Multigrid Relaxation Methods and the Analysis of Lightness, Shading and Flow
Image analysis problems, posed mathematically as variational principles or as partial differential equations, are amenable to numerical solution by relaxation algorithms that are local, iterative, and often parallel. Although they are well suited structurally for implementation on massively pa...
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| Language: | en_US |
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2004
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| Online Access: | http://hdl.handle.net/1721.1/5633 |
| _version_ | 1811082081123434496 |
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| author | Terzopoulos, Demetri |
| author_facet | Terzopoulos, Demetri |
| author_sort | Terzopoulos, Demetri |
| collection | MIT |
| description | Image analysis problems, posed mathematically as variational principles or as partial differential equations, are amenable to numerical solution by relaxation algorithms that are local, iterative, and often parallel. Although they are well suited structurally for implementation on massively parallel, locally-interconnected computational architectures, such distributed algorithms are seriously handicapped by an inherent inefficiency at propagating constraints between widely separated processing elements. Hence, they converge extremely slowly when confronted by the large representations necessary for low-level vision. Application of multigrid methods can overcome this drawback, as we established in previous work on 3-D surface reconstruction. In this paper, we develop efficient multiresolution iterative algorithms for computing lightness, shape-from-shading, and optical flow, and we evaluate the performance of these algorithms on Synthetic images. The multigrid methodology that we describe is broadly applicable in low-level vision. Notably, it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill-posed visual reconstruction problems. |
| first_indexed | 2024-09-23T11:57:16Z |
| id | mit-1721.1/5633 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:57:16Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/56332019-04-12T08:26:47Z Multigrid Relaxation Methods and the Analysis of Lightness, Shading and Flow Terzopoulos, Demetri computer vision lightness optical flow partialsdifferential equations multigrid relaxation shape from shading svariational principles parallel Image analysis problems, posed mathematically as variational principles or as partial differential equations, are amenable to numerical solution by relaxation algorithms that are local, iterative, and often parallel. Although they are well suited structurally for implementation on massively parallel, locally-interconnected computational architectures, such distributed algorithms are seriously handicapped by an inherent inefficiency at propagating constraints between widely separated processing elements. Hence, they converge extremely slowly when confronted by the large representations necessary for low-level vision. Application of multigrid methods can overcome this drawback, as we established in previous work on 3-D surface reconstruction. In this paper, we develop efficient multiresolution iterative algorithms for computing lightness, shape-from-shading, and optical flow, and we evaluate the performance of these algorithms on Synthetic images. The multigrid methodology that we describe is broadly applicable in low-level vision. Notably, it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill-posed visual reconstruction problems. 2004-10-01T20:17:44Z 2004-10-01T20:17:44Z 1984-10-01 AIM-803 http://hdl.handle.net/1721.1/5633 en_US AIM-803 23 p. 5076182 bytes 3972784 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | computer vision lightness optical flow partialsdifferential equations multigrid relaxation shape from shading svariational principles parallel Terzopoulos, Demetri Multigrid Relaxation Methods and the Analysis of Lightness, Shading and Flow |
| title | Multigrid Relaxation Methods and the Analysis of Lightness, Shading and Flow |
| title_full | Multigrid Relaxation Methods and the Analysis of Lightness, Shading and Flow |
| title_fullStr | Multigrid Relaxation Methods and the Analysis of Lightness, Shading and Flow |
| title_full_unstemmed | Multigrid Relaxation Methods and the Analysis of Lightness, Shading and Flow |
| title_short | Multigrid Relaxation Methods and the Analysis of Lightness, Shading and Flow |
| title_sort | multigrid relaxation methods and the analysis of lightness shading and flow |
| topic | computer vision lightness optical flow partialsdifferential equations multigrid relaxation shape from shading svariational principles parallel |
| url | http://hdl.handle.net/1721.1/5633 |
| work_keys_str_mv | AT terzopoulosdemetri multigridrelaxationmethodsandtheanalysisoflightnessshadingandflow |