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Error-Controlled Model Approximation for Gaussian Process Morphable Models

  • Jürgen Dölz
  • Thomas Gerig
  • Marcel Lüthi
  • Helmut Harbrecht
  • Thomas Vetter
Article
  • 99 Downloads

Abstract

Gaussian Process Morphable Models (GPMMs) unify a variety of non-rigid deformation models for surface and image registration. Deformation models, such as B-splines, radial basis functions, and PCA models are defined as a probability distribution using a Gaussian process. The method depends heavily on the low-rank approximation of the Gaussian process, which is mandatory to obtain a parametric representation of the model. In this article, we propose the use of the pivoted Cholesky decomposition for this task, which has the following advantages: (1) Compared to the current state of the art used in GPMMs, it provides a fully controllable approximation error. The algorithm greedily computes new basis functions until the user-defined approximation accuracy is reached. (2) Unlike the currently used approach, this method can be used in a black-box-like scenario, whereas the method automatically chooses the amount of basis functions for a given model and accuracy. (3) We propose the Newton basis as an alternative basis for GPMMs. The proposed basis does not need an SVD computation and can be iteratively refined. We show that the proposed basis functions achieve competitive registration results while providing the mentioned advantages for its computation.

Keywords

Non-rigid registration Gaussian process Image registration Shape registration Pivoted Cholesky Gaussian Process Morphable Models GPMM Statistical shape modeling 

Notes

Acknowledgements

This work has been funded as part of two Swiss National Science foundation projects in the context of the Projects SNF153297 and SNF156101. We thank Andreas Morel-Forster and Volker Roth for interesting and enlightening discussions. A special thanks goes to Ghazi Bouabene and Christoph Langguth for their work on the Scalismo software, in which all the methods are implemented.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of BaselBaselSwitzerland

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