Shape Identification and Classification in Echolocation

This paper introduces a new approach to shape perception in wave imaging. It aims at proposing an efficient shape identification and classification algorithm in echolocation. This approach is based on first extracting geometric features from the reflected waves and then matching them with precomputed ones associated with a dictionary of targets. The construction of such frequency-dependent shape descriptors is based on some important properties of scattering coefficients and new invariants. Stability and resolution of the proposed identification algorithm with respect to measurement noise and limited-view aspect are analytically and numerically quantified.