Catálogo de publicaciones - libros

This paper presents new results about digital straight segments, their recognition and related properties. They come from the study of the arithmetically based recognition algorithm proposed by I. Debled-Rennesson and J.-P. Reveillès in 1995 [1]. We indeed exhibit the relations describing the possible changes in the parameters of the digital straight segment under investigation. This description is achieved by considering new parameters on digital segments: instead of their arithmetic description, we examine the parameters related to their combinatoric description. As a result we have a better understanding of their evolution during recognition and analytical formulas to compute them. We also show how this evolution can be projected onto the Stern-Brocot tree. These new relations have interesting consequences on the geometry of digital curves. We show how they can for instance be used to bound the slope difference between consecutive maximal segments.

Moment-based procedures are commonly used in computer vision, image analysis, or pattern recognition. Basic shape features such as size, position, orientation, or elongation are estimated by moments of order ≤2. Shape invariants are defined by higher order moments. In contrast to a theory of moments in continuous mathematics, shape moments in imaging have to be estimated from digitized data. Infinitely many different shapes in Euclidean space are represented by an identical digital shape. There is an inherent loss of information, impacting moment estimation. This paper discusses accuracy limitations in moment reconstruction in dependency of order of reconstructed moments and applied resolution of digital pictures. We consider moments of arbitrary order, which is not assumed to be bounded by a constant.

A defuzzification method based on feature distance minimization is further improved by incorporating into the distance function feature values measured on object representations at different scales. It is noticed that such an approach can improve defuzzification results by better preserving the properties of a fuzzy set; area preservation at scales in-between local (pixel-size) and global (the whole object) provides that characteristics of the fuzzy object are more appropriately exhibited in the defuzzification. For the purpose of comparing sets of different resolution, we propose a feature vector representation of a (fuzzy and crisp) set, utilizing a resolution pyramid. The distance measure is accordingly adjusted. The defuzzification method is extended to the 3D case. Illustrative examples are given.

Differential operators are required to compute several characteristics for continuous surfaces, as e.g. tangents, curvature, flatness, shape descriptors. We propose to replace differential operators by the combined action of sets of feature detectors and locally adapted difference operators. A set of simple local feature detectors is used to find the fitting function which locally yields the best approximation for the digitized image surface. For each class of fitting functions, we determine which difference operator locally yields the best result in comparison to the differential operator. Both the set of feature detectors and the difference operator for a function class have a rigid mathematical structure, which can be described by Groebner bases. In this paper we describe how to obtain discrete approximates for the Laplacian differential operator and how these difference operators improve the performance of the Laplacian of Gaussian edge detector.

We consider the problem of determining if a given word, which encodes the boundary of a discrete figure, tiles the plane by translation. These words have been characterized by the Beauquier-Nivat condition, for which we provide a linear time algorithm in the case of pseudo-square polyominoes, improving the previous quadratic algorithm of Gambini and Vuillon.

The aim of this article is to present a reversible and topologically correct construction of a polyhedron from a binary object. The proposed algorithm is based on a Marching Cubes (MC) surface, a digital plane segmentation of the binary object surface and an optimization step to simplify the MC surface using the segmentation information.

In the framework of the arithmetic discrete geometry, a discrete object is provided with its own analytical definition corresponding to a discretization scheme. It can thus be considered as the equivalent, in a discrete space, of a Euclidean object. Linear objects, namely lines and hyperplanes, have been widely studied under this assumption and are now deeply understood. This is not the case for discrete circles and hyperspheres for which no satisfactory definition exists. In the present paper, we try to fill this gap. Our main results are a general definition of discrete hyperspheres and the characterization of the k -minimal ones thanks to an arithmetic definition based on a non-constant thickness function. To reach such topological properties, we link adjacency and separatingness with norms.

Eccentricity measures the shortest length of the paths from a given vertex v to reach any other vertex w of a connected graph. Computed for every vertex v it transforms the connectivity structure of the graph into a set of values. For a connected region of a digital image it is defined through its neighbourhood graph and the given metric. This transform assigns to each element of a region a value that depends on it’s location inside the region and the region’s shape. The definition and several properties are given. Presented experimental results verify its robustness against noise, and its increased stability compared to the distance transform. Future work will include using it for shape decomposition, representation, and matching.

Because the appearance of 3D objects changes according to viewing directions, it is not easy to evaluate similarity between two objects in a few appearances. In this paper we propose similarity measure between two shapes of 3D objects. The feature of a shape is represented by a distribution of a projected area on a unit sphere, and the distribution is expanded in spherical harmonics. The degree of similarity between several kinds of shape is calculated and is compared with human sense. The results of computer simulation demonstrate the validity of our method.

Recent advances in graphics hardware provide new possibilities to successfully integrate and improve multiresolution models. In this paper, we present a new continuous multiresolution model that maintains its geometry, based on triangle strips, in high-performance memory in the GPU. This model manages the level of detail by performing fast strip updating operations. We show how this approach takes advantage of the new capabilities of GPUs in an efficient manner.