Análise de formas usando wavelets em grafos

Abstract

This document describes the PhD thesis entitled Shape Analysis by using Wavelets on Graphs. The addressed theme is related to Computer Vision, particularly to the Characterization, Description and Classification topics. Amongst the methods presented in an extensive literature on Shape Analysis 2D, it is perceived a smaller presence of graph-based methods with arbitrary and irregular topologies. The contributions of this thesis aim at fulfilling this gap. A methodology based on the following pipeline is proposed: (i) Shape sampling, (ii) Samples structuring in graphs, (iii) Function defined on vertices, (iv) Multiscale analysis of graphs through the Spectral Wavelet Transform, (v) Features extraction from the Wavelet Transforms and (vi) Classification. For the stages (i), (ii), (iii), (v) and (vi), there are numerous possible approaches. One great challenge is to find a proper combination of approaches from the several available alternatives, which may be able to yield an effective pipeline for our purposes. In particular, for the stage (iii), given a graph representing a shape, the challenge is to identify a feature, which may be defined over the graph vertices. This feature should capture the underlying influence from the combinatorial structure of the entire network over each vertex, in multiple scales. The Spectral Graph Wavelet Transform will reveal such an underpining influence over each vertex. Yielded results from experiments on 2D benchmarks shapes widely known in literature, as well as results from astronomy applications to the analysis of unlabeled galaxies shapes from the Sloan Digital Sky Survey and labeled galaxies shapes by the Galaxy Zoo 2 Project are presented, demonstrating the achievements of the proposed technique, in comparison to classic approaches such as the 2D Fourier Transform and the 2D Continuous Wavelet Transform.