Total variation regularization of shape signals

Baust M, Demaret L, Storath M, Navab N, Weinmann A (2015)

Publication Type: Conference contribution

Publication year: 2015

Journal

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition IEEE Computer Society; 1999

Publisher: IEEE Computer Society

Book Volume: 07-12-June-2015

Pages Range: 2075-2083

Conference Proceedings Title: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

Event location: Boston, MA, USA

ISBN: 9781467369640

DOI: 10.1109/CVPR.2015.7298819

Abstract

This paper introduces the concept of shape signals, i.e., series of shapes which have a natural temporal or spatial ordering, as well as a variational formulation for the regularization of these signals. The proposed formulation can be seen as the shape-valued generalization of the Rudin-Osher-Fatemi (ROF) functional for intensity images. We derive a variant of the classical finite-dimensional representation of Kendall, but our framework is generic in the sense that it can be combined with any shape space. This representation allows for the explicit computation of geodesics and thus facilitates the efficient numerical treatment of the variational formulation by means of the cyclic proximal point algorithm. Similar to the ROF-functional, we demonstrate experimentally that ℓ1-type penalties both for data fidelity term and regularizer perform best in regularizing shape signals. Finally, we show applications of our method to shape signals obtained from synthetic, photometric, and medical data sets.

Involved external institutions

Technische Universität München (TUM) DE Germany (DE) Helmholtz Zentrum München - Deutsches Forschungszentrum für Gesundheit und Umwelt (HMGU) / Helmholtz Munich DE Germany (DE) École Polytechnique Fédérale de Lausanne (EPFL) CH Switzerland (CH)

How to cite

APA:

Baust, M., Demaret, L., Storath, M., Navab, N., & Weinmann, A. (2015). Total variation regularization of shape signals. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (pp. 2075-2083). Boston, MA, USA: IEEE Computer Society.

MLA:

Baust, Maximilian, et al. "Total variation regularization of shape signals." Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015, Boston, MA, USA IEEE Computer Society, 2015. 2075-2083.

BibTeX: Download