection.</p>
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<p>The unified sphere model for omnidirectional cameras. It consists of two linear projection steps.</p>
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<p>The images captured for omnidirectional camera calibration.</p>
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<p>The simulated virtual environment and the image created by the omnidirectional camera model’s projection.</p>
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<p>The parallel lines generated using the Cartesian coordinate system and captured by an omnidirectional camera.</p>
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<p>The parallel lines generated using the polar coordinate system and captured by an omnidirectional camera.</p>
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<p>The line matching between the virtual room and the real room.</p>
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<p>The computation of relative camera position and robot motion using the efficient perspective-n-point (EPnP) algorithm.</p>
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<p>A mobile robot equipped with an omnidirectional camera is used in this work.</p>
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<p>The omnidirectional images used for the self-localization in the first experiment. The mobile robot moved in a straight line when capturing the images.</p>
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<p>The mobile robot self-localization using omnidirectional images. (<b>a</b>) An input real image; (<b>b</b>) the edge detection result; (<b>c</b>) the parallel horizontal and vertical lines constructed in the vertical space; (<b>d</b>) the overlay of the edge image with the virtual lines projected on the omnidirectional image; (<b>e</b>) the identified horizontal and vertical lines in the real world scene; (<b>f</b>) the corresponding lines in the virtual space for localization computation.</p>
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<p>The omnidirectional images used for the mobile robot localization in the second experiment. The images were captured when the mobile moved on non-smooth ground to evaluate the self-localization capability.</p>
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<p>The localization results of the experiments. The mobile robot moved on smooth and non-smooth ground for the first and second experiments, respectively. The blue dot represents the localization of the mobile robot in the environment. It consists of the forward, horizontal and vertical displacements.</p>
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18 pages, 12249 KiB  
Article
Three-Dimensional Reconstruction of Indoor and Outdoor Environments Using a Stereo Catadioptric System
by Diana-Margarita Córdova-Esparza, Juan Terven, Julio-Alejandro Romero-González and Alfonso Ramírez-Pedraza
Appl. Sci. 2020, 10(24), 8851; https://doi.org/10.3390/app10248851 - 10 Dec 2020
Cited by 5 | Viewed by 3186
Abstract
In this work, we present a panoramic 3D stereo reconstruction system composed of two catadioptric cameras. Each one consists of a CCD camera and a parabolic convex mirror that allows the acquisition of catadioptric images. We describe the calibration approach and propose the [...] Read more.
In this work, we present a panoramic 3D stereo reconstruction system composed of two catadioptric cameras. Each one consists of a CCD camera and a parabolic convex mirror that allows the acquisition of catadioptric images. We describe the calibration approach and propose the improvement of existing deep feature matching methods with epipolar constraints. We show that the improved matching algorithm covers more of the scene than classic feature detectors, yielding broader and denser reconstructions for outdoor environments. Our system can also generate accurate measurements in the wild without large amounts of data used in deep learning-based systems. We demonstrate the system’s feasibility and effectiveness as a practical stereo sensor with real experiments in indoor and outdoor environments. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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<p>Panoramic 3D reconstruction system formed by two catadioptric cameras (upper camera and lower camera), each composed by a parabolic mirror and a Marlin F-080c camera.</p>
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<p>Calibration pattern. (<b>a</b>) Chessboard pattern (<b>b</b>) Images of the pattern using the upper camera. (<b>c</b>) Images of the pattern using the lower camera.</p>
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<p>Epipolar geometry between two catadioptric cameras with parabolic mirrors. <span class="html-italic">R</span> is the rotation matrix and <math display="inline"><semantics> <mi mathvariant="bold">T</mi> </semantics></math> is the translation vector, between the upper and lower mirrors (PMU→PML) expressed as a skew symmetric matrix. <math display="inline"><semantics> <mi mathvariant="sans-serif">Π</mi> </semantics></math> is the epipolar plane.</p>
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<p>Panoramic 3D reconstruction (best seen in color). The procedure is the following: (1) Capture images from the catadioptric camera system, (2) unwrap the omnidirectional images to obtain panoramic images (3) to search for feature matches and (4) filter the matches using epipolar constraints. (5) Convert features back to catadioptric image coordinates and (6) to mirror coordinates. (7) Perform 3D reconstruction.</p>
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<p>Feature point and epipolar curve (best seen in color). (<b>a</b>) Feature point (red mark) in the upper catadioptric image, (<b>b</b>) Feature point (red mark) and epipolar curve in the lower catadioptric image, (<b>c</b>) Feature point (red mark) in the upper panoramic image, (<b>d</b>) Feature point (red mark) and epipolar curve in the lower panoramic image.</p>
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<p>Feature matching points on the upper and lower cameras and 3D reconstruction for each comparing method.</p>
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<p>DeepMatching features and reconstruction. (<b>a</b>,<b>b</b>) show the original DeepMatching on the upper and lower camera, respectively. (<b>c</b>) shows the 3D reconstruction using the original DeepMatching. (<b>d</b>,<b>e</b>) show the filtered DeepMatching using epipolar constraints with <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>30</mn> </mrow> </semantics></math> on the upper and lower cameras. (<b>f</b>) shows the 3D reconstruction using filtered DeepMatching.</p>
