Deformation energy for size functions

Size functions are functions from the real plane to thenatural numbers useful for describing shapes of objects. Theyallow to translate the problem of comparing shapes to the problemof comparing functions, that is a much simpler task. In order toperform the comparison between size functions we present a methodto measure the energy necessary to deform size functions into eachother. Minimizing such an energy allows for a measure of thesimilarity between shapes. Some experimental results concerningthe comparison of free hand-drawn sketches are shown.