Work in collaboration with Narcís Sayols Baixeras. The general research theme is pattern theory, in the sense of Ulf Grenander and David Mumford. The starting work is Sayols' memoir Pattern modelling and pattern processing in image and speech signals defended on 24.7.2012 as the final project for the telecommunications engineering degree at the ETSETB. Here are the slides of his defense.
Abstract. The purpose of this article is to describe a pattern-theoretic approach to the analysis an synthesis of plane mosaics by computer. In synthesis, a mosaic is constructed by picking one of the 17 possible symmetry groups, choosing values for the free parameters of the corresponding principal tile and adding a patterned decoration to it. In the implemented algorithms, all the choices may be done by the user or at random. In analysis, the other side of the coin, the main part is an algorithm that ouputs, given a mosaic picture, the (most probable) class to which it belongs and a picture of the principal cell. When the mosaic image is generated by our synthesis algorithm, then the analysis algorithm also delivers the decoration structure.