On the Axiomatic Foundations of Linear Scale-Space
Since the pioneering work by Witkin (1983) and Koenderink (1984) on the notion of “scale-space representation”, a large number of different scale-space formulations have been stated, based on different types of assumptions (usually referred to as scale-space axioms). The main subject of this chapter is to provide a synthesis between these linear scale-space formulations and to show how they are related. Another aim is to show how the scale-space formulations, which were originally expressed for continuous data on spatial domains without preferred directions, can be extended to discrete data as well as to spatio-temporal domains with preferred directions. Connections will also be pointed out to approaches based on non-uniform smoothing.