An Approach for Applying Large Filters on Large Images using FPGA

The computational complexity of a two-dimensional filter is basically O(N times N) (N is the size of the filters), though in some filters in which coefficients can be separated as to x and y axes {separable), the complexity can be reduced to O(N) by decomposing a filter to two one-dimensional filters. The computation time of non-separable filters becomes very long for large N even with hardware systems. In this paper, we propose an approach for applying large non-separable filters on large images using an FPGA. Our current targets are circularly symmetric filters whose coefficients on same concentric circles are the same. In our approach, regular polygons inscribed in those circles are used to approximate them. With this approach, the computational complexity can be reduced to O(N). A circuit based on this approach was implemented on Xilinx XC2V6000. It can apply filters more than N = 127 in one clock cycle to each pixel in an given image, which makes it possible to achieve real-time processing of HD images.