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Error-Controlled Model Approximation for Gaussian Process Morphable Models

Dölz, Jürgen and Gerig, Thomas and Lüthi, Marcel and Harbrecht, Helmut and Vetter, Thomas. (2019) Error-Controlled Model Approximation for Gaussian Process Morphable Models. Journal of Mathematical Imaging and Vision, 61 (4). pp. 443-457.

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Official URL: https://edoc.unibas.ch/69076/

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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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Informatik > Computergraphik Bilderkennung (Vetter)
UniBasel Contributors:Vetter, Thomas and Harbrecht, Helmut and Lüthi, Marcel and Gerig, Thomas
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Springer
ISSN:0924-9907
e-ISSN:1573-7683
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
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Last Modified:22 Jan 2020 13:34
Deposited On:27 Feb 2019 08:58

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