Polygonal Shapes Reconstruction from Acoustic Echoes Using a Mobile Sensor and Beamforming

This paper proposes a beamforming approach to recover the geometry of arbitrary polygonal-shaped bounded areas from acoustic reflections with the aim to generalize a previous method~\cite{ouabi2021} restricted to rectangular geometries. The considered setup only requires a single omnidirectional emitter-receiver acoustic device mounted on a mobile platform. Our approach applies beamforming to the acoustic measurements in the boundary geometrical space. The edges are subsequently retrieved from the beamforming results via the minimization of a regularized cost criterion using a simulated annealing optimizer. We also design a boundary rejection criterion, so that their exact number can be recovered based only on a specified upper bound. We assess our method on different geometries in a simulation environment, as well on a real-world setting using ultrasonic guided waves measurements. The results demonstrate that it is efficient for achieving the target objectives.