The Joy of Sampling

A standard method for handling Bayesian models is to use Markov chain Monte Carlo methods to draw samples from the posterior. We demonstrate this method on two core problems in computer vision—structure from motion and colour constancy. These examples illustrate a samplers producing useful representations for very large problems. We demonstrate that the sampled representations are trustworthy, using consistency checks in the experimental design. The sampling solution to structure from motion is strictly better than the factorisation approach, because: it reports uncertainty on structure and position measurements in a direct way; it can identify tracking errors; and its estimates of covariance in marginal point position are reliable. Our colour constancy solution is strictly better than competing approaches, because: it reports uncertainty on surface colour and illuminant measurements in a direct way; it incorporates all available constraints on surface reflectance and on illumination in a direct way; and it integrates a spatial model of reflectance and illumination distribution with a rendering model in a natural way. One advantage of a sampled representation is that it can be resampled to take into account other information. We demonstrate the effect of knowing that, in our colour constancy example, a surface viewed in two different images is in fact the same object. We conclude with a general discussion of the strengths and weaknesses of the sampling paradigm as a tool for computer vision.