According to a recent mathematical theory a shape can be represented b
y size functions, which convey information on both the topological and
metric properties of the viewed shape. In this paper the relevance of
the theory of size functions to visual perception is investigated. An
algorithm for the computation of the size functions is presented, and
many theoretical properties of the theory are demonstrated on real im
ages. It is shown that the representation of shape in terms of size fu
nctions (1) can be tailored to suit the invariance of the problem at h
and and (2) is stable against small qualitative and quantitative chang
es of the viewed shape. A distance between size functions is used as a
measure of similarity between the representations of two different sh
apes. The results obtained indicate that size functions are likely to
be very useful for object recognition. In particular, they seem to be
well suited for the recognition of natural and articulated objects.