A Coupled PDE Model of Nonlinear Diffusion for Image Smoothing and Segmentation

Abstract

Image denoising and segmentation are fundamental problems in the field of image processing and computer vision with numerous applications. We propose a partial differential equation (PDE) based smoothing and segmentation framework wherein the image data are smoothed via an evolution equation that is controlled by a vector field describing a viscous fluid flow. Image segmentation in this framework is defined by locations in the image where the fluid velocity is a local maximum. The nonlinear image smoothing is selectively achieved to preserve edges in the image. The novelty of this approach lies in the fact that the selective term is derived from a nonlinearly regularized image gradient field unlike most earlier techniques which either used a constant (with respect to time) selective term or a time varying nonlinearly smoothed scalar valued term. Implementation results on synthetic and real images are presented to depict the performance of the technique in comparison to methods recently reported in literature.