SIAM Features Boutin’s Work on Shape From Echoes


Mireille (Mimi) Boutin and co-author Gregor Kemper from TU Munich have recently shown that one can reconstruct the walls of a room from first order echoes acquired by four microphones placed in a non-planar configuration on a drone. In the first case considered, a loudspeaker is placed inside the room and emits one high-frequency impulse. In the second case, the loudspeaker is placed on the drone and navigates in a rigid fashion with the microphone arrangements. Reconstruction algorithms are provided for both cases, and a proof is given that the set of drone placements for which the reconstruction might lead to ghost walls (i.e. walls that are not there) is of measure zero. Specifically, the bad drone placements are contained in a dimension 5 structure within the 6-dimensional space of drone positions and orientations. The research, published in SIAM J. Appl. Alg and Geometry, is featured in SIAM News.