Catálogo de publicaciones - libros

This paper proposes a new greedy algorithm to improve the specified b-coloring partition while satisfying b-coloring property. The b-coloring based clustering method in [3] enables to build a fine partition of the data set (classical or symbolic) into clusters even when the number of clusters is not pre-defined. It has several desirable clustering properties: utilization of topological relations between objects, robustness to outliers, all types of data can be accommodated, and identification of each cluster by at least one . However, it does not consider the of the clusters in the construction of a b-coloring graph. The proposed algorithm in this paper can complement its weakness by re-coloring the objects to improve the quality of the constructed partition under the property and the dominance constraints. The proposed algorithm is evaluated against benchmark datasets and its effectiveness is confirmed.

In this paper, a new way to express complex spatial relations is proposed in order to integrate them in a Constraint Satisfaction Problem with bilevel constraints. These constraints allow to build semantic graphs, which can describe more precisely the spatial relations between subparts of a composite object that we look for in an image. For example, it allows to express complex spatial relations such as “is surrounded by”. This approach can be applied to image interpretation and some examples on real images are presented.

The vascular structure of the retina consists of two kinds of vessels: arteries and veins. Together these vessels form the vascular graph. In this paper we present an approach to separating arteries and veins based on a pre-segmentation and a few hand-labelled vessel segments. We use a rule-based method to propagate the vessel labels through the vascular graph. We embed this task as double-layered constrained search problem steered by a heuristical AC-3 algorithm to overcome the NP-hard computational complexity. Results are presented on vascular graphs generated from hand-made as well as on automatical segmentation.

It has been demonstrated that the difficult problem of classifying heterogeneous projection images, similar to those found in 3D electron microscopy (3D-EM) of macromolecules, can be successfully solved by finding an approximate Max k-Cut of an appropriately constructed weighted graph. Despite of the large size (thousands of nodes) of the graph and the theoretical computational complexity of finding even an approximate Max k-Cut, an algorithm has been proposed that finds a good (from the classification perspective) approximate solution within several minutes (running on a standard PC). However, the task of constructing the complete weighted graph (that represents an instance of the projection image classification problems) is computationally expensive. Due to the large number of edges, the computation of edge weights can take tens of hours for graphs containing several thousand nodes. We propose a method, which utilizes an early termination technique, to significantly reduce the computational cost of constructing such graphs. We compare, on synthetic data sets that resemble projection sets encountered in 3D-EM, the performance of our method with that of a brute-force approach and a method based on nearest neighbor search.

This paper proposes a novel expert peering system for information exchange. Our objective is to develop a real-time search engine for an online community where users can query experts, who are simply other participating users knowledgeable in that area, for help on various topics. We consider a graph-based scheme consisting of an ontology tree where each node represents a (sub)topic. Consequently, the fields of expertise or profiles of the participating experts correspond to subtrees of this ontology. Since user queries can also be mapped to similar tree structures, assigning queries to relevant experts becomes a problem of graph matching. A serialization of the ontology tree allows us to use simple dot products on the ontology vector space effectively to address this problem. As a demonstrative example, we conduct extensive experiments with different parameterizations. We observe that our approach is efficient and yields promising results.

We introduce a method for computing homology groups and their generators of a 2D image, using a hierarchical structure i.e. irregular graph pyramid. Starting from an image, a hierarchy of the image is built, by two operations that preserve homology of each region. Instead of computing homology generators in the base where the number of entities (cells) is large, we first reduce the number of cells by a graph pyramid. Then homology generators are computed efficiently on the top level of the pyramid, since the number of cells is small, and a top down process is then used to deduce homology generators in any level of the pyramid, including the base level i.e. the initial image. We show that the new method produces valid homology generators and present some experimental results.

The traveling salesperson problem (TSP) is difficult to solve for input instances with large number of cities. Instead of finding the solution of an input with a large number of cities, the problem is approximated into a simpler form containing smaller number of cities, which is then solved optimally. Graph pyramid solution strategies, in a bottom-up manner using Borůvka’s minimum spanning tree, convert a 2D Euclidean TSP problem with a large number of cities into successively smaller problems (graphs) with similar layout and solution, until the number of cities is small enough to seek the optimal solution. Expanding this tour solution in a top-down manner to the lower levels of the pyramid approximates the solution. The new model has an adaptive spatial structure and it simulates visual acuity and visual attention. The model solves the TSP problem sequentially, by moving attention from city to city with the same quality as humans. Graph pyramid data structures and processing strategies are a plausible model for finding near-optimal solutions for computationally hard pattern recognition problems.

The Bounded Irregular Pyramid (BIP) is a mixture of regular and irregular pyramids whose goal is to combine their advantages. Thus, its data structure combines a regular decimation process with a union-find strategy to build the successive levels of the structure. The irregular part of the BIP allows to solve the main problems of regular structures: their inability to preserve connectivity or to represent elongated objects. On the other hand, the BIP is computationally efficient because its height is constrained by its regular part. In this paper the features of the Bounded Irregular Pyramid are discussed, presenting a comparison with the main pyramids present in the literature when applied to a colour segmentation task.

In this paper, we present a topological algorithm which allows to fill contours images. The filling problem has been widely treated and it recently appeared that it can always be split into two different process : a generic topological process and a dedicated geometrical post-processing which depends on the application. Our algorithm, based on a 2D topological map description of the image, addresses the first step of processing. It is fast, generic and robust. Moreover, the complete topological description allows to easily integrate geometrical constrains and makes our approach an interesting basis for every filling process.

When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing (co)homology, representative (co)cycles of (co)homology generators and the cup product on cohomology of nD digital images as well as for controlling topological information when the image suffers local changes [6,7,9]. In this paper, we formalize the notion of -AT-model ( being an integer) which extends the one of AT-model and allows the computation of homological information in the integer domain without computing the Smith Normal Form of the boundary matrices. We present an algorithm for computing such a model, obtaining Betti numbers, the prime numbers involved in the invariant factors (corresponding to the torsion subgroup of the homology), the amount of invariant factors that are a power of and a set of representative cycles of the generators of homology mod , for such .