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2004 Technical Reports

Three-Dimensional nth Derivative of Gaussian Separable Steerable Filters

Konstantinos G. Derpanis and Jacob M. Gryn

Technical Report CS-2004-05

York University

November 22, 2004

Abstract

The following report details the construction of three-dimensional (e.g.,X-Y-Z) separable steerable filters. The approach presented is an extension of the construction of two-dimensional (X-Y) separable steerable filters outlined in [1]. Additionally, three-dimensional separable steerable filters, both continuous and discrete versions, for the second derivative of the Gaussian and its Hilbert transform are reported. Experimental evaluation demonstrate that the error in the constructed separable filters are negligible. Finally, an application of the filters for surveillance based on visual motion is presented.

[1] "The Design and Use of Steerable Filters" by William T. Freeman and Edward H. Adelson, IEEE Transactions on Pattern Analysis and Machine Intelligence., 1991.

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