Variational PDE models in image processing

Abstract

The paper discusses some recent approaches to mathematical vision and vision analysis via the variational method of partial differential equations (PDE) which appears in the search for local or global minima using the gradient descent technique. The authors survey inpainting and segmentation problems, adaptive image enhancement and scale-space theory, geometric processing of curves and surfaces, optical flows of motion pictures and dynamic object tracking. The conclusion displays some prospects for future research.