Improvements on "Fast space-variant elliptical filtering using box splines"

TL;DR

This paper presents improvements to a fast, space-variant elliptical filtering algorithm based on box splines, enhancing control over covariance and accuracy while maintaining constant computational cost.

Contribution

The authors modify the existing O(1) Gaussian-like filtering algorithm to improve covariance control and approximation accuracy.

Findings

Enhanced covariance control in space-variant filtering

Improved approximation accuracy of Gaussian kernels

Maintained fixed computational cost per pixel

Abstract

It is well-known that box filters can be efficiently computed using pre-integrations and local finite-differences [Crow1984,Heckbert1986,Viola2001]. By generalizing this idea and by combining it with a non-standard variant of the Central Limit Theorem, a constant-time or O(1) algorithm was proposed in [Chaudhury2010] that allowed one to perform space-variant filtering using Gaussian-like kernels. The algorithm was based on the observation that both isotropic and anisotropic Gaussians could be approximated using certain bivariate splines called box splines. The attractive feature of the algorithm was that it allowed one to continuously control the shape and size (covariance) of the filter, and that it had a fixed computational cost per pixel, irrespective of the size of the filter. The algorithm, however, offered a limited control on the covariance and accuracy of the Gaussian approximation. In this work, we propose some improvements by appropriately modifying the algorithm in [Chaudhury2010].