It is suggested that there exists a minimal set of rules for the perceptual composition of the unending variety of spatio-temporal patterns in our perceptual world. Driven by perceptual discernment of "sudden change" and "unexpectedness", these rules specify conditions (such as co-linearity and virtual continuation) for perceptual grouping and for recursive compositions of perceptual "modalities" and "signatures". Beginning with a smallset of primitive perceptual elements, selected contextually at some relevant level of abstraction, perceptual compositions can graduate to an unlimited variety of spatiotemporal signatures, scenes and activities. Local discernible elements, often perceptually ambiguous by themselves, may be integrated into spatiotemporal compositions, which generate unambiguous perceptual separations between "figure" and "ground". The definition of computational algorithms for the effective instantiation of the rules of perceptual grouping remains a principal problem. In this paper we present our approach for solving the problem of perceptual recognition within the confines of one-D variational profiles. More specifically, concerning "early" (pre-attentive) recognition, we define the "structural identity of a k-norm, k ∈ K,"--SkID--as a tool for discerning and locating the instantiation of spatiotemporal objects or events. The SkID profile also serves a s a reference coordinate framework for the "perceptual focusing of attention" and the eventual assessment of resemblance. Neural network implementations of pre-attentive and attentive recognition are also discussed briefly. Our principles are exemplified by application to one-D perceptual profiles, which allows simplicity of definitions and of the rules of perceptual composition.