Minimal Structure and Motion Problems for TOA and TDOA Measurements with Collinearity Constraints

Structure from sound can be phrased as the problem of determining the position of a number of microphones and a number of sound sources given only the recorded sounds. In this paper we study minimal structure from sound problems in both TOA (time of arrival) and TDOA (time difference of arrival) settings with collinear constraints on e.g. the microphone positions. Three such minimal cases are analyzed and solved with efficient and numerically stable techniques. An experimental validation of the solvers are performed on both simulated and real data. In the paper we also show how such solvers can be utilized in a RANSAC framework to perform robust matching of sound features and then used as initial estimates in a robust non-linear leastsquares optimization