Elementary techniques from real analysis, and singularity theory are applied to deriveanalytical results for the behaviour in scale-space of critical points and related entities. The mainresults of the treatment comprise

• a description of the general nature of trajectories of critical points in scale-space

• estimates of the drift velocity of critical points and straight edges

• an analysis of the qualitative behaviour of critical points in bifurcation situations

• a classification of what types of blob events are possible