Decision regions of Fourier plane nonlinear filtering for image recognition
Bahram Javidi, Nasser Towghi, Jian Li · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
In image recognition applications, complex decision regions in the image space are needed. Linear filtering forms the decision regions by hyperplanes in the image space. We determine the decision region formed by Fourier plane nonlinear filtering. In the case that power law nonlinearity is applied in the Fourier plane, the decision region turns out to be approximately an n-dimensional parabola which opens toward the direction of the reference vector. That is, the intersection of the decision region with any plan (two dimensional vector space) not containing any vector parallel to the reference vector, is a bounded convex region enclosed by a closed curve. The size of the convex region depends on the filter nonlinearity, which determines the distortion robustness and discrimination capability of the filter. It can be adjusted by choosing different Fourier plane nonlinearities and/or different threshold values at the output plane. These types of regions are desirable and well suited in image recognition.