Scale-sets image analysis

Abstract

This paper addresses the problem of multiscale region-oriented image analysis. It first deals with a representational issue: how to represent all the solutions of a multiscale partitioning algorithm, i.e. of an algorithm returning ordered partitions with respect to a one-dimensional 'scale' parameter? To achieve this, we propose the scale-sets representation which can be viewed as a region-oriented version of the scale-space representation. In a second time, we present an energy minimization based approach to obtain scale-sets image descriptions. We consider a general class of energies on partitions which involve two terms: a goodness-of-fit term and a regularization term. The scale parameter is then the relative weight between the two terms. We derive a condition at which such energies lead to monotone minimal cuts in a hierarchy of regions and we provide an algorithm to compute the whole set of those minimal cuts exactly and efficiently. This leads us to a parameter-free principle to build scale-sets image descriptions, which we call scale climbing. This principle can be viewed as an exact continuation method in scale and produces scale invariant image descriptions. Some results obtained with Mumford-Shah's cartoon model are provided. Different applications of scale-sets image descriptions are finally browsed.