Fast and Accurate Bilateral Filtering using Gauss-Polynomial Decomposition

TL;DR

This paper introduces a novel approximation algorithm for the Gaussian bilateral filter that reduces computational complexity to constant time per pixel using Gauss-polynomial decomposition, enabling faster and accurate image filtering.

Contribution

The paper presents a new Gauss-polynomial based approximation method that significantly accelerates bilateral filtering while maintaining high accuracy.

Findings

Achieves constant-time complexity per pixel for bilateral filtering.

Demonstrates favorable speed and accuracy compared to existing methods.

Utilizes separability and recursion for efficient implementation.

Abstract

The bilateral filter is a versatile non-linear filter that has found diverse applications in image processing, computer vision, computer graphics, and computational photography. A widely-used form of the filter is the Gaussian bilateral filter in which both the spatial and range kernels are Gaussian. A direct implementation of this filter requires $O(\sigma^2)$ operations per pixel, where $\sigma$ is the standard deviation of the spatial Gaussian. In this paper, we propose an accurate approximation algorithm that can cut down the computational complexity to $O(1)$ per pixel for any arbitrary $\sigma$ (constant-time implementation). This is based on the observation that the range kernel operates via the translations of a fixed Gaussian over the range space, and that these translated Gaussians can be accurately approximated using the so-called Gauss-polynomials. The overall algorithm emerging from this approximation involves a series of spatial Gaussian filtering, which can be implemented in constant-time using separability and recursion. We present some preliminary results to demonstrate that the proposed algorithm compares favorably with some of the existing fast algorithms in terms of speed and accuracy.