Francesc Serratosa

Fast computation of Bipartite graph matching

Abstract We present a new algorithm to compute the Graph Edit Distance in a sub-optimal way. We demonstrate that the distance value is exactly the same than the one obtained by the algorithm called Bipartite but with a reduced run time. The only restriction we impose is that the edit costs have to be defined such that the Graph Edit Distance can be really defined as a distance function, that is, the cost of insertion plus deletion of nodes (or arcs) have to be lower or equal than the cost of substitution of nodes (or arcs). Empirical validation shows that higher is the order of the graphs, higher is the obtained Speed up.

Generalized median graph computation by means of graph embedding in vector spaces

The median graph has been presented as a useful tool to represent a set of graphs. Nevertheless its computation is very complex and the existing algorithms are restricted to use limited amount of data. In this paper we propose a new approach for the computation of the median graph based on graph embedding. Graphs are embedded into a vector space and the median is computed in the vector domain. We have designed a procedure based on the weighted mean of a pair of graphs to go from the vector domain back to the graph domain in order to obtain a final approximation of the median graph. Experiments on three different databases containing large graphs show that we succeed to compute good approximations of the median graph. We have also applied the median graph to perform some basic classification tasks achieving reasonable good results. These experiments on real data open the door to the application of the median graph to a number of more complex machine learning algorithms where a representative of a set of graphs is needed.

Function-described graphs for modelling objects represented by sets of attributed graphs

We present in this article the model function-described graph (FDG), which is a type of compact representation of a set of attributed graphs (AGs) that borrow from random graphs the capability of probabilistic modelling of structural and attribute information. We define the FDGs, their features and two distance measures between AGs (unclassified patterns) and FDGs (models or classes) and we also explain an efficient matching algorithm. Two applications of FDGs are presented: in the former, FDGs are used for modelling and matching 3D-objects described by multiple views, whereas in the latter, they are used for representing and recognising human faces, described also by several views.

Graph-based representations and techniques for image processing and image analysis☆

In this paper we will discuss the use of some graph-based representations and techniques for image processing and analysis. Instead of making an extensive review of the graph techniques in this field, we will explain how we are using these techniques in an active vision system for an autonomous mobile robot developed in the Institut de Robotica i Informatica Industrial within the project “Active Vision System with Automatic Learning Capacity for Industrial Applications (CICYT TAP98-0473)”. Specifically we will discuss the use of graph-based representations and techniques for image segmentation, image perceptual grouping and object recognition. We first present a generalisation of a graph partitioning greedy algorithm for colour image segmentation. Next we describe a novel fusion of colour-based segmentation and depth from stereo that yields a graph representing every object in the scene. Finally we describe a new representation of a set of attributed graphs (AGs), denominated Function Described Graphs (FDGs), a distance measure for matching AGs with FDGs and some applications for robot vision.

ON THE GRAPH EDIT DISTANCE COST: PROPERTIES AND APPLICATIONS

We model the edit distance as a function in a labeling space. A labeling space is an Euclidean space where coordinates are the edit costs. Through this model, we define a class of cost. A class of cost is a region in the labeling space that all the edit costs have the same optimal labeling. Moreover, we characterize the distance value through the labeling space. This new point of view of the edit distance gives us the opportunity of defining some interesting properties that are useful for a better understanding of the edit distance. Finally, we show the usefulness of these properties through some applications.

SECOND-ORDER RANDOM GRAPHS FOR MODELING SETS OF ATTRIBUTED GRAPHS AND THEIR APPLICATION TO OBJECT LEARNING AND RECOGNITION

The aim of this article is to present a random graph representation, that is based on second-order relations between graph elements, for modeling sets of attributed graphs (AGs). We refer to these models as Second-Order Random Graphs (SORGs). The basic feature of SORGs is that they include both marginal probability functions of graph elements and second-order joint probability functions. This allows a more precise description of both the structural and semantic information contents in a set of AGs and, consequently, an expected improvement in graph matching and object recognition. The article presents a probabilistic formulation of SORGs that includes as particular cases the two previously proposed approaches based on random graphs, namely the First-Order Random Graphs (FORGs) and the Function-Described Graphs (FDGs). We then propose a distance measure derived from the probability of instantiating a SORG into an AG and an incremental procedure to synthesize SORGs from sequences of AGs. Finally, SORGs are shown to improve the performance of FORGs, FDGs and direct AG-to-AG matching in three experimental recognition tasks: one in which AGs are randomly generated and the other two in which AGs represent multiple views of 3D objects (either synthetic or real) that have been extracted from color images. In the last case, object learning is achieved through the synthesis of SORG models.

