Seminário Matemática, Sistemas e Robótica 

04/04/2008, 15:00 — 16:00 — Sala de Conferências, Instituto de Sistemas e Robótica, Torre Norte, 7º andar, IST
José Rodrigues, ISR

An Analytic Signature for Permutation-Invariant Two-Dimensional Shape Representation

Many applications require a computer representation of a two-dimensional (2D) shape, usually described by a set of 2D points. The challenge of this representation is that it must not only capture the characteristics of the shape but also be invariant to relevant transformations. Invariance to geometric transformations such as translation, rotation and scale, has received attention in the past, usually under the assumption that the points are previously labeled, i.e., that the shape is characterized by an ordered set of landmarks. However, in many practical scenarios the points describing the shape are obtained from an automatic process, e.g., edge detection, thus without natural ordering. Obviously, the combinatorial problem of computing the correspondences between the points of two shapes in the presence of geometrical distortions becomes a quagmire when the number of points is large. Within our framework, a 2D shape is mapped to an analytic function on the complex plane, leading to what we call its analytic signature (ANSIG), circumventing the combinatorial search. We further show how easy it is to factor out geometric transformations when comparing shapes using the ANSIG representation. We illustrate these ANSIG capabilities for shape-based image classification, particularly in automatic trademark retrieval.