Curve Evolution, Boundary-Value Stochastic Processes, the Mumford-Shah Problem, and Missing Data Applications

Tsai, Andy; Yezzi, Anthony; Willsky, Alan S.

Title:

Curve Evolution, Boundary-Value Stochastic Processes, the Mumford-Shah Problem, and Missing Data Applications

dc.contributor.author	Tsai, Andy
dc.contributor.author	Yezzi, Anthony
dc.contributor.author	Willsky, Alan S.
dc.contributor.corporatename	Georgia Institute of Technology. School of Electrical and Computer Engineering	en_US
dc.contributor.corporatename	Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science	en_US
dc.date.accessioned	2013-09-09T14:25:43Z
dc.date.available	2013-09-09T14:25:43Z
dc.date.issued	2000-09
dc.description	© 2000 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.	en_US
dc.description	Presented at the 2000 IEEE International Conference on Image Processing (ICIP 2000), 10-13 September 2000, Vancouver, BC.
dc.description	DOI: 10.1109/ICIP.2000.899521
dc.description.abstract	We present an estimation-theoretic approach to curve evolution for the Mumford-Shah problem. By viewing an active contour as the set of discontinuities in the Mumford-Shah problem, we may use the corresponding functional to determine gradient descent evolution equations to deform the active contour. In each gradient descent step, we solve a corresponding optimal estimation problem, connecting the Mumford-Shah functional and curve evolution with the theory of boundary-value stochastic processes. In employing the Mumford-Shah functional, our active contour model inherits its attractive ability to generate, in a coupled manner, both a smooth reconstruction and a segmentation of the image. Next, by generalizing the data fidelity term of the original Mumford-Shah functional to incorporate a spatially varying penalty, we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing. This more general model leads us to a novel PDE-based approach for simultaneous image magnification, segmentation, and smoothing, thereby extending the traditional applications of the Mumford-Shah functional which only considers simultaneous segmentation and smoothing.	en_US
dc.embargo.terms	null	en_US
dc.identifier.citation	Tsai, A.; Yezzi, A., Jr; & Willsky, A.S. (2000). "Curve Evolution, Boundary-Value Stochastic Processes, the Mumford-Shah Problem, and Missing Data Applications". Proceedings of the 2000 International Conference on Image Processing (ICIP 2000), Vol.3, (September 2000), pp.588-591.	en_US
dc.identifier.doi	10.1109/ICIP.2000.899521
dc.identifier.isbn	0-7803-6297-7
dc.identifier.issn	1522-4880
dc.identifier.uri	http://hdl.handle.net/1853/48847
dc.language.iso	en_US	en_US
dc.publisher	Georgia Institute of Technology	en_US
dc.publisher.original	Institute of Electrical and Electronics Engineers
dc.subject	Boundary-value stochastic processes	en_US
dc.subject	Contour	en_US
dc.subject	Curve evolution	en_US
dc.subject	Estimation-theoretic approach	en_US
dc.subject	Gradient descent	en_US
dc.subject	Image magnification	en_US
dc.subject	Mumford-Shah functional	en_US
dc.subject	Segmentation	en_US
dc.subject	Smoothing	en_US
dc.title	Curve Evolution, Boundary-Value Stochastic Processes, the Mumford-Shah Problem, and Missing Data Applications	en_US
dc.type	Text
dc.type.genre	Proceedings
dspace.entity.type	Publication
local.contributor.author	Yezzi, Anthony
local.contributor.corporatename	School of Electrical and Computer Engineering
local.contributor.corporatename	College of Engineering
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