Title:
Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification
Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification
| dc.contributor.author | Tsai, Andy | en_US |
| dc.contributor.author | Yezzi, Anthony | en_US |
| dc.contributor.author | Willsky, Alan S. | en_US |
| dc.contributor.corporatename | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems | en_US |
| dc.contributor.corporatename | Georgia Institute of Technology. School of Electrical and Computer Engineering | en_US |
| dc.date.accessioned | 2013-09-10T14:37:00Z | |
| dc.date.available | 2013-09-10T14:37:00Z | |
| dc.date.issued | 2001-08 | |
| dc.description | ©2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. | en_US |
| dc.description | DOI: 10.1109/83.935033 | en_US |
| dc.description.abstract | In this work, we first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford–Shah paradigm from a curve evolution perspective. In particular, we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Each gradient step involves solving an optimal estimation problem for the data within each region, connecting curve evolution and the Mumford–Shah functional with the theory of boundary-value stochastic processes. The resulting active contour model offers a tractable implementation of the original Mumford–Shah model (i.e., without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation) to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner. Various implementations of this algorithm are introduced to increase its speed of convergence.We also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions. 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.identifier.citation | A. Tsai, A. Yezzi, and A. Willsky, "Curve Evolution Implementation of the Mumford-Shah Functional for Image Segmentation, Denoising, Interpolation, and Magnification," IEEE Transactions on Image Processing, 10 (8), 1169-1186 (August 2001) | en_US |
| dc.identifier.doi | 10.1109/83.935033 | |
| dc.identifier.issn | 1057-7149 | |
| dc.identifier.uri | http://hdl.handle.net/1853/48919 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Georgia Institute of Technology | en_US |
| dc.publisher.original | Institute of Electrical and Electronics Engineers | en_US |
| dc.subject | Active contours | en_US |
| dc.subject | Boundary-value stochastic processes | en_US |
| dc.subject | Curve evolution | en_US |
| dc.subject | Denoising | en_US |
| dc.subject | Image interpolation | en_US |
| dc.subject | Image magnification | en_US |
| dc.subject | Level sets methods | en_US |
| dc.subject | Missing data problems | en_US |
| dc.subject | Mumford– Shah functional | en_US |
| dc.subject | Reconstruction | en_US |
| dc.subject | Segmentation | en_US |
| dc.subject | Snakes | en_US |
| dc.title | Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification | en_US |
| dc.type | Text | |
| dc.type.genre | Article | |
| dspace.entity.type | Publication | |
| local.contributor.author | Yezzi, Anthony | |
| local.contributor.corporatename | School of Electrical and Computer Engineering | |
| local.contributor.corporatename | College of Engineering | |
| relation.isAuthorOfPublication | 53ee63a2-04fd-454f-b094-02a4601962d8 | |
| relation.isOrgUnitOfPublication | 5b7adef2-447c-4270-b9fc-846bd76f80f2 | |
| relation.isOrgUnitOfPublication | 7c022d60-21d5-497c-b552-95e489a06569 |
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