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Modeling Three-Dimensional Morse and Morse-Smale Complexes Read chapter Read first chapter

2013 | OriginalPaper | Chapter

5. Nested Sphere Statistics of Skeletal Models

Authors : Stephen M. Pizer, Sungkyu Jung, Dibyendusekhar Goswami, Jared Vicory, Xiaojie Zhao, Ritwik Chaudhuri, James N. Damon, Stephan Huckemann, J. S. Marron

Published in: Innovations for Shape Analysis

Publisher: Springer Berlin Heidelberg

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Abstract

We seek a form of object model that exactly and completely captures the interior of most non-branching anatomic objects and simultaneously is well suited for probabilistic analysis on populations of such objects. We show that certain nearly medial, skeletal models satisfy these requirements. These models are first mathematically defined in continuous three-space, and then discrete representations formed by a tuple of spoke vectors are derived. We describe means of fitting these skeletal models into manual or automatic segmentations of objects in a way stable enough to support statistical analysis, and we sketch means of modifying these fits to provide good correspondences of spoke vectors across a training population of objects. Understanding will be developed that these discrete skeletal models live in an abstract space made of a Cartesian product of a Euclidean space and a collection of spherical spaces. Based on this understanding and the way objects change under various rigid and nonrigid transformations, a method analogous to principal component analysis called composite principal nested spheres will be seen to apply to learning a more efficient collection of modes of object variation about a new and more representative mean object than those provided by other representations and other statistical analysis methods. The methods are illustrated by application to hippocampi.

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previous chapter Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods
next chapter 3D Curve Skeleton Computation and Use for Discrete Shape Analysis
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Metadata
Title
Nested Sphere Statistics of Skeletal Models
Authors
Stephen M. Pizer
Sungkyu Jung
Dibyendusekhar Goswami
Jared Vicory
Xiaojie Zhao
Ritwik Chaudhuri
James N. Damon
Stephan Huckemann
J. S. Marron
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Innovations for Shape Analysis

Print ISBN: 978-3-642-34140-3

Electronic ISBN: 978-3-642-34141-0

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-34141-0_5

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