Efficient and Accurate Gaussian Image Filtering Using Running Sums

TL;DR

This paper introduces a fast and accurate Gaussian image filtering method using running sums and kernel approximation, significantly reducing computation time while maintaining high accuracy.

Contribution

The paper proposes a novel efficient Gaussian filtering technique based on running sums and optimized kernel approximation, outperforming existing methods in speed with comparable accuracy.

Findings

Faster Gaussian filtering than state-of-the-art methods

Maintains similar accuracy to traditional approaches

Uses kernel approximation to reduce computational complexity

Abstract

This paper presents a simple and efficient method to convolve an image with a Gaussian kernel. The computation is performed in a constant number of operations per pixel using running sums along the image rows and columns. We investigate the error function used for kernel approximation and its relation to the properties of the input signal. Based on natural image statistics we propose a quadratic form kernel error function so that the output image l2 error is minimized. We apply the proposed approach to approximate the Gaussian kernel by linear combination of constant functions. This results in very efficient Gaussian filtering method. Our experiments show that the proposed technique is faster than state of the art methods while preserving a similar accuracy.