A Priori Scale in Classical Scalar and Density Fields

Models involving elds often rely on details of a spatiotemporal scale range that is considered relevant to a particular phenomenon. We propose a generic representation for classical IR-valued scalar and density elds incorporating scale a priori . To this end a eld is embedded into a causal, versal family with scale as the control parameter, such that no scale bias is introduced and physical content is not a ected. Image data can be processed so as to re ect the source eld's multiscale di erential structure in a well-posed way. Physically relevant scales can be selected a posteriori .