Research And Application Of Gray-scale Morphological Operator Algebra Representation

Complete lattice is the theoretical basis of the binary morphology and gray-scalemorphology, all of the morphological operators are transforms which based on the ordinalrelations of the lattice and the infimun and supermum, operators’ representations are moreabstract as well. In this paper, through the sup-generating family and the transformation groupwhich is composed of automorphisms of the complete lattice, morphology operators can berepresented more clearly. On this basis, we systematically establish the algebraicrepresentations of gray-scale morphological operators which under a fixed structure and avariant element structure respectively. Through a comparative study of morphologicaltransformation on the iris image processing,we give a new idea and way of iris featurelocation.The main work of this paper is concluded as following several aspects：1. The algebraic representation of morphology operators which base on thesup-generating family and the transformation group;According to the binary morphological translation, we give the transformation groupwhich is composed of automorphoisms on the lattice an algebraic character and thenmorphology operator can be represented more clearly, and prove the morphological operatorson the complete lattice representation theorem from the algebraic point of view.2. Established gray-scale morphological operators’ algebraic representations which underthe additive structure and multiplicative structure element respectively;As a pair of operators of complete lattice which satisfying adjunction are dilation anderosion, we choose transformations groups are additive translation group and themultiplicative group,establish and demonstrate the algebraic representation ways of gray-scalemorphological operators under an additive structure and a multiplicative structure elementrespectively. And using the anamorphosis, we describe the relation between additive andmultiplicative structure element of grayscale morphological operators.3. Proposed the Spatially-Variant morphological operators’ algebraic representations’methods under Boolean lattice and SV gray-scale morphological operators’ algebraicrepresentations under an additive and a multiplicative structure element respectively;Based on the methods of morphological operators’ algebraic representations underBoolean lattice, we establish the SV morphological operators’ algebraic representations underthe Boolean lattice, and study SV gray-scale morphological operators’ algebraicrepresentation under an additive and a multiplicative structure element respectively.According to the studies, it is show that the properties which valid under the additive structureelement are still valid under the multiplicative structure element;4. Applied morphological methods to the iris image preprocessing and feature location;In the background of iris image recognition, we detaily descript the morphologicaltransformation in the preprocessing and feature location, and focus on the positioning of the iris image. Different from the traditional location whcih is circled by looking for the center ofthe iris area; we use an alternating sequential morphological filtering to remove the eyelashesand eyelids, thus achieving the effect of positioning of the iris outer boundary.