Multiscale flat norm signatures for shapes and images

In this paper we begin to explore the application of the multiscale flat norm introduced in Morgan and Vixie to shape and image analysis. In particular, we look at the use of the multiscale flat norm signature for the identification of shapes. After briefly reviewing the multiscale flat norm, the L1TV functional and the relation between these two, we introduce multiscale signatures that naturally follow from the multiscale flat norm and its components. A numerical method based on the min-cut, max-flow graph-cut is briefly recalled. We suggest using L2 minimization, rather than the usual Crofton's formula based approximation, for choosing the required weights. The resulting weights have the dual benefits of being analytically computable and of giving more accurate approximations to the anisotropic TV energy. Finally, we demonstrate the usefulness of the signatures on simple shape classification tasks.