Confidence measures for consensus sets in transformation uncertainty

Many applications in image processing require the fitting of transformation models to sets of points. We propose a technique that optimizes the model fitting process by employing parametric consistency as an additional constraint. The technique is used to find affine transformations between data points. The uncertainty about the exact location of a data point is modelled by defining a convex uncertainty region in which the data point must be situated. The uncertainty of a transformation is represented by a convex polytope in the parameter space. For each polytope we introduce a consensus set and a confidence level. The consistency of different parameter polytopes is evaluated with an intersection graph. Consensus sets for fitting models correspond to large cliques in the consistency graph. Not only the size of the consensus set, but also the confidence that we have in it plays an important role. From the size of the uncertainty regions induced by an uncertainty transformation, we compute an expected size of the consensus that would occur by coincidence. These results are used to compute a confidence measure for the consensus set, which results in a further enhancement of the clique finding algorithm. Keywords— transformation uncertainty, transformation polytopes, consensus, confidence measures