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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Main Authors: Yuille, A.L., Poggio, T.
Language:en_US
Published: 2004
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.
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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