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<p>Amount of DeepMatching features obtained with different levels of filtering. The more we increase the distance threshold, the more matches we get, but also, the more error we are allowing in the reconstruction.</p>
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<p>Matching points in the panoramic mirrors (best seen in color). Pink points denote the features in the panoramic upper mirror PMU, and blue points are the features on the panoramic lower mirror PML. (<b>a</b>) Shows Harris corners on the mirrors, and (<b>b</b>) shows the DeepMatching points on the mirrors.</p>
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<p>3D reconstruction using DeepMatching. Figures (<b>a</b>–<b>c</b>) show the reconstruction with features filtered at <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> respectively.</p>
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<p>DeepMatching and filtered DeepMatching for 3D reconstruction of a known pattern.</p>
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<p>Qualitative reconstructions results using filtered DeepMatching. (<b>a</b>) Shows the reconstruction of a squared box, (<b>b</b>) shows the reconstruction of a hat, and (<b>c</b>) shows the reconstruction of a clay pot.</p>
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17 pages, 3592 KiB  
Article
3D Human Pose Estimation with a Catadioptric Sensor in Unconstrained Environments Using an Annealed Particle Filter
by Fakhreddine Ababsa, Hicham Hadj-Abdelkader and Marouane Boui
Sensors 2020, 20(23), 6985; https://doi.org/10.3390/s20236985 - 7 Dec 2020
Cited by 3 | Viewed by 3200
Abstract
The purpose of this paper is to investigate the problem of 3D human tracking in complex environments using a particle filter with images captured by a catadioptric vision system. This issue has been widely studied in the literature on RGB images acquired from [...] Read more.
The purpose of this paper is to investigate the problem of 3D human tracking in complex environments using a particle filter with images captured by a catadioptric vision system. This issue has been widely studied in the literature on RGB images acquired from conventional perspective cameras, while omnidirectional images have seldom been used and published research works in this field remains limited. In this study, the Riemannian varieties was considered in order to compute the gradient on spherical images and generate a robust descriptor used along with an SVM classifier for human detection. Original likelihood functions associated with the particle filter are proposed, using both geodesic distances and overlapping regions between the silhouette detected in the images and the projected 3D human model. Our approach was experimentally evaluated on real data and showed favorable results compared to machine learning based techniques about the 3D pose accuracy. Thus, the Root Mean Square Error (RMSE) was measured by comparing estimated 3D poses and truth data, resulting in a mean error of 0.065 m when walking action was applied. Full article
(This article belongs to the Special Issue Human Activity Recognition Based on Image Sensors and Deep Learning)
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<p>The Overview of the proposed 3D human tracking scheme. HoG (histogram of oriented gradients) features and Support Vector Machine (SVM) classifier are combined to detect the human body in the images. The predicted 3D human model and the extracted 2D features are associated and fed into the Likelihood estimator providing the 3D pose update for the particle filter.</p>
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<p>3D Human body model. Head and trunk are modeled by cylinders whereas the upper and lower limbs by truncated cones. 34 degrees of freedom are considered to represent the 3D posture with vertex and joints.</p>
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<p>3D human body model projected on the omnidirectional image. The geometrical model of the Catadioptic sensor has been taken into account in the projection process.</p>
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<p>Geodesic distances in the spherical image. An example of sampled points from a part of the 3D model projected in the image. The dots represented by yellow circles correspond to the sampled points of a part of the 3D model projected in the image.</p>
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<p>Data acquisition setup. The SmartTrack device and the Omnidirectional camera are mounted on a tripod. A calibration process was carried out to determine the rigid transformation between the two systems.</p>
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<p>Path Movement for the three sequences. The blue lines correspond to the path followed by the person during his movement around the sensor. The green areas represent the regions where the person is tracked by the SmartTrack system. (<b>a</b>) Sequence 1 and 2, (<b>b</b>) Sequence 3.</p>
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<p>Influence of the parameter <math display="inline"><semantics> <mi>α</mi> </semantics></math>—sequence n° 2. The results suggest that a good choice for the alpha parameter can improve the performance of the annealed particle filter (APF) and consequently increase the accuracy of 3D tracking.</p>
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<p>Obtained results on sequence 4 using the combined likelihood function (DS+GG). Average 2D distance between the projected 3D model and the annotated data. This error increases significantly when the tracking of the upper limbs is lost due to self-occlusion, this is the case between frame 40 and 50.</p>
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<p>Tracking errors of the body extremities. Placing the omnidirectional camera at a height of 1.5 m allows the person’s head to be visible in all images, which facilitates its tracking and explains the good obtained accuracy.</p>
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<p>Head tracking results. The average location error between the estimated 3D pose of the head and the ground-truth data is about 20 mm.</p>
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25 pages, 26467 KiB  
Article
OmniSCV: An Omnidirectional Synthetic Image Generator for Computer Vision
by Bruno Berenguel-Baeta, Jesus Bermudez-Cameo and Jose J. Guerrero
Sensors 2020, 20(7), 2066; https://doi.org/10.3390/s20072066 - 7 Apr 2020
Cited by 11 | Viewed by 5323
Abstract
Omnidirectional and 360° images are becoming widespread in industry and in consumer society, causing omnidirectional computer vision to gain attention. Their wide field of view allows the gathering of a great amount of information about the environment from only an image. However, the [...] Read more.
