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Symmetry sensitivities of Derivative-of-Gaussian filters

Griffin, LD; Lillholm, M; (2010) Symmetry sensitivities of Derivative-of-Gaussian filters. IEEE Transactions on Pattern Analysis and Machine Intelligence , 32 (6) 1072 - 1083. 10.1109/TPAMI.2009.91. Green open access

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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.

Type:Article
Title:Symmetry sensitivities of Derivative-of-Gaussian filters
Open access status:An open access version is available from UCL Discovery
DOI:10.1109/TPAMI.2009.91
Publisher version:http://dx.doi.org/10.1109/TPAMI.2009.91
Language:English
Additional information:© 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
Keywords:Group theory, invariance, pattern analysis, LOCAL-IMAGE-STRUCTURE, TEXTURE-DISCRIMINATION, DIFFERENTIAL STRUCTURE, SPATIAL FILTERS, MIRROR SYMMETRY, PERCEPTION, MODEL, FIELD, CLASSIFICATION, STATISTICS
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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