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Scale-space properties of quadratic feature detectors

Kube, Paul and Perona, Pietro (1996) Scale-space properties of quadratic feature detectors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18 (10). pp. 987-999. ISSN 0162-8828. http://resolver.caltech.edu/CaltechAUTHORS:KUBieeetpami96

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Abstract

We consider the scale-space properties of quadratic feature detectors and, in particular, investigate whether, like linear detectors, they permit a scale selection scheme with the “causality property”, which guarantees that features are never created as the scale is coarsened. We concentrate on the design of one dimensional detectors with two constituent filters, with the scale selection implemented as convolution and a scaling function. We consider two special cases of interest: the constituent filter pairs related by the Hilbert transform, and by the first spatial derivative. We show that, under reasonable assumptions, Hilbert-pair quadratic detectors cannot have the causality property. In the case of derivative-pair detectors, we describe a family of scaling functions related to fractional derivatives of the Gaussian that are necessary and sufficient for causality. In addition, we report experiments that show the effects of these properties in practice. We thus demonstrate that at least one class of quadratic feature detectors has the same desirable scaling property as the more familiar detectors based on linear filtering.


Item Type:Article
Additional Information:© Copyright 1996 IEEE. Reprinted with permission. Manuscript received Dec. 15, 1984. Recommended for acceptance by J. Daugman. An earlier version of this work appeared in the Proceedings of the Third European Conference on Computer Vision, May 1994. This research was supported in part by the U.S. National Science Foundation (RIA-IRI 9211651, NYI-IRI 9306155, Caltech ERC for Neuromorphic Engineering), and by the U.S. Office of Naval Research (N00014-93-1-0990). The authors are grateful to John Canny, Bill Helton, Jean-Michel Morel, and Christian Ronse for helpful discussions and for reading drafts of the paper. Comments and suggestions by PAMI Associate Editor John Daugman were very useful and much appreciated.
Subject Keywords:Feature detection, edge detection, scale space, nonlinear filtering, energy filters, quadratic filters, causality
Record Number:CaltechAUTHORS:KUBieeetpami96
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KUBieeetpami96
Alternative URL:http://dx.doi.org/10.1109/34.541408
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6335
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:04 Dec 2006
Last Modified:26 Dec 2012 09:20

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