Catálogo de publicaciones - libros

In this paper, we show how to use the three dimensional topological map in order to compute efficiently topological features on objects contained in a 3D image. These features are useful for example in image processing to control operations or in computer vision to characterize objects. Topological map is a combinatorial model which represents both topological and geometrical information of a three dimensional labeled image. This model can be computed incrementally by using only two basic operations: the removal and the fictive edge shifting. In this work, we show that Euler characteristic can be computed incrementally during the topological map construction. This involves an efficient algorithm and open interesting perspectives for other features.

An important concept in combinatorial image analysis is that of gap. In this paper we derive a simple formula for the number of gaps in a 2D binary picture. Our approach is based on introducing the notions of free vertex and free edge and studying their properties from point of view of combinatorial topology. The number of gaps characterizes the topological structure of a binary picture and is of potential interest in property-based image analysis.

We provide in this paper an algorithm for the exact computation of the lattice width of an integral polygon K with n vertices in O ( n log s ) arithmetic operations where s is a bound on all integers defining vertices and edges. We also provide an incremental version of the algorithm whose update complexity is shown to be O (log n + log s ). We apply this algorithm to construct the arithmetical line with minimal thickness, which contains a given set of integer points.

Branch indices of points on curves (introduced by Urysohn and Menger) are of basic importance in the mathematical theory of curves, defined in Euclidean space. This paper applies the concept of branch points in the 3D orthogonal grid, motivated by the need to analyze curve-like structures in digital images. These curve-like structures have been derived as 3D skeletons (by means of thinning). This paper discusses approaches of defining branch indices for voxels on 3D skeletons, where the notion of a junction will play a crucial role. We illustrate the potentials of using junctions in 3D image analysis based on a recent project of analyzing the distribution of astrocytes in human brain tissue.

Critical kernels constitute a general framework settled in the category of abstract complexes for the study of parallel thinning in any dimension. In this context, we propose several new parallel algorithms, which are both fast and simple to implement, to obtain symmetrical skeletons of 2D objects in 2D or 3D grids. We prove some properties of these skeletons, related to topology preservation, and to the inclusion of the topological axis which may be seen as a generalization of the medial axis.

In this paper, we study topological watersheds on perfect fusion graphs, an ideal framework for region merging. An important result is that contrarily to the general case, in this framework, any topological watershed is thin. Then we investigate a new image transformation called C-watershed and we show that, on perfect fusion graphs, the segmentations obtained by C-watershed correspond to segmentations obtained by topological watersheds. Compared to topological watershed, a major advantage of this transformation is that, on perfect fusion graph, it can be computed thanks to a simple linear-time immersion-like algorithm. Finally, we derive characterizations of perfect fusion graphs based on thinness properties of both topological watersheds and C-watersheds.

This paper extends the concepts of image matching in the non-parametric space and binary distance measures. Matching in the nonparametric domain exhibits many desirable properties at relatively small computation complexity: It concentrates on capturing mutual relation among pixels in a small neighbourhoods rather than bare intensity values, thus improving matching discrimination. It is also more resistive against noise and uneven lighting conditions of the matched images. Last but not least, the matching algorithms operate in the integer domain and can be easily implemented in hardware what benefits in dramatic improvement of their run times. In this paper we extend the concept of nonparametric image transformation into the realm of colour images taking into consideration different colour spaces and different distances defined in these spaces. We propose significant bit reduction for aggregated block matching in the Census domain. We propose also the sparse sampling model for the Census transformation that increase the discriminative power of this representation and allows even further reduction of bits necessary for matching. The presented techniques have been applied to matching of the stereo images but can be employed in any computer vision task that requires comparison of images, such as image registration, object detection and recognition, etc. Presented experiments exhibit interesting properties of the described techniques.

In image processing, it is often of great importance to have small rotational dependency for distance functions. We present an optimization for distances based on neighbourhood sequences for the face-centered cubic (fcc) and body-centered cubic (bcc) grids. In the optimization, several error functions are used measuring different geometrical properties of the balls obtained when using these distances.

We present a method for calculating fuzzy distances between pairs of points in an image using the A^ ∗  algorithm and, furthermore, apply this method for fuzzy distance based hierarchical clustering. The method is general and can be of use in numerous applications. In our case we intend to use the clustering in an algorithm for delineation of objects corresponding to parts of proteins in 3D images. The image is defined as a fuzzy object and represented as a graph, enabling a path finding approach for distance calculations. The fuzzy distance between two adjacent points is used as edge weight and a heuristic is defined for fuzzy sets. A^ ∗  is applied to the calculation of fuzzy distance between pair of points and hierarchical clustering is used to group the points. The normalised Hubert’s statistic is used as validity index to determine the number of clusters. The method is tested on three 2D images; two synthetic images and one fuzzy distance transformed microscopy image of stem cells. All experiments show promising initial results.

Planar maps have been proposed as a powerful and easy-to-use representation for various kinds of image analysis results, but so far they are restricted to pixel accuracy. This leads to limitations in the representation of complex structures (such as junctions, triangulations, and skeletons) and discards the sub-pixel information available in grayvalue and color images. We extend the planar map formalism to sub-pixel accuracy and introduce various algorithms to create such a map, thereby demonstrating significant gains over the existing approaches.