BAYESIAN STOCHASTIC MESH OPTIMISATION FOR 3D RECONSTRUCTION
George Vogiatzis, Philip Torr and Roberto Cipolla
September 2003
We describe a mesh based approach to the problem of structure from motion. The input to the algorithm is a small set of images, sparse noisy feature correspondences (such as those provided by a Harris corner detector and cross correlation) and the camera geometry plus calibration. The output is a 3D mesh, that when projected onto each view, is visually consistent with the images. There are two contributions in this paper. The first is a Bayesian formulation in which simplicity and smoothness assumptions are encoded in the prior distribution. The resulting posterior is optimized by simulated annealing. The second and more important contribution is a way to make this optimization scheme more efficient. Generic simulated annealing has been long studied in computer vision and is thought to be highly inefficient. This is often because the proposal distribution searches regions of space which are far from the modes. In order to improve the performance of simulated annealing it has long been acknowledged that choice of the correct proposal distribution is of paramount importance to convergence. Taking inspiration from RANSAC and importance sampling we craft a proposal distribution that is tailored to the problem of structure from motion. This makes our approach particularly robust to noise and ambiguity. We show results for an artificial object and an architectural scene.
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