22 July 1997 Morphological approach to smoothing
Author Affiliations +
In this paper, we present some fundamental theoretical results pertaining to the question of how many randomly selected labelled example points it takes to reconstruct a set in euclidean space. Drawing on results and concepts from mathematical morphology and learnability theory, we pursue a set-theoretic approach and demonstrate some provable performances pertaining to euclidean-set-reconstruction from stochastic samples. In particular, we demonstrate a stochastic version of the Nyquist Sampling Theorem - that, under weak assumptions on the situation under consideration, the number of randomly-drawn example points needed to reconstruct the target set is at most polynomial in the performance parameters and also the complexity of the target set as loosely captured by size, dimension and surface-area. Utilizing only rigorous techniques, we can similarly establish many significant attributes - such as those relating to robustness, cumulativeness and ease-of- implementation - pertaining to smoothing over labelled example points. In this paper, we formulate and demonstrate a certain fundamental well-behaving aspect of smoothing.
© (1997) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Woonkyung Michael Kim, Woonkyung Michael Kim, Samuel Moon-Ho Song, Samuel Moon-Ho Song, } "Morphological approach to smoothing", Proc. SPIE 3074, Visual Information Processing VI, (22 July 1997); doi: 10.1117/12.280619; https://doi.org/10.1117/12.280619

Back to Top