Omnidirectional and 360° images are becoming widespread in industry and in consumer society, causing omnidirectional computer vision to gain attention. Their wide field of view allows the gathering of a great amount of information about the environment from only an image. However, the distortion of these images requires the development of specific algorithms for their treatment and interpretation. Moreover, a high number of images is essential for the correct training of computer vision algorithms based on learning. In this paper, we present a tool for generating datasets of omnidirectional images with semantic and depth information. These images are synthesized from a set of captures that are acquired in a realistic virtual environment for Unreal Engine 4 through an interface plugin. We gather a variety of well-known projection models such as equirectangular and cylindrical panoramas, different fish-eye lenses, catadioptric systems, and empiric models. Furthermore, we include in our tool photorealistic non-central-projection systems as non-central panoramas and non-central catadioptric systems. As far as we know, this is the first reported tool for generating photorealistic non-central images in the literature. Moreover, since the omnidirectional images are made virtually, we provide pixel-wise information about semantics and depth as well as perfect knowledge of the calibration parameters of the cameras. This allows the creation of ground-truth information with pixel precision for training learning algorithms and testing 3D vision approaches. To validate the proposed tool, different computer vision algorithms are tested as line extractions from dioptric and catadioptric central images, 3D Layout recovery and SLAM using equirectangular panoramas, and 3D reconstruction from non-central panoramas. Full article
(This article belongs to the Section Intelligent Sensors)
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<p>(<b>a</b>): Kannala–Brandt projection obtained from Unreal Engine 4. (<b>b</b>): Kannala–Brandt projection obtained from POV-Ray.</p>
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<p>Client–server communication between Unreal Engine 4 and an external program via UnrealCV.</p>
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<p>Capture options available in UnrealCV. (<b>a</b>): Lit RGB image; (<b>b</b>): Object mask; (<b>c</b>): Depth; (<b>d</b>): Surface normal.</p>
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<p>Non-central systems schemes.</p>
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<p>(<b>a</b>): Simplification of the sphere into the cube map; (<b>b</b>): Unfolded cube map from a scene.</p>
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<p>(<b>a</b>): Coordinate system used in graphic engines focused on first-person video games; (<b>b</b>): Coordinate system of our image simulator.</p>
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<p>Results of CFL using a synthetic image from a 4-wall environment. (<b>a</b>): Edges ground truth; (<b>b</b>): Edges output from CFL; (<b>c</b>): Corners ground truth; (<b>d</b>): Corners output from CFL.</p>
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<p>Results of CFL using a synthetic image from a 6-wall environment. (<b>a</b>): Edges ground truth; (<b>b</b>): Edges output from CFL; (<b>c</b>): Corners ground truth; (<b>d</b>): Corners output from CFL.</p>
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<p>Line extraction on fish-eye camera. (<b>a</b>,<b>b</b>): Real fisheye images from examples of [<a href="#B34-sensors-20-02066" class="html-bibr">34</a>]; (<b>c</b>,<b>d</b>): Synthetic images from our simulator.</p>
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<p>Line extraction on catadioptric systems. (<b>a</b>,<b>b</b>): Real catadioptric images from examples of [<a href="#B34-sensors-20-02066" class="html-bibr">34</a>]; (<b>c</b>,<b>d</b>): Synthetic images from our simulator.</p>
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<p>Normalized result for the calibration parameters using different omnidirectional cameras. (<b>a</b>): Calibration results from [<a href="#B34-sensors-20-02066" class="html-bibr">34</a>]; (<b>b</b>): Calibration results using images from our simulator.</p>
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<p>Visual odometry from SLAM algorithm. The red line is the ground-truth trajectory while the blue line is the scaled trajectory of the SLAM algorithm.</p>
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<p>(<b>a</b>): Position error of the SLAM reconstruction. (<b>b</b>): Orientation error of the SLAM reconstruction. Both errors are measured in degrees.</p>
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<p>(<b>a</b>) Extracted line projections and segments on the non-central panorama. (<b>b</b>) Ground-truth point-cloud obtained from depth-map.</p>
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<p>3D line segments reconstructed from line extraction in non-central panorama. In red the reconstructed 3D line segments. In black the ground truth. In blue the circular location of the optical center and the Z axis. In green the axis of the vertical direction. (<b>a</b>) Orthographic view. (<b>b</b>) Top view. (<b>c</b>) Lateral view.</p>
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<p>Lit mode.</p>
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<p>Semantic mode.</p>
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<p>Depth mode.</p>
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<p>Lit mode.</p>
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<p>Semantic mode.</p>
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<p>Depth mode.</p>
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<p>Lit mode.</p>
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<p>Semantic mode.</p>
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<p>Depth mode.</p>
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<p>Scaramuzza and Kannala-Brandt empiric models.</p>
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