Diffusion Geometry in Shape Analysis
Abstract
Over the last decade, the intersections between 3D shape analysis and image processing have become a topic of increasing interest in the computer graphics community. Nevertheless, when attempting to apply current image analysis methods to 3D shapes (feature-based description, registration, recognition, indexing, etc.) one has to face fundamental differences between images and geometric objects. Shape analysis poses new challenges that are non-existent in image analysis. The purpose of this tutorial is to overview the foundations of shape analysis and to formulate state-of-the-art theoretical and computational methods for shape description based on their intrinsic geometric properties. The emerging field of diffusion geometry provides a generic framework for many methods in the analysis of geometric shapes and objects. The tutorial will present in a new light the problems of shape analysis based on diffusion geometric constructions such as manifold embeddings using the Laplace-Beltrami and heat operator, heat kernel local descriptors, diffusion and commute-time metrics.
BibTeX
@inproceedings {10.2312:conf:EG2012:tutorials:t2,
booktitle = {Eurographics 2012 - Tutorials},
editor = {Renato Pajarola and Michela Spagnuolo},
title = {{Diffusion Geometry in Shape Analysis}},
author = {Bronstein, Michael and Castellani, Umberto and Bronstein, Alex},
year = {2012},
publisher = {The Eurographics Association},
ISSN = {1017-4656},
DOI = {10.2312/conf/EG2012/tutorials/t2}
}
booktitle = {Eurographics 2012 - Tutorials},
editor = {Renato Pajarola and Michela Spagnuolo},
title = {{Diffusion Geometry in Shape Analysis}},
author = {Bronstein, Michael and Castellani, Umberto and Bronstein, Alex},
year = {2012},
publisher = {The Eurographics Association},
ISSN = {1017-4656},
DOI = {10.2312/conf/EG2012/tutorials/t2}
}