Gaussian Kernel Approximations Require Only Bit-Shifts

An approach to approximate the 2D Gaussian filter for all possible kernel sizes based on the binary optimization technique is introduced. The approximate filter coefficients are designed as negative powers of two, allowing hardware implementation with remarkable savings in the chip area. The proposed approximate filters were evaluated and compared with competing methods using both similarity analysis and edge detection applications. The proposed method and the competing works for masks of size 3×3, 5×5, and 7×7 were implemented in a Xilinx Artix-7 FPGA. The proposed method showed up to a 60.0% reduction in DSP usage and a 75.0% increase in the maximum operating frequency when compared with state-of-art methods for the 7×7 kernel size case and a 48.8% reduction in the dynamic power normalized by the maximum operating frequency.