<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Segmentation is a typical task in image processing having as main goal the partitioning of the image into multiple segments in order to simplify its interpretation and analysis. One of the more popular segmentation model, formulated by Chan-Vese, is the piecewise constant Mumford-Shah model restricted to the case of two-phase segmentation. We consider a convex relaxation formulation of the segmentation model, that can be regarded as a nonsmooth optimization problem, because the presence of the l1-term. Two basic approaches in optimization can be distinguished to deal with its non differentiability: the smoothing methods and the nonsmoothing methods. In this work, a numerical comparison of some first order methods belongs of both approaches are presented. The relationships among the different methods are shown, and accuracy and efficiency tests are also performed on several images.</p></abstract>

Segmentation is a typical task in image processing having as main goal the partitioning of the image into multiple segments in order to simplify its interpretation and analysis. One of the more popular segmentation model, formulated by Chan-Vese, is the piecewise constant Mumford-Shah model restricted to the case of two-phase segmentation. We consider a convex relaxation formulation of the segmentation model, that can be regarded as a nonsmooth optimization problem, because the presence of the l1-term. Two basic approaches in optimization can be distinguished to deal with its non differentiability: the smoothing methods and the nonsmoothing methods. In this work, a numerical comparison of some first order methods belongs of both approaches are presented. The relationships among the different methods are shown, and accuracy and efficiency tests are also performed on several images.

Comparison of minimization methods for nonsmooth image segmentation

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Comparison of minimization methods for nonsmooth image segmentation"}

Segmentation is a typical task in image processing having as main goal the partitioning of the image into multiple segments in order to simplify its...

Comparison of minimization methods for nonsmooth image segmentation

Published Online: Mar 24, 2018

Page range: 68 - 86

Received: Aug 01, 2017

Accepted: Feb 02, 2018

DOI: https://doi.org/10.1515/caim-2018-0005

Keywords
nonsmooth optimization, first order methods, image segmentation

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Comparison of minimization methods for nonsmooth image segmentation

Published Online: Mar 24, 2018

Page range: 68 - 86

Received: Aug 01, 2017

Accepted: Feb 02, 2018

DOI: https://doi.org/10.1515/caim-2018-0005

Keywordsnonsmooth optimization, first order methods, image segmentation

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
nonsmooth optimization, first order methods, image segmentation