Biomedical subjects

Andrea Torsello

Publications and source records attributed to Andrea Torsello.

4 recordsLinked to original sources

PubMed2006

Correcting curvature-density effects in the Hamilton-Jacobi skeleton.

The Hamilton-Jacobi approach has proven to be a powerful and elegant method for extracting the skeleton of two-dimensional (2-D) shapes. The approach is based on the observation that the normalized flux associated with the inward evolution of the object boundary at nonskeletal points tends to zero as the size of the integration area tends to zero, while the flux is negative at the locations of skeletal points. Nonetheless, the error in calculating the flux on the image lattice is both limited by the pixel resolution and also proportional to the curvature of the boundary evolution front and, hence, unbounded near endpoints. This makes the exact location of endpoints difficult and renders the performance of the skeleton extraction algorithm dependent on a threshold parameter. This problem can be overcome by using interpolation techniques to calculate the flux with subpixel precision. However, here, we develop a method for 2-D skeleton extraction that circumvents the problem by eliminating the curvature contribution to the error. This is done by taking into account variations of density due to boundary curvature. This yields a skeletonization algorithm that gives both better localization and less susceptibility to boundary noise and parameter choice than the Hamilton-Jacobi method.

Algorithms↗

PubMed2006

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 2D shapes using a shock graph representation.

Algorithms↗

PubMed2006

Payoff-monotonic game dynamics and the maximum clique problem.

Evolutionary game-theoretic models and, in particular, the so-called replicator equations have recently proven to be remarkably effective at approximately solving the maximum clique and related problems. The approach is centered around a classic result from graph theory that formulates the maximum clique problem as a standard (continuous) quadratic program and exploits the dynamical properties of these models, which, under a certain symmetry assumption, possess a Lyapunov function. In this letter, we generalize previous work along these lines in several respects. We introduce a wide family of game-dynamic equations known as payoff-monotonic dynamics, of which replicator dynamics are a special instance, and show that they enjoy precisely the same dynamical properties as standard replicator equations. These properties make any member of this family a potential heuristic for solving standard quadratic programs and, in particular, the maximum clique problem. Extensive simulations, performed on random as well as DIMACS benchmark graphs, show that this class contains dynamics that are considerably faster than and at least as accurate as replicator equations. One problem associated with these models, however, relates to their inability to escape from poor local solutions. To overcome this drawback, we focus on a particular subclass of payoff-monotonic dynamics used to model the evolution of behavior via imitation processes and study the stability of their equilibria when a regularization parameter is allowed to take on negative values. A detailed analysis of these properties suggests a whole class of annealed imitation heuristics for the maximum clique problem, which are based on the idea of varying the parameter during the imitation optimization process in a principled way, so as to avoid unwanted inefficient solutions. Experiments show that the proposed annealing procedure does help to avoid poor local optima by initially driving the dynamics toward promising regions in state space. Furthermore, the models outperform state-of-the-art neural network algorithms for maximum clique, such as mean field annealing, and compare well with powerful continuous-based heuristics.

Journal Article↗

PubMed2005

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.

Algorithms↗