Abstract: The aim of this paper is to revisit an old theory of texture perception and
update its computational implementation by extending it to colour. With this in mind we try to capture the optimality of perceptual systems. This is achieved in the proposed approach by sharing well-known early stages of the visual processes and extracting low-dimensional features that perfectly encode adequate properties for a large variety of textures without needing further learning stages. We propose several descriptors in a bag-of-words framework that are derived from different quantisation models on to the feature spaces. Our perceptual features are directly given by the shape and colour attributes of image blobs, which are the textons. In this way we avoid learning visual words and directly build the vocabularies on these lowdimensionaltexton spaces. Main differences between proposed descriptors rely on how co-occurrence of blob attributes is represented in the vocabularies. Our approach overcomes current state-of-art in colour texture description which is proved in several experiments on large texture datasets.

Abstract: We describe an equivalence of categories between the category of mixed Hodge structures and a category of equivariant vector bundles on a toric model of the complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalizes the notion of R-split mixed Hodge structure and give calculations for the first group of cohomology of possibly non smooth or non-complete curves of genus 0 and 1. Finally, we describe some extension groups of mixed Hodge structures in terms of equivariant extensions of coherent sheaves. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim