Symmetry sensitivities of derivative-of-gaussian filters

Lewis D. Griffin; Martin Lillholm

doi:10.1109/TPAMI.2009.91

Symmetry sensitivities of derivative-of-gaussian filters

18 Citations (Scopus)

Abstract

We consider the measurement of image structure using linear filters, in particular derivative-of-Gaussian (DtG) filters, which are an important model of V1 simple cells and widely used in computer vision, and whether such measurements can determine local image symmetry. We show that even a single linear filter can be sensitive to a symmetry, in the sense that specific responses of the filter can rule it out. We state and prove a necessary and sufficient, readily computable, criterion for filter symmetry-sensitivity. We use it to show that the six filters in a second order DtG family have patterns of joint sensitivity which are distinct for 12 different classes of symmetry. This rich symmetry-sensitivity adds to the properties that make DtG filters well-suited for probing local image structure, and provides a set of landmark responses suitable to be the foundation of a nonarbitrary system of feature categories.

Original language	English
Journal	I E E E Transactions on Pattern Analysis and Machine Intelligence
Volume	32
Issue number	6
Pages (from-to)	1072-1083
Number of pages	12
ISSN	0162-8828
DOIs	https://doi.org/10.1109/TPAMI.2009.91
Publication status	Published - 2010
Externally published	Yes

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10.1109/TPAMI.2009.91

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AB - We consider the measurement of image structure using linear filters, in particular derivative-of-Gaussian (DtG) filters, which are an important model of V1 simple cells and widely used in computer vision, and whether such measurements can determine local image symmetry. We show that even a single linear filter can be sensitive to a symmetry, in the sense that specific responses of the filter can rule it out. We state and prove a necessary and sufficient, readily computable, criterion for filter symmetry-sensitivity. We use it to show that the six filters in a second order DtG family have patterns of joint sensitivity which are distinct for 12 different classes of symmetry. This rich symmetry-sensitivity adds to the properties that make DtG filters well-suited for probing local image structure, and provides a set of landmark responses suitable to be the foundation of a nonarbitrary system of feature categories.

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JF - I E E E Transactions on Pattern Analysis and Machine Intelligence

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Symmetry sensitivities of derivative-of-gaussian filters

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