Andrea Torsello

Graph-Based Representations in Pattern Recognition

Hypergraphs.- Generalization of Two Hypergraphs. Algorithm of Calculation of the Greatest Sub-Hypergraph Common to Two Hypergraphs Annotated by Semantic Information.- Recognition and Detection.- Recognition of Polymorphic Patterns in Parameterized Graphs for 3D Building Reconstruction.- A Graph-Based Representation to Detect Linear Features.- Edge Detection as Finding the Minimum Cost Path in a Graph.- Matching.- Subgraph Transformations for the Inexact Matching of Attributed Relational Graphs.- Efficient Graph Matching for Video Indexing.- Isomorphism between Strong Fuzzy Relational Graphs Based on k-Formulae.- Segmentation.- A Graph Structure for Grey Value and Texture Segmentation.- Discrete Maps: a Framework for Region Segmentation Algorithms.- Image Sequence Segmentation by a Single Evolutionary Graph Pyramid.- Implementation Problems.- Dual Graph Contraction with LEDA.- Implementing Image Analysis with a Graph-Based Parallel Computing Model.- Representation.- The Frontier-Region Graph.- Optimization Techniques on Pixel Neighborhood Graphs for Image Processing.

Learning shape-classes using a mixture of tree-unions

This paper poses the problem of tree-clustering as that of fitting a mixture of tree unions to a set of sample trees. The tree-unions are structures from which the individual data samples belonging to a cluster can be obtained by edit operations. The distribution of observed tree nodes in each cluster sample is assumed to be governed by a Bernoulli distribution. The clustering method is designed to operate when the correspondences between nodes are unknown and must be inferred as part of the learning process. We adopt a minimum description length approach to the problem of fitting the mixture model to data. We make maximum-likelihood estimates of the Bernoulli parameters. The tree-unions and the mixing proportions are sought so as to minimize the description length criterion. This is the sum of the negative logarithm of the Bernoulli distribution, and a message-length criterion that encodes both the complexity of the union-trees and the number of mixture components. We locate node correspondences by minimizing the edit distance with the current tree unions, and show that the edit distance is linked to the description length criterion. The method can be applied to both unweighted and weighted trees. We illustrate the utility of the resulting algorithm on the problem of classifying 20 shapes using a shock graph representation.

Polynomial-time metrics for attributed trees

We address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree. The proposed measures are general and defined on trees endowed with either symbolic or continuous-valued attributes and can be applied to rooted as well as unrooted trees. We prove that our measures satisfy the metric constraints and provide a polynomial-time algorithm to compute them. This is a remarkable and attractive property, since the computation of traditional edit-distance-based metrics is, in general, NP-complete, at least in the unordered case. We experimentally validate the usefulness of our metrics on shape matching tasks and compare them with (an approximation of) edit-distance.

A Scale Independent Selection Process for 3D Object Recognition in Cluttered Scenes

During the last years a wide range of algorithms and devices have been made available to easily acquire range images. The increasing abundance of depth data boosts the need for reliable and unsupervised analysis techniques, spanning from part registration to automated segmentation. In this context, we focus on the recognition of known objects in cluttered and incomplete 3D scans. Locating and fitting a model to a scene are very important tasks in many scenarios such as industrial inspection, scene understanding, medical imaging and even gaming. For this reason, these problems have been addressed extensively in the literature. Several of the proposed methods adopt local descriptor-based approaches, while a number of hurdles still hinder the use of global techniques. In this paper we offer a different perspective on the topic: We adopt an evolutionary selection algorithm that seeks global agreement among surface points, while operating at a local level. The approach effectively extends the scope of local descriptors by actively selecting correspondences that satisfy global consistency constraints, allowing us to attack a more challenging scenario where model and scene have different, unknown scales. This leads to a novel and very effective pipeline for 3D object recognition, which is validated with an extensive set of experiments and comparisons with recent techniques at the state of the art.

Computing approximate tree edit distance using relaxation labeling

This paper presents a new method for computing the tree edit distance problem with uniform edit cost. We commence by showing that any tree obtained with a sequence of cut operations is a subtree of the transitive closure of the original tree, we show that the necessary condition for any subtree to be a solution can be reduced to a clique problem in a derived structure. Using this idea we transform the problem of computing tree edit distance into a series of maximum weight clique problems. We, then use relaxation labeling to find an approximation to the tree edit distance.

Grouping with Asymmetric Affinities: A Game-Theoretic Perspective

Pairwise grouping and clustering approaches have traditionally worked under the assumption that the similarities or compatibilities between the elements to be grouped are symmetric. However, asymmetric compatibilities arise naturally in many areas of computer vision and pattern recognition. Hence, there is a need for a new generic approach to clustering and grouping that can deal with asymmetries in the compatibilities. In this paper, we present a generic framework for grouping and clustering derived from a game-theoretic formalization of the competition between the hypotheses of group membership, and apply it to perceptual grouping. In the proposed approach groups correspond to evolutionary stable strategies, a classic notion in evolutionary game theory. We also provide a combinatorial characterization of the stable strategies, and, hence, of the elements that belong to a group. Experiments show that our approach outperforms both state-of-the-art clustering-based perceptual grouping approacheswith symmetric compatibilities, and other approaches explicitly designed to make use of asymmetric compatibilities.

Matching as a non-cooperative game

With this paper we offer a game-theoretic perspective for the all-pervasive matching problem in computer vision. Specifically, we formulate the matching problem as a (population) non-cooperative game where the potential associations between the items to be matched correspond to (pure) strategies, while payoffs reflect the degree of compatibility between competing hypotheses. Within this formulation, the solutions of the matching problem correspond to evolutionary stable states (ESSs), a robust population-based generalization of the notion of a Nash equilibrium. In order to find ESSs of our matching game, we propose using a novel, fast evolutionary game dynamics motivated by Darwinian selection processes, which let the pure strategies play against each other until an equilibrium is reached. A distinguishing feature of the proposed framework is that it allows one to naturally deal with general many-to-many matching problems even in the presence of asymmetric compatibilities. The potential of the proposed approach is demonstrated via two sets of image matching experiments, both of which show that our results outperform those obtained using well-known domain-specific algorithms.

Partial Functional Correspondence

In this paper, we propose a method for computing partial functional correspondence between non‐rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace–Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular (in the Mumford–Shah sense) parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings.

Beyond partitions: Allowing overlapping groups in pairwise clustering

The field of pairwise clustering is currently dominated by the idea of dividing a set of objects into disjoints classes, thereby giving rise to (hard) partitions of the input data. However, in many computer vision and pattern recognition problems this approach is too restrictive as objects might reasonably belong to more than one class. In this paper, we adopt a game-theoretic perspective to the iterative extraction of possibly overlapping clusters: Game dynamics are used to locate individual groups, and after each extraction the similarity matrix is transformed in such a way as to make the located cluster unstable under the dynamics, without affecting the remaining groups.

Editorial: Similarity-based pattern recognition

The goal of this special issue was to solicit and publish high-quality papers that bring a clear picture of the state of the art in this area. We received 71 submissions, confirming that this topic arouses lively interest in the field of Pattern Recognition and Computer Vision. Each paper was reviewed by at least two reviewers, with most being reviewed by three. This meant that we needed the assistance of some 200 reviewers which we thank for their invaluable assistance. Further, each paper was checked out by the editors. Based on the reviews, and giving authors the chance to revise their papers in the light of reviewers, comments, we selected the 10 papers that appear in the current special section, together with five papers that will appear in subsequent regular issues. The papers span a diverse set of methods and applications.