A Bayesian reflection on surfaces -: The multiresolution inference of continuous-basis fields

The topic of this paper is a novel continuous-basis field representation and inference framework applied to the inference of continuous surfaces from measurements (for example camera image data). Traditional approaches to surface representation and inference are briefly reviewed. The new field representation and inference paradigm is then introduced within a maximally informative (MI) (see [1]) inference framework. The knowledge representation is introduced and discussed in the context of MI inference. Then, using the MI inference approach, the here-named Generalized Kalman Filter (GKF) equations are derived. The GKF equations allow the update of field knowledge from previous knowledge at any scale, and new data, to new knowledge at any other scale. The GKF equations motivate a location-dependent scale or multigrid approach to the MI inference of continuous-basis fields. Several problems are uniquely solved: The MI inference of fields, where the basis for the field is itself a continuous object and generally is not representable in a finite manner; the tradeoff between accuracy of representation in terms of information learned, and memory or storage capacity in bits the approximation of probability distributions so that a maximal amount of information about the object being inferred is preserved by the approximation.