A new graph matching method for point-set correspondence using the EM algorithm and Softassign

Finding correspondences between two point-sets is a common step in many vision applications (e.g., image matching or shape retrieval). We present a graph matching method to solve the point-set correspondence problem, which is posed as one of mixture modelling. Our mixture model encompasses a model of structural coherence and a model of affine-invariant geometrical errors. Instead of absolute positions, the geometrical positions are represented as relative positions of the points with respect to each other. We derive the Expectation-Maximization algorithm for our mixture model. In this way, the graph matching problem is approximated, in a principled way, as a succession of assignment problems which are solved using Softassign. Unlike other approaches, we use a true continuous underlying correspondence variable. We develop effective mechanisms to detect outliers. This is a useful technique for improving results in the presence of clutter. We evaluate the ability of our method to locate proper matches as well as to recognize object categories in a series of registration and recognition experiments. Our method compares favourably to other graph matching methods as well as to point-set registration methods and outlier rejectors.

SYNTHESIS OF FUNCTION-DESCRIBED GRAPHS AND CLUSTERING OF ATTRIBUTED GRAPHS

Function-Described Graphs (FDGs) have been introduced by the authors as a representation of an ensemble of Attributed Graphs (AGs) for structural pattern recognition alternative to first-order random graphs. Both optimal and approximate algorithms for error-tolerant graph matching, which use a distance measure between AGs and FDGs, have been reported elsewhere. In this paper, both the supervised and the unsupervised synthesis of FDGs from a set of graphs is addressed. First, two procedures are described to synthesize an FDG from a set of commonly labeled AGs or FDGs, respectively. Then, the unsupervised synthesis of FDGs is studied in he context of clustering a set of AGs and obtaining an FDG model for each cluster. Two algorithms based on incremental and hierarchical clustering, respectively, are proposed, which are parameterized by a graph matching method. Some experimental results both on synthetic data and a real 3D-object recognition application show that the proposed algorithms are effective for clustering a set of AGs and synthesizing the FDGs that describe the classes. Moreover, the synthesized FDGs are shown to be useful for pattern recognition thanks to the distance measure and matching algorithm previously reported.

Enabling semantic similarity estimation across multiple ontologies: An evaluation in the biomedical domain

The estimation of the semantic similarity between terms provides a valuable tool to enable the understanding of textual resources. Many semantic similarity computation paradigms have been proposed both as general-purpose solutions or framed in concrete fields such as biomedicine. In particular, ontology-based approaches have been very successful due to their efficiency, scalability, lack of constraints and thanks to the availability of large and consensus ontologies (like WordNet or those in the UMLS). These measures, however, are hampered by the fact that only one ontology is exploited and, hence, their recall depends on the ontological detail and coverage. In recent years, some authors have extended some of the existing methodologies to support multiple ontologies. The problem of integrating heterogeneous knowledge sources is tackled by means of simple terminological matchings between ontological concepts. In this paper, we aim to improve these methods by analysing the similarity between the modelled taxonomical knowledge and the structure of different ontologies. As a result, we are able to better discover the commonalities between different ontologies and hence, improve the accuracy of the similarity estimation. Two methods are proposed to tackle this task. They have been evaluated and compared with related works by means of several widely-used benchmarks of biomedical terms using two standard ontologies (WordNet and MeSH). Results show that our methods correlate better, compared to related works, with the similarity assessments provided by experts in biomedicine.

Speeding up Fast Bipartite Graph Matching Through a New Cost Matrix

Bipartite (BP) has been seen to be a fast and accurate suboptimal algorithm to solve the Error-Tolerant Graph Matching problem. Recently, Fast Bipartite (FBP) has been presented that obtains the sa...