Catálogo de publicaciones - libros

In the field of structural pattern recognition graphs constitute a very common and powerful way of representing patterns. In contrast to string representations, graphs allow us to describe relational information in the patterns under consideration. One of the main drawbacks of graph representations is that the computation of standard graph similarity measures is exponential in the number of involved nodes. Hence, such computations are feasible for rather small graphs only. One of the most flexible error-tolerant graph similarity measures is based on graph edit distance. In this paper we propose an approach for the efficient compuation of edit distance based on bipartite graph matching by means of Munkres’ algorithm, sometimes referred to as the Hungarian algorithm. Our proposed algorithm runs in polynomial time, but provides only suboptimal edit distance results. The reason for its suboptimality is that implied edge operations are not considered during the process of finding the optimal node assignment. In experiments on semi-artificial and real data we demonstrate the speedup of our proposed method over a traditional tree search based algorithm for graph edit distance computation. Also we show that classification accuracy remains nearly unaffected.

Many medical applications require a registration of different images of the same organ. In many cases, such a registration is accomplished by manually placing landmarks in the images. In this paper we propose a method which is able to find reasonable landmarks automatically. To achieve this, nodes of the vessel systems, which have been extracted from the images by a segmentation algorithm, will be assigned by the so-called association graph method and the coordinates of these matched nodes can be used as landmarks for a non-rigid registration algorithm.

In this paper, we propose a highly robust point-matching method ( - GTM) relying on finding the consensus graph emerging from putative matches. Such method is a two-phased one in the sense that after finding the consensus graph it tries to complete it as much as possible. We successfully apply GTM to image registration in the context of finding mosaics from retinal images. Feature points are obtained after properly segmenting such images. In addition, we also introduce a novel topological descriptor for quantifying disease by characterizing the arterial/venular trees. Such descriptor relies on diffusion kernels on graphs. Our experiments have showed only statistical significance for the case of arterial trees, which is consistent with previous findings.

We propose a new approach to stereo matching for obstacle detection in the autonomous navigation framework. An accurate but slow reconstruction of the 3D scene is not needed; rather, it is more important to have a fast localization of the obstacles to avoid them. All the methods in the literature, based on a punctual stereo matching, are ineffective in realistic contexts because they are either computationally too expensive, or unable to deal with the presence of uniform patterns, or of perturbations between the left and right images. Our idea is to face the stereo matching problem as a matching between homologous regions. The stereo images are represented as graphs and a graph matching is computed to find homologous regions. Our method is strongly robust in a realistic environment, requires little parameter tuning, and is adequately fast, as experimentally demonstrated in a comparison with the best algorithms in the literature.

In this paper, we propose to represent shapes by graphs. Based on graphic primitives extracted from the binary images, attributed relational graphs were generated. Thus, the nodes of the graph represent shape primitives like vectors and quadrilaterals while arcs describing the mutual primitives relations. To be invariant to transformations such as rotation and scaling, relative geometric features extracted from primitives are associated to nodes and edges as attributes. Concerning graph matching, due to the fact of NP-completeness of graph-subgraph isomorphism, a considerable attention is given to different strategies of inexact graph matching. We also present a new scoring function to compute a similarity score between two graphs, using the numerical values associated to the nodes and edges of the graphs. The adaptation of a greedy graph matching algorithm with the new scoring function demonstrates significant performance improvements over traditional exhaustive searches of graph matching.

In many applications of computer vision and pattern recognition which use graph-based knowledge representation, it is of great interest to be able to extract the largest cliques in a graph, but most methods are geared either towards extracting the single clique of maximum size, or enumerating all cliques, without following any particular order. In this paper we present a novel approach for partial clique enumeration, that is, the extraction of the largest cliques of a graph. Our approach is based on a continuous formulation of the clique problem developed by Motzkin and Straus, and is able to avoid extracting the same clique multiple times. This is done by casting the problem into a game-theoretic framework and iteratively rendering unstable the solutions that have already been extracted.

In this paper we propose a new lower bound to a subgraph isomorphism problem. This bound can provide a proof that no subgraph isomorphism between two graphs can be found. The computation is based on the SDP relaxation of a – to the best of our knowledge – new combinatorial optimisation formulation for subgraph isomorphism. We consider problem instances where only the structures of the two graph instances are given and therefore we deal with simple graphs in the first place. The idea is based on the fact that a subgraph isomorphism for such problem instances always leads to 0 as lowest possible optimal objective value for our combinatorial optimisation problem formulation. Therefore, a lower bound that is larger than 0 represents a proof that a subgraph isomorphism don’t exist in the problem instance. But note that conversely, a negative lower bound does not imply that a subgraph isomorphism must be present and only indicates that a subgraph isomorphism is still possible.

In this paper we consider how coined quantum walks can be applied to graph matching problems. The matching problem is abstracted using an auxiliary graph that connects pairs of vertices from the graphs to be matched by way of auxiliary vertices. A coined quantum walk is simulated on this auxiliary graph and the quantum interference on the auxiliary vertices indicates possible matches. When dealing with graphs for which there is no exact match, the interference amplitudes together with edge consistencies are used to define a consistency measure. We have tested the algorithm on graphs derived from the NCI molecule database and found it to significantly reduce the space of possible matchings thereby allowing the graphs to be matched directly. An analysis of the quantum walk in the presence of structural errors between graphs is used as the basis of the consistency measure. We test the performance of this measure on graphs derived from images in the COIL-100 database.

In this paper we propose a quadratic programming approach to computing the edit distance of graphs. Whereas the standard edit distance is defined with respect to a minimum-cost edit path between graphs, we introduce the notion of fuzzy edit paths between graphs and provide a quadratic programming formulation for the minimization of fuzzy edit costs. Experiments on real-world graph data demonstrate that our proposed method is able to outperform the standard edit distance method in terms of recognition accuracy on two out of three data sets.

We propose in this article an image classification technique based on kernel methods and graphs. Our work explores the possibility of applying marginalized kernels to image processing. In machine learning, performant algorithms have been developed for data organized as real valued arrays; these algorithms are used for various purposes like classification or regression. However, they are inappropriate for direct use on complex data sets. Our work consists of two distinct parts. In the first one we model the images by graphs to be able to represent their structural properties and inherent attributes. In the second one, we use kernel functions to project the graphs in a mathematical space that allows the use of performant classification algorithms. Experiments are performed on medical images acquired with various modalities and concerning different parts of the body.