Can one hear the shape of a room: The 2-D polygonal case

We consider the problem of estimating room geometry from the acoustic room impulse response (RIR). Existing approaches addressing this problem exploit the knowledge of multiple RIRs. In contrast, we are interested in reconstructing the room geometry from a single RIR - a 1-D function of time. We discuss the uniqueness of the mapping between the geometry of a planar polygonal room and a single RIR. In addition to this theoretical analysis, we also propose an algorithm that performs the "blindfolded" room estimation. Furthermore, the derived results are used to construct an algorithm for localization in a known room using only a single RIR. Verification of the theoretical developments with numerical simulations is given before concluding the paper.