Indicators basis for functional shape analysis

Step functions are widely used in several applications from geometry processing and shape analysis. Shape segmentation, partial matching and self similarity detection just to name a few. The standard signal processing tools do not allow us to fully handle this class of functions. The classical Fourier series, for instance, does not give a good representation for these non smooth functions. In this paper we define a new basis for the approximation and transfer of the step functions between shapes. Our definition is fully spectral, allowing for a concise representation and an efficient computation. Furthermore our basis is specifically built in order to enhance its use in combination with the functional maps framework. The functional approach also enable us to handle shape deformations. Thanks to that our basis achieves a large improvement not only in the approximation of step functions but also in the transfer, exploiting the functional maps framework. We perform a large set of experiments showing the improvement achieved by the proposed basis in the approximation and transfer of step functions and its stability with respect to non isometric deformations.