Stochastic Analysis of Image Acquisition, Interpolation and Scale-space Smoothing

In the high-level operations of computer vision it is taken for granted that image features have been reliably detected. This paper addresses the problem of feature extraction by scale-space methods. There has been a strong development in scale-space theory and its applications to low-level vision in the last couple of years. Scale-space theory for continuous signals is on a firm theoretical basis. However, discrete scale-space theory is known to be quite tricky, particularly for low levels of scale-space smoothing. The paper is based on two key ideas: to investigate the stochastic properties of scale-space representations and to investigate the interplay between discrete and continuous images. These investigations are then used to predict the stochastic properties of sub-pixel feature detectors. The modeling of image acquisition, image interpolation and scale-space smoothing is discussed, with particular emphasis on the influence of random errors and the interplay between the discrete and continuous representations. In doing so, new results are given on the stochastic properties of discrete and continuous random fields. A new discrete scale-space theory is also developed. In practice this approach differs little from the traditional approach at coarser scales, but the new formulation is better suited for the stochastic analysis of sub-pixel feature detectors. The interpolated images can then be analyzed independently of the position and spacing of the underlying discretisation grid. This leads to simpler analysis of sub-pixel feature detectors. The analysis is illustrated for edge detection and correlation. The stochastic model is validated both by simulations and by the analysis of real images. Mathematics Subject Classification: 68U10, 60D05, 60G60