Convolution and Fourier Transform of Second Order Tensor Fields

M. Hlawitschka, J. Ebling, and G. Scheuermann (Germany)


Tensor Fields, Feature Detection, Fourier Transform


The goal of this paper is to transfer convolution, correlation and Fourier transform to second order tensor fields. Convo lution of two tensor fields is defined using matrix multipli cation. Convolution of a tensor field with a scalar mask can thus be described by multiplying the scalars with the real unit matrix. The Fourier transform of tensor fields defined in this paper corresponds to Fourier transform of each of the tensor components in the field. It is shown that for this convolution and Fourier transform, the well known con volution theorem holds and optimization in speed can be achieved by using Fast Fourier transform algorithms. Fur thermore, pattern matching on tensor fields based on this convolution is described.

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