A PDE Solution of Brownian Warping

Mads Nielsen; Peter Johansen

doi:10.1007/b97873

A PDE Solution of Brownian Warping

Abstract

A Brownian motion model in the group of diffeomorphisms has been introduced as creating a least committed prior on warps. This prior is source destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 create invertible warps. In this paper, we formulate a Partial Differential Equation for obtaining the maximum likelihood warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice source-destination symmetric.

Original language	English
Title of host publication	Computer Vision - ECCV 2004 : 8th European Conference on Computer Vision, Prague, Czech Republic, May 11-14, 2004. Proceedings, Part IV
Publisher	<Forlag uden navn>
Publication date	2004
Pages	180-191
ISBN (Print)	978-3-540-21981-1
DOIs	https://doi.org/10.1007/b97873
Publication status	Published - 2004
Externally published	Yes
Event	European Conference on Computer Vision - Prague, Czech Republic Duration: 29 Nov 2010 → … Conference number: 8

Conference

Conference	European Conference on Computer Vision
Number	8
Country/Territory	Czech Republic
City	Prague
Period	29/11/2010 → …

Series	Lecture notes in computer science
Volume	3024/2004
ISSN	0302-9743

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Cite this

A PDE Solution of Brownian Warping. / Nielsen, Mads; Johansen, Peter.

Computer Vision - ECCV 2004: 8th European Conference on Computer Vision, Prague, Czech Republic, May 11-14, 2004. Proceedings, Part IV. <Forlag uden navn>, 2004. p. 180-191 (Lecture notes in computer science, Vol. 3024/2004).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Nielsen, M & Johansen, P 2004, A PDE Solution of Brownian Warping. in Computer Vision - ECCV 2004: 8th European Conference on Computer Vision, Prague, Czech Republic, May 11-14, 2004. Proceedings, Part IV. <Forlag uden navn>, Lecture notes in computer science, vol. 3024/2004, pp. 180-191, European Conference on Computer Vision, Prague, Czech Republic, 29/11/2010. https://doi.org/10.1007/b97873

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A PDE Solution of Brownian Warping

Abstract

Conference

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