Critical Point Events in Affine Scale-Space

Abstract

There are (at least) three lines of argument motivating the interest in scale space: ecological, physiological and pragmatic. The ecological line runs thus. It is desirable for an agent that the environmental information it can extract by visual means should depend as little as possible upon the agent’s location and pose. This is confounded by several factors: occlusion, limited field of view and physical limitations on the measurements it can make of the luminance incident upon its receptors. Consideration of physical limitations inspires scale space (Koenderink, 1984). It is acknowledged that the apertures of physically plausible measurements must be of non-zero size. Hence there will be an unavoidable loss of information as the agent recedes from a scene. If the agent produces a scale space (i.e. it measures the luminance with apertures at all sizes not smaller than its smallest set) then it achieves a semi-invariance to viewing distance: it ensures that although it loses information by receding, it never loses by approaching. The physiological line is to observe that receptive fields in mammalian visual systems have a range of sizes; to realize that this means that the retinal image is represented at multiple scales; and then to seek a formal framework to describe and investigate such a representation (Marr, 1982). The pragmatic line is the computer scientist’s. He observes that image objects come in a range of sizes and that operations that can extract small objects fail with larger objects and vice versa. Rather than design his operators separately for each scale of interest he conceives the plan of using one set of operators and changing the scale of his image (Witkin, 1983).