This chapter describes the basic concepts of partial differential equations (PDEs) based image modelling and their applications to image restoration. The general basic concepts of partial differential equation (PDE)-based image modelling and processing techniques are discussed for image restoration problems. These techniques can also be used in the design and development of efficient tools for various image processing and vision related tasks such as restoration, enhancement, segmentation, registration, inpainting, shape from shading, 3D reconstruction of objects from multiple views, and many more. As a case study, the topic in consideration is oriented towards image restoration using PDEs formalism since image restoration is considered to be an important pre-processing task for 3D surface geometry, reconstruction, and many other applications. An image may be subjected to various types of noises during its acquisition leading to degraded quality of the image, and hence, the noise must be reduced. The noise may be additive or multiplicative in nature. Here, the PDE-based models for removal of both types of noises are discussed. As examples, some PDE-based schemes have been implemented and their comparative study with other existing techniques has also been presented.
An Impulse Detector for Color Image Restoration