Slow and Smooth: A Bayesian Theory for the Combination of Local Motion Signals in Human Vision

In order to estimate the motion of an object, the visual system needs to combine multiple local measurements, each of which carries some degree of ambiguity. We present a model of motion perception whereby measurements from different image regions are combined according to a Bayesian estimator --- the estimated motion maximizes the posterior probability assuming a prior favoring slow and smooth velocities. In reviewing a large number of previously published phenomena we find that the Bayesian estimator predicts a wide range of psychophysical results. This suggests that the seemingly complex set of illusions arise from a single computational strategy that is optimal under reasonable assumptions.

Priors Stabilizers and Basis Functions: From Regularization to Radial, Tensor and Additive Splines

We had previously shown that regularization principles lead to approximation schemes, as Radial Basis Functions, which are equivalent to networks with one layer of hidden units, called Regularization Networks. In this paper we show that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models, Breiman's hinge functions and some forms of Projection Pursuit Regression. In the probabilistic interpretation of regularization, the different classes of basis functions correspond to different classes of prior probabilities on the approximating function spaces, and therefore to different types of smoothness assumptions. In the final part of the paper, we also show a relation between activation functions of the Gaussian and sigmoidal type.