The Application Research Of Image Analysis Method Based On The Relative Shape In The Projective Morphology

This paper generalizes the model of absolute forms based on orthogonal projections and relative forms based on oblique projections in Pyt'ev morphology from two image spaces to three image spaces,and uses projection operator,Equations,limit,eigenvalue and eigenvector to establish the relative theory of absolute forms and relative forms in the three image spaces.Then the paper analyses the correlation and independence about different shapes,and obtains the index of morphological independence of relative forms and the index of morphological connection of absolute forms.This results provide an effective tool for image shape comparison,image recognition,image recognition and image classification.This paper will discuss the main content from the following three aspects:Firstly,by the nature of the finite dimensional Hilbert space and absolute shape theory based on orthogonal projection it constructs all relative shape of orthonormal basis.Based on all relative shape of orthonormal basis,it constructs oblique projection through the idea of equations.Secondly,on the basis of block and elementary transformation,analyzes of the matrix as the coefficient matrix is symmetry and half qualitative.In the process of the analysis of the coefficient matrix,by assuming the relationship between relative shape of orthonormal basis,it respectively analyzes the correlation of relative shape under the three conditions.Moreover,it analyzes connection of absolute forms in the three image spaces.Then the paper analyses the correlation and independence about different shapes,and obtains the index of morphological independence of relative forms and the index of morphological connection of absolute forms.Finally,the paper derives and proves in detail the property of index of morphological connection of absolute form and index of morphological independence of relative form.And it is concluded that the size of the two kinds of index is quantitative indicator of image analysis quality based on the relative shape in the projective morphology.