Applying rapid numerical approximation of convolutions with filters for image processing purposes

摘要

A computer implemented method for applying a numerical approximation of a convolution of image I as represented by hierarchical signals al of level l with filter f, said method including the steps of: generating a forward transformation by applying a convolution between al and kernel h1 for each level of hierarchy l and by down-sampling the result of convolved al and h1; generating a backward transformation by applying, for each level of hierarchy l, a convolution between kernel h2 and an up-sampled forward transformation and combining the result with a convolution of al with kernel g; and combining the forward transformation with the backward transformation, to yield â0 being an approximation of a convolution between a and f, wherein kernels h1, h1, and g are optimized kernels of filter f.

主权项

1. A computer implemented method to generate a filtered image, the method comprising:
receiving image I as represented by input pixels al where l denotes a level in a hieracarchy; generating with a processor, a forward transformation by applying a convolution between the input pixels al and kernel h1 for each level of hierarchy l and by down-sampling the result of convolved al and h1, generating a backward transformation by applying, for each level of hierarchy l, a convolution between kernel h2 and an up-sampled forward transformation and combining the result with a convolution of al with kernel g; generating the filtered image by combining the forward transformation with the backward transformation, to yield approximate convolution pixels â0 ,wherein the approximate convolution pixels â0 are an approximation of a convolution between a1 and a filter f, wherein kernels h1, h2, and g are optimized kernels of the filter f, and wherein generating the filtered image has a lower computational cost compared to generating the filtered image using an unapproximated convolution; and displaying the filtered image.