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Robust Fréchet Mean and PGA on Riemannian Manifolds with Applications to Neuroimaging Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Constructing Shape Spaces from a Topological Perspective

Authors : Christoph Hofer, Roland Kwitt, Marc Niethammer, Yvonne Höller, Eugen Trinka, Andreas Uhl, for the ADNI

Published in: Information Processing in Medical Imaging

Publisher: Springer International Publishing

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Abstract

We consider the task of constructing (metric) shape space(s) from a topological perspective. In particular, we present a generic construction scheme and demonstrate how to apply this scheme when shape is interpreted as the differences that remain after factoring out translation, scaling and rotation. This is achieved by leveraging a recently proposed injective functional transform of 2D/3D (binary) objects, based on persistent homology. The resulting shape space is then equipped with a similarity measure that is (1) by design robust to noise and (2) fulfills all metric axioms. From a practical point of view, analyses of object shape can then be carried out directly on segmented objects obtained from some imaging modality without any preprocessing, such as alignment, smoothing, or landmark selection. We demonstrate the utility of the approach on the problem of distinguishing segmented hippocampi from normal controls vs. patients with Alzheimer’s disease in a challenging setup where volume changes are no longer discriminative.

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previous chapter From Label Maps to Generative Shape Models: A Variational Bayesian Learning Approach
next chapter A Discriminative Event Based Model for Alzheimer’s Disease Progression Modeling
Footnotes
1
For dimension \(k>0\), we can take the interior of the convex hull of the defining vertices and, for dimension 0, a simplex is mapped to its defining vertex.
 
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Metadata
Title
Constructing Shape Spaces from a Topological Perspective
Authors
Christoph Hofer
Roland Kwitt
Marc Niethammer
Yvonne Höller
Eugen Trinka
Andreas Uhl
for the ADNI
Copyright Year
2017
Book
Information Processing in Medical Imaging

Print ISBN: 978-3-319-59049-3

Electronic ISBN: 978-3-319-59050-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-59050-9_9

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