Image denoising and segmentation via nonlinear diffusion

Image denoising and segmentation are fundamental problems in the field of image processing and computer vision with numerous applications. In this paper, we present a nonlinear PDE-based model for image denoising and segmentation which unifies the popular model of Alvarez, Lions and Morel (ALM) for image denoising and the Caselles, Kimmel and Sapiro model of geodesic “snakes”. Our model includes nonlinear diffusive as well as reactive terms and leads to quality denoising and segmentation results as depicted in the experiments presented here. We present a proof for the existence, uniqueness, and stability of the viscosity solution of this PDE-based model. The proof is in spirit similar to the proof of the ALM model; however, there are several differences which arise due to the presence of the reactive terms that require careful treatment/consideration. A fast implementation of our model is realized by embedding the model in a scale space and then achieving the solution via a dynamic system governed by a coupled system of first-order differential equations. The dynamic system finds the solution at a coarse scale and tracks it continuously to a desired fine scale. We demonstrate the smoothing and segmentation results on several real images.