We revisit the Chan-Vese model of image segmentation with a focus on the encoding with several integer-valued labeling functions. We relate several representations with varying amount of complexity and demonstrate the connection to recent relaxations for product sets and to dual maxflow-based formulations. For some special cases, it can be shown that it is possible to guarantee binary minimizers. While this is not true in general, we show how to derive a convex approximation of the combinatorial problem for more than 4 phases. We also provide a method to avoid overcounting of boundaries in the original Chan-Vese model without departing from the efficient product-set representation. Finally, we derive an algorithm to solve the associated discretized problem, and demonstrate that it allows to obtain good approximations for the segmentation problem with various number of regions. © 2013 Springer-Verlag.
|Original language||English (US)|
|Title of host publication||Energy Minimization Methods in Computer Vision and Pattern Recognition|
|Number of pages||14|
|State||Published - 2013|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This research has been supported by the Norwegian Re-search Council eVita project 214889, Award No. KUK-I1-007-43, made by KingAbdullah University of Science and Technology (KAUST), EPSRC first grantNo. EP/J009539/1, EPSRC/Isaac Newton Trust Small Grant, and Royal SocietyInternational Exchange Award No. IE110314.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.