Convex room geometry estimation from acoustic echoes using iterative convex hull expansion technique

Abstract

This thesis proposes a methodology to estimate room geometry from times of arrival of early reflections in room impulse responses measured at multiple microphones. Room shape can be inferred by estimating the wall positions constituting a room, and several methods have been proposed for estimating the wall positions. The conventional methods to estimate wall positions require the times of arrival of the first-order reflections from the same wall. However, when microphones are widely distributed in space, the times of arrival from the same wall arrive at each microphone in a different order, which induces the echo labeling problem. Thus, in order to estimate wall positions, the echo labeling problem, which can be solved by associating the times of arrival with each wall, is the most critical problem for room geometry inference. In this thesis, the echo labeling problem is tackled by proposing the iterative echo labeling algorithm. The iterative echo labeling algorithm constructs ellipses using the first-arriving reflections between all loudspeakers and microphones in the first iteration and estimates the walls tangent to the convex hull calculated by the ellipses. In the next iteration, the convex hull is expanded by utilizing subsequent times of arrival. The tangents of the intersection between the expanded convex hull and the estimated room in the previous iteration are investigated to estimate other walls. As this iteration is repeated, the convex hull is continuously expanded in space, and walls tangent to the convex hull are estimated in each iteration. In some iteration, the convex hull contains the estimated room in the previous iteration. In this iteration, the estimated room becomes the real room, and the iterative echo labeling algorithm is terminated. As a result, the iterative echo labeling algorithm can efficiently solve the echo labeling problem within a reasonable time, compared to previous research. Besides, the search space is greatly reduced by the geometrical constraints induced by the proposed method, which results in improved echo labeling performance. However, there is a limitation that the iterative echo labeling algorithm cannot solve the echo labeling problem if all microphones do not acquire all times of arrival of the first-order reflections from each wall. The reason for this is that the iterative echo labeling algorithm always expands the convex hull. To address the problem induced by undetected times of arrival of the first-order reflections, the inner convex hull search algorithm is proposed. The inner convex hull search algorithm contracts the convex hull constructed by the iterative echo labeling algorithm from the outermost convex hull to the inner convex hull to estimate walls possibly missed by the iterative echo labeling algorithm in subiterations. The simulation and experiment results show that room geometry can be estimated even when some undetected times of arrival exist.