Logical context of nonlinear filtering
Edward R. Dougherty, Robert M. Haralick · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
The mathematical structure of binary nonlinear filtering is expressed in the context of binary cellular logic and the relevance of existing image algebras is discussed. Operator properties such as antiextensively and idempotence are examined from a discrete logical perspective, as are the classical Matheron representations. The simplicity of the operational properties is exposed by such an approach, as is the use of commonplace logic design methods for the composition and decomposition of nonlinear filters, in particular, binary morphological filters.