We apply elementary techniques from real analysis and singularity theory to derive analytical results for the behaviour in scale-space of critical points and related entities. The main results of the treatment comprise:

• a description of the general nature of trajectories of critical points in scale-space.
• an estimation of the drift velocity of critical points and edges.
• an analysis of the qualitative behaviour of critical points in bifurcation situations.
• a classification of what types of blob bifurcations are possible.