6 April 1998 Compact representation of W-operators
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It is well known that the family of hit-miss operators constitutes a sup-generating family for W-operators, that is, any W-operator can be represented as the supremum of hit-miss operators. We present here a new sup-generating family for W- operators: compositions of hit-miss operators with dilations. The representation based on this sup-generating family is called compact, since it may use less sup-generating operators than the hit-miss representation. Considering the W-operators that are both anti-extensive and idempotent (in a strict sense), we have also gotten a simplification of the compact representation. Furthermore, adding the hypothesis of increasingness, we have shown that the simplified compact representation reduces to a minimal realization of the classical representation of Matheron for translation invariant openings.
© (1998) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Junior Barrera, Junior Barrera, Ronaldo F. Hashimoto, Ronaldo F. Hashimoto, } "Compact representation of W-operators", Proc. SPIE 3304, Nonlinear Image Processing IX, (6 April 1998); doi: 10.1117/12.304613; https://doi.org/10.1117/12.304613

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