Image processing and registration in a point set representation

Abstract

An image, being a continuous function, is commonly discretely represented as a set of sample values, namely the intensities, associated with the spatial grids. After that, all types of the operations are then carried out there in. We denote such representation as the discrete function representation (DFR). In this paper we provide another discrete representation for images using the point sets, called the point set representation (PSR). Essentially, the image is normalized to have the unit integral and is treated as a probability density function of some random variable. Then the PSR is formed by drawing samples of such random variable. In contrast with the DFR, here the image is purely represented as points and no values are associated. Besides being an equivalent discrete representation for images, we show that certain image operations benefit from such representation in the numerical stability, performance, or both. Examples are given in the Perona-Malik type diffusion where in the PSR there is no such problem as the numerical instability. Furthermore, PSR naturally bridges the fields of image registration with the point set registration. This helps handle some otherwise difficult problems in image registration such as partial image registration, with much faster convergence speed.