Study Of Granule Analysis Operator

The works of Serra and Matheron have given a lot of methods about granuleanalysis which were widely used，but the research about granule analysis operatortheory is relatively rare.This paper starts complete lattices theory. First，give completelattices corrosion and inflation operator theory，opening and closing operation theory，adjunction，and give granule analysis operator theory based on complete lattices，basedon this, study the up semi-continuity of granule analysis on the complete lattices,criticality, regularization.The work of this paper is as follows:(1) Started from binary morphology theory,establish binary of granule analysistheory,give the experiment of granule analysis processing binary image. On the basis ofbinary morphology theory,give Euclidean granule analysis definition，and prove theEuclidean granule analysis properties.(2) On the basis of complete lattices granule analysis theory, and study the upsemi-continuity of granule analysis, criticality and regularization of granule analysisrespectively.(3) Give the definition of sup-generating family λ,and the definition of dilation anderosion on sup-generating family λ,combined with complete lattices granule analysiskernel concepts and binary morphology granule analysis theory, try to discusses therelationship between them.And use the opening operator of the invariant domain toconstruct granule analysis operator on complete lattices.