Search Results

Voxel based modeling is an attractive way to represent complex multi-material objects. Multi-labeled voxel models are also ubiquitous in material sciences, medical imaging or numerical simulations. We present here a variational method to regularize ...

We consider the problem of digitalizing Euclidean line segments from $\mathbb{R}^d$ to $\mathbb{Z}^d$. Christ, Pálvölgyi, and Stojaković, [Discrete Comput. Geom., 47 (2012), pp. 691--710] showed how to construct a set of consistent digital segments (CDS) ...

The digital spaces have some properties that are not present in the Euclidean space. A digitized circle do not necessarily have the smallest digital arc length perimeter of all objects having a given area. In digital geometry various measures of ...

Given a Digital Straight Line (DSL) of known characteristics (a,b,μ), we address the problem of computing the characteristics of any of its subsegments. We propose a new algorithm as a smart walk in the so called Farey Fan. We take profit of the fact ...

In many geometry processing applications, the estimation of differential geometric quantities such as curvature or normal vector field is an essential step. In this paper, we investigate a new class of estimators on digital shape boundaries based on ...

It is well known that a digitized circle doesn't have the smallest (digital arc length) perimeter of all objects having a given area. There are various measures of perimeter and area in digital geometry, and so there can be various definitions of ...

In this paper we formulate an alternative approach to the sketch recognition problem. The figure to be recognized from a sketch is specified as a set of geometric line relationship rules. This approach normally has a high computational cost as it ...

We determine the number of Khalimsky-continuous functions defined on an interval, having two fixed endpoints, and with values in Z, in N, or in a bounded interval. The number of Khalimsky-continuous functions with two points in their codomain gives an ...

An annulus is defined as a set of points contained between two circles. This paper presents a method for fitting an annulus to a given set of points in a 2D images in the presence of noise by maximizing the number of inliers, namely the consensus set, ...

A novel algorithm to recognize hand-drawn graphs is proposed. The algorithm uses properties of digital-geometric straightness combined with a new idea of Farey sequence, followed by geometric refinement, in order to speed up the recognition of graph ...

We propose an algorithm to generate random digital curves of finite length, generating points of a digital path $\rho$ on the fly. Path $\rho$ never intersects or touches itself, and hence becomes simple and irreducible. This is ensured by detecting ...

The issue of decomposing digital shapes into sets of digital primitives has been widely studied over the years. Practically all existing approaches require perfect or cleaned shapes. Those are obtained using various pre-processing techniques such as ...

We introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms naturally arising from Euclidean axioms. In particular, we show how to derive such a system of digital segments from any total ...

In this paper we investigate properties of a digital object obtained by taking the integer points within an offset of a certain radius of the object. Our considerations apply to digitizations of arbitrary path-connected sets in an arbitrary dimension n. ...

In digital image processing digital distances are useful; distances based on neighborhood sequences are widely used. In this paper the diamond grid is considered, that is the three-dimensional grid of Carbon atoms in the diamond crystal. This grid can ...

The paper studies local convexity properties of parts of digital boundaries. An online and linear-time algorithm is introduced for the decomposition of a digital boundary into convex and concave parts. In addition, other data are computed at the same ...

This paper presents a brief survey of some recently discovered properties of digital circles, digital discs, and digital surfaces of revolution, which are related with many theoretical challenges in the digital space and have diverse applications in ...

Estimation of discrete curvature is a challenging problem, since a mere replacement of functional derivatives by numerical differences fails to produce the desired result. Several algorithms have been proposed so far, which are mostly based on the ...

In this paper we investigate an approach of constructing a digital curve by taking the integer points within an offset of a certain radius of a continuous curve. Our considerations apply to digitizations of arbitrary curves in arbitrary dimension n. As ...

There are several algorithms for digitization of a real disc (circle) to derive a digital disc, and also for finding the real disc corresponding to a digital disc. However, the correspondence of a digital disc with a regular polygon in the real plane is ...