SOME PROBLEMS CONCERNING NON CONVEX ANALYSIS AND THEIR APPLICATIONS

Abstract

This thesis aimed to study non convex analysis by a new approach. The new approach is to define a p-convex analysis and apply it on digital image processing. At the same time we extend the notion of infimal convolution to a p-infimal convolution, and show that it is commutative and associative operation on functions. We also use p-infimal convolution to get some p- norms that define p-distances and to get some class of p-convex neighborhoods which are more appropriate to handle with and to get better performance for image processing (01p<≤ ). Indeed, we have discussed morphological image processing. We study the concepts of two operations, erosion and dilation. We remark that these operations are duals of each other with respect to set complementation and reflection. We extend the notion of convex hull for a given set to p-convex hull, 01p<≤.