On the use of size functions for shape analysis

According to a recent mathematical theory a shape can be represented by functions, named size functions, which convey information on both the topological and metric properties of the viewed shape. The relevance of the theory of size functions to computer vision is investigated. An algorithm for the computation of the size functions is presented and many theoretical properties of the theory are demonstrated on real images. It is shown that the representation of shape in terms of size functions (i) can be tailored to suit the invariance of the problem at hand and (ii) is stable against small qualitative and quantitative changes of the viewed shape. A distance between size functions is used as a similarity measure between the representation of two different shapes. The obtained results 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