EM, MCMC, and Chain Flipping for Structure from Motion with Unknown Correspondence
Learning spatial models from sensor data raises the challenging data association problem of relating model parameters to individual measurements. This paper proposes an EM-based algorithm, which solves the model learning and the data association problem in parallel. The algorithm is developed in the context of the the structure from motion problem, which is the problem of estimating a 3D scene model from a collection of image data. To accommodate the spatial constraints in this domain, we compute virtual measurements as sufficient statistics to be used in the M-step. We develop an efficient Markov chain Monte Carlo sampling method called chain flipping, to calculate these statistics in the E-step. Experimental results show that we can solve hard data association problems when learning models of 3D scenes, and that we can do so efficiently. We conjecture that this approach can be applied to a broad range of model learning problems from sensordata, such as the robot mapping problem.