Reshuffling: a fast algorithm for filtering with arbitrary kernels

Abstract

A Novel method to accelerate the application of linear filters that have multiple identical coefficients on arbitrary kernels is presented. Such filters, including Gabor filters, gray level morphological operators, volume smoothing functions, etc., are wide used in many computer vision tasks. By taking advantage of the overlapping area between the kernels of the neighboring points, the reshuffling technique prevents from the redundant multiplications when the filter response is computed. It finds a set of unique, constructs a set of relative links for each coefficient, and then sweeps through the input data by accumulating the responses at each point while applying the coefficients using their relative links. Dual solutions, single input access and single output access, that achieve 40% performance improvement are provided. In addition to computational advantage, this method keeps a minimal memory imprint, which makes it an ideal method for embedded platforms. The effects of quantization, kernel size, and symmetry on the computational savings are discussed. Results prove that the reshuffling is superior to the conventional approach. Real-Time Image Proc., Feb. 2008 This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. SPIE Electronic Imaging, Proceedings of ABSTRACTA novel method to accelerate the application of linear filters that have multiple identical coefficients on arbitrary kernels is presented. Such filters, including Gabor filters, gray level morphological operators, volume smoothing functions, etc., are widely used in many computer vision tasks. By taking advantage of the overlapping area between the kernels of the neighboring points, the reshuffling technique prevents from the redundant multiplications when the filter response is computed. It finds a set of unique coefficients, constructs a set of relative links for each coefficient, and then sweeps through the input data by accumulating the responses at each point while applying the coefficients using their relative links. Dual solutions, single input access and single output access, that achieve 40% performance improvement are provided. In addition to computational advantage, this method keeps a minimal memory imprint, which makes it an ideal method for embedded platforms. The effects of quantization, kernel size, and symmetry on the computational savings are discussed.Results prove that the reshuffling is superior to the...

Border Handling for 2D Transpose Filter Structures on an FPGA

“…Rather than calculating the output as the weighted sum of window pixels, the input pixels are weighted immediately, and are accumulated into the window position of the corresponding output pixel. Where there are common filter coefficients, for example with symmetric filters, the associated multiplications are in parallel, enabling the set of common multiplications to be replaced by a single multiplier [4]. In the direct form, this is equivalent to using the distributive property to factor out the common multiplications.…”