Nonlinear Scale Space with Spatially Varying Stopping Time

A general scale-space algorithm is presented for denoising signals and images with spatially varying dominant scales. The process is formulated as a partial differential equation with spatially varying time. The proposed adaptivity is semilocal and is in conjunction with the classical gradient-based diffusion coefficient, designed to preserve edges. The new algorithm aims at maximizing a local SNR measure of the denoised image. It is based on a generalization of a global stopping time criterion presented recently by the author and his colleagues. Most notably, the method also works well for partially textured images and outperforms any selection of a global stopping time. Given an estimate of the noise variance, the procedure is automatic and can be applied well to most natural images.