TY - GEN
T1 - The Beltrami-Mumford-Shah functional
AU - Sochen, Nir
AU - Bar, Leah
PY - 2012
Y1 - 2012
N2 - We present in this paper a unifying generalization of the Mumford-Shah functional, in the Ambrosio-Totorelli set up, and the Beltrami framework. The generalization of the Ambrosio-Tortorelli is in using a diffusion tensor as an indicator of the edge set instead of a function. The generalization of the Beltrami framework is in adding a penalty term on the metric such that it is defined dynamically from minimization of the functional. We show that we are able, in this way, to have the benefits of true anisotropic diffusion together with a dynamically tuned metric/diffusion tensor. The functional is naturally defined in terms of the vielbein-the metric's square root. Preliminary results show improvement on both the Beltrami flow and the Mumford-Shah flow.
AB - We present in this paper a unifying generalization of the Mumford-Shah functional, in the Ambrosio-Totorelli set up, and the Beltrami framework. The generalization of the Ambrosio-Tortorelli is in using a diffusion tensor as an indicator of the edge set instead of a function. The generalization of the Beltrami framework is in adding a penalty term on the metric such that it is defined dynamically from minimization of the functional. We show that we are able, in this way, to have the benefits of true anisotropic diffusion together with a dynamically tuned metric/diffusion tensor. The functional is naturally defined in terms of the vielbein-the metric's square root. Preliminary results show improvement on both the Beltrami flow and the Mumford-Shah flow.
KW - Ambrosio-Tortorelli functional
KW - Beltrami framework
KW - Inhomogeneous diffusion
KW - Mumford-Shah functional
KW - anisotropic diffusion
UR - http://www.scopus.com/inward/record.url?scp=84855682340&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-24785-9_16
DO - 10.1007/978-3-642-24785-9_16
M3 - منشور من مؤتمر
SN - 9783642247842
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 183
EP - 193
BT - Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers
T2 - 3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011
Y2 - 29 May 2011 through 2 June 2011
ER -