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2017 | OriginalPaper | Chapter

Spectral Kernels for Probabilistic Analysis and Clustering of Shapes

Authors : Loic Le Folgoc, Aditya V. Nori, Antonio Criminisi

Published in: Information Processing in Medical Imaging

Publisher: Springer International Publishing

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Abstract

We propose a framework for probabilistic shape clustering based on kernel-space embeddings derived from spectral signatures. Our root motivation is to investigate practical yet principled clustering schemes that rely on geometrical invariants of shapes rather than explicit registration. To that end we revisit the use of the Laplacian spectrum and introduce a parametric family of reproducing kernels for shapes, extending WESD [12] and shape DNA [20] like metrics. Parameters provide control over the relative importance of local and global shape features and can be adjusted to emphasize a scale of interest. As a result of kernelization, shapes are embedded in an infinite-dimensional inner product space. We leverage this structure to formulate shape clustering via a Bayesian mixture of kernel-space Principal Component Analysers. We derive simple variational Bayes inference schemes in Hilbert space, addressing technicalities stemming from the infinite dimensionality. The proposed approach is validated on tasks of unsupervised clustering of sub-cortical structures, as well as classification of cardiac left ventricles w.r.t. pathological groups.

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Footnotes
1
Publicly available from http://​imageprocessingp​lace.​com. Developed by Vaibhav E. Waghmare, Govt. College of Engineering Aurangabad, 431 005 MS, INDIA.
 
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Metadata
Title
Spectral Kernels for Probabilistic Analysis and Clustering of Shapes
Authors
Loic Le Folgoc
Aditya V. Nori
Antonio Criminisi
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-59050-9_6

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