Stochastic Analysis of Image Acquisition and Scale-Space Smoothing

1.1 Introduction Low level image processing is often used to detect and localise features such as edges and corners. It is also used to correlate or match small parts of one image with parts in another. Methods for doing this have been developed for some time, However, the stochastic analysis of these algorithms have often been based upon poorly motivated stochastic models. In particular, the eeects of image discretisation, interpolation and scale-space smoothing is often neglected or not analysed in detail. In this chapter, image acquisition, interpolation and scale-space smoothing are modelled into some detail. Image acquisition is viewed as a composition of blurring, ideal sampling and added noise, similar to 18]. The discrete signal is analysed after interpolation. This makes it possible to detect features on a sub-pixel level. Averaging or scale-space smoothing is used to reduce the eeects of noise. To understand feature detection in this framework, one has to analyse the eeect of noise on interpolated and smoothed signals. In doing so a theory is obtained that connects the discrete and continuous scale-space theories. The chapter is organised as follows. Section 1.2 treats the image acquisition model. In Section 1.3 a method is proposed where the discrete scale-space is induced from the continuous scale-space theory. The stochastic properties of the 1