Chapter 8: Theoretical analysis of scale-space

Chapter 8 in Scale-Space Theory in Computer Vision demonstrates how the behaviour of image structures over scales can be analysed using elementary techniques from real analysis, singularity theory, and statistics.

The implicit function theorem describes how critical points form trajectories across scales when the scale parameter changes, and gives direct estimates of their drift velocity. Momentarily, the drift velocity may tend to infinity. Generically, this occurs in bifurcation situations only.

The qualitative behaviour of critical points at bifurcations is analysed, and the generic blob events are classified. A set of illustrative examples is presented, demonstrating how blobs behave in characteristic situations.