Sparse representation of step functions on manifolds
Step functions are non-smooth and piecewise constant functions with a finite number of pieces. Each of these pieces indicates a local region contained in the entire domain. Several geometry processing applications involve step functions defined on non-Euclidean domains, such as shape segmentation, partial matching and self-similarity detection. Standard signal processing cannot handle this class of functions. The classical Fourier series, for instance, does not give a good representation of these non-smooth functions.