Discrete Applied Mathematics

In (Ayala et al. (Discrete Appl. Math. 125 (1) (2003) 3) it was introduced the notion of a digital fundamental group π₁^d(O/S; σ) for a set of pixels O in relation to another set S which plays the role of an "obstacle". This notion intends to be a ...

This paper concerns the digital circle recognition problem, especially in the form of the circular separation problem. General fundamentals, based on classical tools, as well as algorithmic details, are given (the latter by providing pseudo-code for ...

In this article, we study the problem of the estimation of the rigid transformations, composed by translations and rotations, of a real object such that the discretizations before and after the transformation are the same. Our method is based on the ...

In digital topology, Euclidean n-space Rⁿ is usually modeled either by the set of points of a discrete grid, or by the set of n-cells in a convex cell complex whose union is Rⁿ. For commonly used grids and complexes in the cases n = 2 and 3, certain ...

Algebraic reconstruction techniques for the reconstruction of distributions from projections have yielded improvements in diverse fields such as medical imaging and electron microscopy. An important property of these methods is that they allow the use ...

This paper presents the methodology and theory for automatic spatial pattern discovery from multiple attributed relational graph samples. The spatial pattern is modelled as a mixture of probabilistic parametric attributed relational graphs. A statistic ...

The reconstruction of hv-convex binary matrices from their absorbed projections is considered. Although this problem is NP-hard if the non-absorbed row and column sums are available, it is proved that such a reconstruction problem can be solved in ...

Image modeling using Gibbs priors was previously shown, based on experiments, to be effective in image reconstruction problems. This motivated us to evaluate three methods for estimating the priors. Two of them accurately recover the parameters of the ...

In this paper, we propose a new methodology to conceive a thinning scheme based on the parallel deletion of P-simple points. This scheme needs neither a preliminary labelling nor an extended neighborhood, in the opposite of the already proposed thinning ...

A digital arc is called 'straight' if it is the digitization of a straight line segment. Since the concept of digital straightness was introduced in the mid-1970s, dozens of papers on the subject have appeared; many characterizations of digital straight ...

We study certain closure operations on Z², with the aim of showing that they can provide a suitable framework for solving problems of digital topology. The Khalimsky topology on Z², which is commonly used as a basic structure in digital topology ...

We consider the problem of computing the largest region in a terrain that is approximately contained in some two-dimensional plane. We reduce this problem to the following one. Given an embedding of a degree-3 graph G on the unit sphere S², whose ...

The discrete radon transform (DRT) forms a set of digital projections of discrete data, similar to the sinogram of the continuous space radon transform. An advantage of the DRT is that it provides an exact and easily invertible representation for any ...

A new class of image processing filters is introduced and analyzed in this paper. The new filters utilize fuzzy measures applied to image pixels connected by digital paths. The performance of the proposed filters is compared to the performance of ...