A General Framework for Bilateral and Mean Shift Filtering

TL;DR

This paper introduces a unified framework for bilateral and mean shift filtering applicable to various data domains, offering competitive accuracy, speed, and convergence guarantees, with applications in feature preservation and enhancement.

Contribution

It generalizes bilateral filtering to irregular domains with a solid theoretical foundation, enabling robust, convergent mean-shift schemes for noisy signals and geometric feature enhancement.

Findings

Discretization matches state-of-the-art accuracy and speed.

Framework reduces to classical bilateral filter on rectangular domains.

Provides unconditionally convergent mean-shift algorithms.

Abstract

We present a generalization of the bilateral filter that can be applied to feature-preserving smoothing of signals on images, meshes, and other domains within a single unified framework. Our discretization is competitive with state-of-the-art smoothing techniques in terms of both accuracy and speed, is easy to implement, and has parameters that are straightforward to understand. Unlike previous bilateral filters developed for meshes and other irregular domains, our construction reduces exactly to the image bilateral on rectangular domains and comes with a rigorous foundation in both the smooth and discrete settings. These guarantees allow us to construct unconditionally convergent mean-shift schemes that handle a variety of extremely noisy signals. We also apply our framework to geometric edge-preserving effects like feature enhancement and show how it is related to local histogram techniques.