Application to Natural Images

The results of Chapters 9 and 10 concerning the stability of phase information were derived mainly with a white Gaussian noise model of the input. We now consider in more detail their application to real images. The issue of phase stability is discussed in Section 11.1 in the context of natural images that contain salient image features, such as edges, and regions with virtually no structure at all to which the filters respond. We then illustrate the results in the context of binocular disparity, for which matching band-pass filtered versions of the left and right views of a scene along epipolar lines can be viewed as a 1-d problem. After discussing the basic approach in Section 11.2, we consider the accuracy of phase-based disparity measurements for 1-d signals with and without the removal of singularity neighbourhoods, and then as a function of scale and translation perturbations between two views. Section 11.4 briefly illustrates some of these points with 2-d images.