Efficient Constant-time Gaussian Filtering with Sliding DCT/DST-5and Dual-domain Error Minimization

Abstract

This paper presents an efficient constant-time algorithm for Gaussian filtering and also Gaussian derivative filtering that provides a high approximate accuracy in a low computational complexity regardless of its filter window size. The proposed algorithm consists of two key techniques: second-order shift properties of the Discrete Cosine/Sine Transforms type-5 and dual-domain error minimization for finding optimal parameters. The former enables us to perform filtering in fewer number of arithmetic operations as compared than some state-of-the-art algorithms without integral images. The latter enables us to find the optimal filter size that provides the most accurate filter kernel approximation. Experiments show that the proposed algorithm clearly outperforms state-of-the-art ones in computational complexity, approximate accuracy, and accuracy stability.