Globally minimal surfaces by continuous maximal flows

Appleton, Ben and Talbot, Hugues (2006) Globally minimal surfaces by continuous maximal flows. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28 1: 106-118. doi:10.1109/TPAMI.2006.12

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Author Appleton, Ben
Talbot, Hugues
Title Globally minimal surfaces by continuous maximal flows
Journal name IEEE Transactions on Pattern Analysis and Machine Intelligence   Check publisher's open access policy
ISSN 0162-8828
Publication date 2006-01
Year available 2005
Sub-type Article (original research)
DOI 10.1109/TPAMI.2006.12
Open Access Status File (Author Post-print)
Volume 28
Issue 1
Start page 106
End page 118
Total pages 13
Place of publication Piscatawa, NJ, U.S.A.
Publisher IEEE
Language eng
Subject 280208 Computer Vision
Abstract In this paper we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction. We present a solution, simulating a continuous maximal flow by a novel system of partial differential equations. Existing methods are either grid-biased (graph-based methods) or sub-optimal (active contours and surfaces). The solution simulates the flow of an ideal fluid with isotropic velocity constraints. Velocity constraints are defined by a metric derived from image data. An auxiliary potential function is introduced to create a system of partial differential equations. It is proven that the algorithm produces a globally maximal continuous flow at convergence, and that the globally minimal surface may be obtained trivially from the auxiliary potential. The bias of minimal surface methods toward small objects is also addressed. An efficient implementation is given for the flow simulation. The globally minimal surface algorithm is applied to segmentation in 2D and 3D as well as to stereo matching. Results in 2D agree with an existing minimal contour algorithm for planar images. Results in 3D segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias.
Keyword partial differential equations
graph-theoretic methods
edge and feature detection
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown
Additional Notes Accepted preprint; final version on available on request.

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Information Technology and Electrical Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 69 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 88 times in Scopus Article | Citations
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Created: Tue, 25 Oct 2005, 10:00:00 EST by Ben Appleton on behalf of School of Information Technol and Elec Engineering