TY - GEN
T1 - Finding optimal convex gray-scale structuring elements for morphological multiscale representation
AU - Morales, Aldo W.
AU - Ko, Sung Jea
PY - 1996
Y1 - 1996
N2 - Recent papers in multiscale morphological filtering, particularly, have renovated the interest in signal representation via multiscale openings. Although most of the analysis was done with flat structuring elements, extensions to grayscale structuring elements (GSE) are certainly possible. In fact, we have shown that opening a signal with convex and symmetric GSE does not introduce additional zero-crossings as the filter moves to a coarser scales. However, the issue of finding an optimal GSE is still an open problem. In this paper, we present a procedure to find an optimal GSE under the least mean square (LMS) algorithm subject to three constraints: The GSE must be convex, symmetric, and non-negative. The use of the basis functions simplifies the problem formulation. In fact, we show that the basis functions for convex and symmetric GSE are concave and symmetric, thus alternative constraints are developed. The results of this algorithm are compared with our previous work.
AB - Recent papers in multiscale morphological filtering, particularly, have renovated the interest in signal representation via multiscale openings. Although most of the analysis was done with flat structuring elements, extensions to grayscale structuring elements (GSE) are certainly possible. In fact, we have shown that opening a signal with convex and symmetric GSE does not introduce additional zero-crossings as the filter moves to a coarser scales. However, the issue of finding an optimal GSE is still an open problem. In this paper, we present a procedure to find an optimal GSE under the least mean square (LMS) algorithm subject to three constraints: The GSE must be convex, symmetric, and non-negative. The use of the basis functions simplifies the problem formulation. In fact, we show that the basis functions for convex and symmetric GSE are concave and symmetric, thus alternative constraints are developed. The results of this algorithm are compared with our previous work.
UR - http://www.scopus.com/inward/record.url?scp=0029708890&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:0029708890
SN - 0819420360
SN - 9780819420367
T3 - Proceedings of SPIE - The International Society for Optical Engineering
SP - 129
EP - 141
BT - Proceedings of SPIE - The International Society for Optical Engineering
A2 - Dougherty, Edward R.
A2 - Astola, Jaakko T.
A2 - Longbotham, Harold G.
T2 - Nonlinear Image Processing VII
Y2 - 29 January 1996 through 30 January 1996
ER -