The Smoothest Velocity Field and Token Matching
This paper presents some mathematical results concerning the measurement of motion of contours. A fundamental problem of motion measurement in general is that the velocity field is not determined uniquely from the changing intensity patterns. Recently Hildreth & Ullman have studied a solut...
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| Language: | en_US |
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2004
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| Online Access: | http://hdl.handle.net/1721.1/5652 |
| _version_ | 1826199660461555712 |
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| author | Yuille, A.L. |
| author_facet | Yuille, A.L. |
| author_sort | Yuille, A.L. |
| collection | MIT |
| description | This paper presents some mathematical results concerning the measurement of motion of contours. A fundamental problem of motion measurement in general is that the velocity field is not determined uniquely from the changing intensity patterns. Recently Hildreth & Ullman have studied a solution to this problem based on an Extremum Principle [Hildreth (1983), Ullman & Hildreth (1983)]. That is, they formulate the measurement of motion as the computation of the smoothest velocity field consistent with the changing contour. We analyse this Extremum principle and prove that it is closely related to a matching scheme for motion measurement which matches points on the moving contour that have similar tangent vectors. We then derive necessary and sufficient conditions for the principle to yield the correct velocity field. These results have possible implications for the design of computer vision systems, and for the study of human vision. |
| first_indexed | 2024-09-23T11:23:28Z |
| id | mit-1721.1/5652 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:23:28Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/56522019-04-12T08:26:56Z The Smoothest Velocity Field and Token Matching Yuille, A.L. motion measurement velocity field optical flow szero crossings motion perception This paper presents some mathematical results concerning the measurement of motion of contours. A fundamental problem of motion measurement in general is that the velocity field is not determined uniquely from the changing intensity patterns. Recently Hildreth & Ullman have studied a solution to this problem based on an Extremum Principle [Hildreth (1983), Ullman & Hildreth (1983)]. That is, they formulate the measurement of motion as the computation of the smoothest velocity field consistent with the changing contour. We analyse this Extremum principle and prove that it is closely related to a matching scheme for motion measurement which matches points on the moving contour that have similar tangent vectors. We then derive necessary and sufficient conditions for the principle to yield the correct velocity field. These results have possible implications for the design of computer vision systems, and for the study of human vision. 2004-10-01T20:18:14Z 2004-10-01T20:18:14Z 1983-08-01 AIM-724 http://hdl.handle.net/1721.1/5652 en_US AIM-724 10 p. 1408443 bytes 1077372 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | motion measurement velocity field optical flow szero crossings motion perception Yuille, A.L. The Smoothest Velocity Field and Token Matching |
| title | The Smoothest Velocity Field and Token Matching |
| title_full | The Smoothest Velocity Field and Token Matching |
| title_fullStr | The Smoothest Velocity Field and Token Matching |
| title_full_unstemmed | The Smoothest Velocity Field and Token Matching |
| title_short | The Smoothest Velocity Field and Token Matching |
| title_sort | smoothest velocity field and token matching |
| topic | motion measurement velocity field optical flow szero crossings motion perception |
| url | http://hdl.handle.net/1721.1/5652 |
| work_keys_str_mv | AT yuilleal thesmoothestvelocityfieldandtokenmatching AT yuilleal smoothestvelocityfieldandtokenmatching |