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The aim of this paper is mainly on using the potential strength of the skeleton of discrete objects in computer vision and pattern recognition. We propose to represent the medial axis characteristic points as an attributed skeletal graph to model the shape. The information about the object shape and its topology is totally embedded in them and this allows the comparison of different objects by graph matching algorithms. The experimental results demonstrate the correctness in detecting its characteristic points and in computing a more regular and effective representation for a perceptual indexing. The matching process, based on a revised graduated assignment algorithm, has produced encouraging results, showing the potential of the developed method in a variety of computer vision and pattern recognition domains. The results demonstrate its robustness in the presence of scale, reflection and rotation transformations and prove the ability to handle noise and occlusions.