Scaling Theorems for Zero-Crossings
We characterize some properties of the zero-crossings of the laplacian of signals - in particular images - filtered with linear filters, as a function of the scale of the filter (following recent work by A. Witkin, 1983). We prove that in any dimension the only filter that does not create zero cross...
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Language: | en_US |
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2004
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Online Access: | http://hdl.handle.net/1721.1/5655 |
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author | Yuille, A.L. Poggio, T. |
author_facet | Yuille, A.L. Poggio, T. |
author_sort | Yuille, A.L. |
collection | MIT |
description | We characterize some properties of the zero-crossings of the laplacian of signals - in particular images - filtered with linear filters, as a function of the scale of the filter (following recent work by A. Witkin, 1983). We prove that in any dimension the only filter that does not create zero crossings as the scale increases is gaussian. This result can be generalized to apply to level-crossings of any linear differential operator: it applies in particular to ridges and ravines in the image density. In the case of the second derivative along the gradient we prove that there is no filter that avoids creation of zero-crossings. |
first_indexed | 2024-09-23T14:45:17Z |
id | mit-1721.1/5655 |
institution | Massachusetts Institute of Technology |
language | en_US |
last_indexed | 2024-09-23T14:45:17Z |
publishDate | 2004 |
record_format | dspace |
spelling | mit-1721.1/56552019-04-10T18:27:45Z Scaling Theorems for Zero-Crossings Yuille, A.L. Poggio, T. We characterize some properties of the zero-crossings of the laplacian of signals - in particular images - filtered with linear filters, as a function of the scale of the filter (following recent work by A. Witkin, 1983). We prove that in any dimension the only filter that does not create zero crossings as the scale increases is gaussian. This result can be generalized to apply to level-crossings of any linear differential operator: it applies in particular to ridges and ravines in the image density. In the case of the second derivative along the gradient we prove that there is no filter that avoids creation of zero-crossings. 2004-10-01T20:18:29Z 2004-10-01T20:18:29Z 1983-06-01 AIM-722 http://hdl.handle.net/1721.1/5655 en_US AIM-722 25 p. 1729675 bytes 1360325 bytes application/postscript application/pdf application/postscript application/pdf |
spellingShingle | Yuille, A.L. Poggio, T. Scaling Theorems for Zero-Crossings |
title | Scaling Theorems for Zero-Crossings |
title_full | Scaling Theorems for Zero-Crossings |
title_fullStr | Scaling Theorems for Zero-Crossings |
title_full_unstemmed | Scaling Theorems for Zero-Crossings |
title_short | Scaling Theorems for Zero-Crossings |
title_sort | scaling theorems for zero crossings |
url | http://hdl.handle.net/1721.1/5655 |
work_keys_str_mv | AT yuilleal scalingtheoremsforzerocrossings AT poggiot scalingtheoremsforzerocrossings |