Efficient algorithm for level set method preserving distance function.

Details

Serval ID
serval:BIB_081AD0661796
Type
Article: article from journal or magazin.
Collection
Publications
Title
Efficient algorithm for level set method preserving distance function.
Journal
IEEE Transactions On Image Processing
Author(s)
Estellers V., Zosso D., Lai R., Osher S., Thiran J.P., Bresson X.
ISSN
1941-0042 (Electronic)
ISSN-L
1057-7149
Publication state
Published
Issued date
2012
Volume
21
Number
12
Pages
4722-4734
Language
english
Notes
Publication types: Journal Article ; Research Support, Non-U.S. Gov't ; Research Support, U.S. Gov't, Non-P.H.S.Publication Status: ppublish
Abstract
The level set method is a popular technique for tracking moving interfaces in several disciplines, including computer vision and fluid dynamics. However, despite its high flexibility, the original level set method is limited by two important numerical issues. First, the level set method does not implicitly preserve the level set function as a distance function, which is necessary to estimate accurately geometric features, s.a. the curvature or the contour normal. Second, the level set algorithm is slow because the time step is limited by the standard Courant-Friedrichs-Lewy (CFL) condition, which is also essential to the numerical stability of the iterative scheme. Recent advances with graph cut methods and continuous convex relaxation methods provide powerful alternatives to the level set method for image processing problems because they are fast, accurate, and guaranteed to find the global minimizer independently to the initialization. These recent techniques use binary functions to represent the contour rather than distance functions, which are usually considered for the level set method. However, the binary function cannot provide the distance information, which can be essential for some applications, s.a. the surface reconstruction problem from scattered points and the cortex segmentation problem in medical imaging. In this paper, we propose a fast algorithm to preserve distance functions in level set methods. Our algorithm is inspired by recent efficient l(1) optimization techniques, which will provide an efficient and easy to implement algorithm. It is interesting to note that our algorithm is not limited by the CFL condition and it naturally preserves the level set function as a distance function during the evolution, which avoids the classical re-distancing problem in level set methods. We apply the proposed algorithm to carry out image segmentation, where our methods prove to be 5-6 times faster than standard distance preserving level set techniques. We also present two applications where preserving a distance function is essential. Nonetheless, our method stays generic and can be applied to any level set methods that require the distance information.
Keywords
Algorithms, Animals, Databases, Factual, Diagnostic Imaging/methods, Humans, Image Processing, Computer-Assisted/methods
Pubmed
Web of science
Create date
06/01/2014 18:05
Last modification date
20/08/2019 12:30
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