Bi-variate pattern spectrum

Bivariate pattern spectrum is the generalization of the concept of usual pattern spectrum. The usual pattern spectrum is the mapping from multidimensional set to 1D vector, whereas bivariate pattern spectrum is the mapping of multidimensional set to 2D vector. The introduction of bivariate pattern spectrum, based upon the geometrical concepts, has the notion to develop a shape-size descriptor, in the true sense. For defining bivariate pattern spectrum we introduce the concept of parametric and conditional parametric morphological operators. The usual binary morphological operators are the special case of parametric morphological operators