TY - GEN
T1 - Morphological approach to smoothing
AU - Kim, Woon K.
AU - Song, S. M.
PY - 1997
Y1 - 1997
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0031361121&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:0031361121
SN - 0819424897
T3 - Proceedings of SPIE - The International Society for Optical Engineering
SP - 171
EP - 179
BT - Proceedings of SPIE - The International Society for Optical Engineering
A2 - Park, Stephen K.
A2 - Juday, Richard D.
PB - Society of Photo-Optical Instrumentation Engineers
T2 - Visual Information Processing VI
Y2 - 21 April 1997 through 22 April 1997
ER -