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Alexander Bronstein: Spectral methods in deformable shape analysis |
Over the last decade, 3D shape analysis has become a topic of increasing
interest in the computer vision 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 lecture 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. Diffusion geometry is
constructed by examining heat propagation on non-Euclidean domains,
naturally extending classical harmonic analysis. The lecture 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.
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