Diffusion Geometry in Shape Analysis

Bronstein, Michael; Castellani, Umberto; Bronstein, Alex

Diffusion Geometry in Shape Analysis

Files

t2.pdf (55.21 MB)

Date

2012

Authors

Bronstein, Michael
Castellani, Umberto
Bronstein, Alex

Publisher

The Eurographics Association

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.

        @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
},
ISBN = {},
DOI = {/10.2312/conf/EG2012/tutorials/t2
}
}