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Published in:
Linear Inverse Problems Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Manifold Intrinsic Similarity

Authors : Alexander M. Bronstein, Michael M. Bronstein

Published in: Handbook of Mathematical Methods in Imaging

Publisher: Springer New York

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Abstract

Nonrigid shapes are ubiquitous in nature and are encountered at all levels of life, from macro to nano. The need to model such shapes and understand their behavior arises in many applications in imaging sciences, pattern recognition, computer vision, and computer graphics. Of particular importance is understanding which properties of the shape are attributed to deformations and which are invariant, i.e., remain unchanged. This chapter presents an approach to nonrigid shapes from the point of view of metric geometry. Modeling shapes as metric spaces, one can pose the problem of shape similarity as the similarity of metric spaces and harness tools from theoretical metric geometry for the computation of such a similarity.

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previous chapter Variational Methods in Shape Analysis
next chapter Image Segmentation with Shape Priors: Explicit Versus Implicit Representations
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Metadata
Title
Manifold Intrinsic Similarity
Authors
Alexander M. Bronstein
Michael M. Bronstein
Copyright Year
2015
Publisher
Springer New York
Book
Handbook of Mathematical Methods in Imaging

Print ISBN: 978-1-4939-0789-2

Electronic ISBN: 978-1-4939-0790-8

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-1-4939-0790-8_57

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