The problem of extraction of medial axis transformation of a gray image with reference to skeletonization, image representation and uncertainty management in a vision system has been addressed. The Fuzzy Medial Axis Transformation (fmat) of a fuzzy setf is a set of fuzzy disks whose sup isf. Unfortunately, specifying thefmat sometimes requires more storage space than specifyingf itself. The present paper describes some techniques to improve the compact representation offmat; thereby making it practically useful to an image for its skeleton extraction and compact representation, for shape analysis and template matching, for representation and retrieval, for uncertainty management in recognition and for creating new images of various poses. The algorithms involve reduction of redundancy infmat, its approximation, and reduction of the searching spaces for its computation. Computational aspects for the convenience of writing an efficient program have been described. Some applications of thefmat have also been mentioned.