The Elastic Ratio: Introducing Curvature Into RatioBased Image Segmentation
(2011) In IEEE Transactions on Image Processing 20(9). p.25652581 Abstract
 We present the first ratiobased image segmentation method that allows imposing curvature regularity of the region boundary. Our approach is a generalization of the ratio framework pioneered by Jermyn and Ishikawa so as to allow penalty functions that take into account the local curvature of the curve. The key idea is to cast the segmentation problem as one of finding cyclic paths of minimal ratio in a graph where each graph node represents a line segment. Among ratios whose discrete counterparts can be globally minimized with our approach, we focus in particular on the elastic ratio integral(L(C))(0) del I(C(S)) . (C'(S)(perpendicular to) ds/nu L(C) + integral(L(C))(0) broken vertical bar kappa(C)(S)broken vertical bar(q) ds that depends,... (More)
 We present the first ratiobased image segmentation method that allows imposing curvature regularity of the region boundary. Our approach is a generalization of the ratio framework pioneered by Jermyn and Ishikawa so as to allow penalty functions that take into account the local curvature of the curve. The key idea is to cast the segmentation problem as one of finding cyclic paths of minimal ratio in a graph where each graph node represents a line segment. Among ratios whose discrete counterparts can be globally minimized with our approach, we focus in particular on the elastic ratio integral(L(C))(0) del I(C(S)) . (C'(S)(perpendicular to) ds/nu L(C) + integral(L(C))(0) broken vertical bar kappa(C)(S)broken vertical bar(q) ds that depends, given an image I, on the oriented boundary C of the segmented region candidate. Minimizing this ratio amounts to finding a curve, neither small nor too curvy, through which the brightness flux is maximal. We prove the existence of minimizers for this criterion among continuous curves with mild regularity assumptions. We also prove that the discrete minimizers provided by our graphbased algorithm converge, as the resolution increases, to continuous minimizers. In contrast to most existing segmentation methods with computable and meaningful, i.e., nondegenerate, global optima, the proposed approach is fully unsupervised in the sense that it does not require any kind of user input such as seed nodes. Numerical experiments demonstrate that curvature regularity allows substantial improvement of the quality of segmentations. Furthermore, our results allow drawing conclusions about global optima of a parameterizationindependent version of the snakes functional: the proposed algorithm allows determining parameter values where the functional has a meaningful solution and simultaneously provides the corresponding global solution. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2161365
 author
 Schoenemann, Thomas ^{LU} ; Masnou, Simon and Cremers, Daniel
 organization
 publishing date
 2011
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Contourbased segmentation, curvature, global optimization, graph, cycles, image segmentation, snakes model, unsupervised segmentation
 in
 IEEE Transactions on Image Processing
 volume
 20
 issue
 9
 pages
 2565  2581
 publisher
 IEEEInstitute of Electrical and Electronics Engineers Inc.
 external identifiers

 wos:000294132800014
 ISSN
 19410042
 DOI
 10.1109/TIP.2011.2118225
 language
 English
 LU publication?
 yes
 id
 5d1c52fa7b2a4946a3a7f5edce068ee8 (old id 2161365)
 date added to LUP
 20110921 13:55:06
 date last changed
 20160920 05:38:34
@article{5d1c52fa7b2a4946a3a7f5edce068ee8, abstract = {We present the first ratiobased image segmentation method that allows imposing curvature regularity of the region boundary. Our approach is a generalization of the ratio framework pioneered by Jermyn and Ishikawa so as to allow penalty functions that take into account the local curvature of the curve. The key idea is to cast the segmentation problem as one of finding cyclic paths of minimal ratio in a graph where each graph node represents a line segment. Among ratios whose discrete counterparts can be globally minimized with our approach, we focus in particular on the elastic ratio integral(L(C))(0) del I(C(S)) . (C'(S)(perpendicular to) ds/nu L(C) + integral(L(C))(0) broken vertical bar kappa(C)(S)broken vertical bar(q) ds that depends, given an image I, on the oriented boundary C of the segmented region candidate. Minimizing this ratio amounts to finding a curve, neither small nor too curvy, through which the brightness flux is maximal. We prove the existence of minimizers for this criterion among continuous curves with mild regularity assumptions. We also prove that the discrete minimizers provided by our graphbased algorithm converge, as the resolution increases, to continuous minimizers. In contrast to most existing segmentation methods with computable and meaningful, i.e., nondegenerate, global optima, the proposed approach is fully unsupervised in the sense that it does not require any kind of user input such as seed nodes. Numerical experiments demonstrate that curvature regularity allows substantial improvement of the quality of segmentations. Furthermore, our results allow drawing conclusions about global optima of a parameterizationindependent version of the snakes functional: the proposed algorithm allows determining parameter values where the functional has a meaningful solution and simultaneously provides the corresponding global solution.}, author = {Schoenemann, Thomas and Masnou, Simon and Cremers, Daniel}, issn = {19410042}, keyword = {Contourbased segmentation,curvature,global optimization,graph,cycles,image segmentation,snakes model,unsupervised segmentation}, language = {eng}, number = {9}, pages = {25652581}, publisher = {IEEEInstitute of Electrical and Electronics Engineers Inc.}, series = {IEEE Transactions on Image Processing}, title = {The Elastic Ratio: Introducing Curvature Into RatioBased Image Segmentation}, url = {http://dx.doi.org/10.1109/TIP.2011.2118225}, volume = {20}, year = {2011}, }