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Globally Minimal Surfaces by Continuous Maximal Flows
January 2006 (vol. 28 no. 1)
pp. 106-118
ASCII Text
x 
 
Ben Appleton, Hugues Talbot, "Globally Minimal Surfaces by Continuous Maximal Flows," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 1, pp. 106-118, January, 2006.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2006.12,
author = {Ben Appleton and Hugues Talbot},
title = {Globally Minimal Surfaces by Continuous Maximal Flows},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {28},
number = {1},
issn = {0162-8828},
year = {2006},
pages = {106-118},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2006.12},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Globally Minimal Surfaces by Continuous Maximal Flows
IS - 1
SN - 0162-8828
SP106
EP118
EPD - 106-118
A1 - Ben Appleton,
A1 - Hugues Talbot,
PY - 2006
KW - Index Terms- Partial differential equations
KW - graph-theoretic methods
KW - edge and feature detection.
VL - 28
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
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 suboptimal (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.

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Index Terms:
Index Terms- Partial differential equations, graph-theoretic methods, edge and feature detection.
Citation:
Ben Appleton, Hugues Talbot, "Globally Minimal Surfaces by Continuous Maximal Flows," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 1, pp. 106-118, Jan. 2006, doi:10.1109/TPAMI.2006.12
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