Fast adaptive elliptical filtering using box splines

TL;DR

This paper introduces a fast, adaptive elliptical filtering method for images that uses box splines, allowing real-time adjustment of window shape and size with fixed computational cost, suitable for feature-aware image processing.

Contribution

The paper develops a novel approach combining global pre-integration and localization meshes for efficient elliptical filtering using box splines, extending theory from 1D to 2D.

Findings

Achieves fixed computational cost per pixel for elliptical filtering

Supports adaptive control of size and ellipticity of the filter

Converges to Gaussian filters as order increases

Abstract

We demonstrate that it is possible to filter an image with an elliptic window of varying size, elongation and orientation with a fixed computational cost per pixel. Our method involves the application of a suitable global pre-integrator followed by a pointwise-adaptive localization mesh. We present the basic theory for the 1D case using a B-spline formalism and then appropriately extend it to 2D using radially-uniform box splines. The size and ellipticity of these radially-uniform box splines is adaptively controlled. Moreover, they converge to Gaussians as the order increases. Finally, we present a fast and practical directional filtering algorithm that has the capability of adapting to the local image features.