The subject of continuous vs. discrete modelling of physical phenomena is discussed and illustrated by an example taken from image analysis. The problem of estimating/predicting fields, i.e. infinite dimensional objects, from a finite set of observations is suitably defined. Deterministic solutions, with the two variants of the reduction of solution space or the Tikhonov regularization approach, are examined. The probabilistic, Bayesian, solution of the same problems is then undertaken, after presenting the basics of infinite dimensional probabilistic models.