Efficient Method for Space-Variant Low-Pass Filtering

We propose a method for efficiently performing space-variant (SV) filtering, which we apply here to the low-pass case. It is based on using a small set of N a priori fixed reference kernels, which are obtained by applying different spatial scaling factors to a mother smoothing filter. The set of 2-D signals obtained by filtering the input image with these kernels is linearly combined to achieve an optimal approximation (in a least square error sense) to the convolution of the input image with the mother filter at any arbitrary scale. We define a 2-D scaling mask, which specifies the scale of the filter to be applied at each spatial location of the input image. This permits an efficient SV filtering, since the number of 2-D convolutions required is small and independent on the scaling mask. We describe a particular space-variant low-pass (SVLP) filtering scheme and include two examples of application.