Anisotropic Diffusion on Curved Surfaces

TL;DR

This paper introduces a novel method for anisotropic diffusion-based image filtering on curved surfaces, utilizing a surface-intrinsic formulation and the closest point method for flexible and effective processing.

Contribution

It formulates surface-intrinsic anisotropic diffusion models and implements a simple, flexible algorithm using the closest point method for filtering images on general curved surfaces.

Findings

Effective noise removal on various surface types

Applicable to smooth, open, and triangulated surfaces

Demonstrates artistic and practical filtering results

Abstract

We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence enhancing diffusion models in a surface-intrinsic way. These diffusion processes are anisotropic and the equations depend non-linearly on the data. The surface-intrinsic equations are dealt with the closest point method, a technique for solving partial differential equations (PDEs) on general surfaces. The resulting algorithm has a very simple structure: we merely alternate a time step of a 3D analog of the in-surface PDE in a narrow 3D band containing the surface with a reconstruction of the surface function. Surfaces are represented by a closest point function. This representation is flexible and the method can treat very general surfaces. Experimental results include image filtering on smooth surfaces, open surfaces, and general triangulated surfaces.