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Scaling Theorems for Zero-Crossings.

Author: A L Yuille; T Poggio; MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB.
Publisher: Ft. Belvoir Defense Technical Information Center JUN 1983.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
The authors 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. They prove that in any dimension the only filter that does not create zero-crossings as the scale increases is the gaussian. This result can be generalized to apply to level-crossings of any linear differential operator: it applies  Read more...
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Document Type: Book
All Authors / Contributors: A L Yuille; T Poggio; MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB.
OCLC Number: 227590822
Description: 26 pages

Abstract:

The authors 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. They prove that in any dimension the only filter that does not create zero-crossings as the scale increases is the 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 intensity. In case of the second derivative along the gradient it is proved that there is no filter that avoids creation of zero-crossings.

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