Morphological smoothing

Using concepts from mathematical morphology and learnability theory, a well-behavedness result pertaining to smoothing is demonstrated, which has fundamental ramifications ranging from physics to cognition, that states that the number of instantiated points needed to adequately reconstruct the underlying finite-sized Euclidean set is tractably large. As can be inferred in the formulation BUPETSS (bounding undershoot perception error through sufficient sampling) theorem 1 has some fundamental implications for smoothing as a cognitive and/or geometrical process. Owing to the quasi-distribution-free nature of the results in theorems 1 and 2, in conjunction with the polynomial complexities implied in eqns. 4 and 5, the interpretations drawn are presented.