Spectral signatures for non-rigid 3D shape retrieval

This thesis addresses problems associated with computing spectral shape signatures for non-rigid 3D object retrieval. More specifically, we use spectral shape analysis tools to describe the characteristics of different 3D object representations. This thesis tries to answer whether spectral shape analysis tools can enhance classical shape signatures to improve the performance of the non-rigid shape retrieval problem. Furthermore, it describes the stages of the framework for composing non-rigid shape signatures, built from the shape Laplacian. This thesis presents four methods to improve each part of the framework for computing spectral shape signatures. The first stage comprises computing the right shape spectrum to describe 3D objects. We introduce the Kinetic Laplace-Beltrami operator which computes enhanced spectral components from 3D meshes specific to non-rigid shape retrieval and we also introduce the Mesh-Free Laplace Operator which computes more precise and robust spectral components from 3D point clouds. After computing the shape spectrum, we propose the Improved Wave Kernel Signature, a more discriminative local descriptor built from the Laplacian eigenfunctions. This descriptor is used throughout this thesis and it achieves, in most cases, state-of-the-art performances. Then, we define a new framework for encoding sparse local descriptors into shape signatures that can be compared to each other. Here, we show how to use the Fisher Vector and Super Vector to encode spectral descriptors and also how to compute dissimilarities between shape signatures using the Efficient Manifold Ranking. Furthermore, we describe the construction of the Point-Cloud Shape Retrieval of Non-Rigid Toys dataset, aimed in testing non-rigid shape signatures on point clouds, after we evidenced a lack of point-cloud benchmarks in the literature. With these ingredients, we are able to construct shape signatures which are specially built for non-rigid shape retrieval.