Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

David Tschumperlé (1) , Rachid Deriche (2)

1 Equipe Image - Laboratoire GREYC - UMR6072
2 ODYSSEE - Computer and biological vision

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation.

Domaines: Traitement des images [eess.IV]

David Tschumperlé, Rachid Deriche. Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications. Advances in Imaging and Electron Physics (AIEP), Academic Press, pp.145--209, 2007. ⟨hal-00332798⟩