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This paper presents a novel approach for object skeleton family extraction. The introduced technique utilizes a 2-D physics-based deformable model that parameterizes the objects shape. Deformation equations are solved exploiting modal analysis, and proportional to model physical characteristics, a different skeleton is produced every time, generating, in this way, a family of skeletons. The theoretical properties and the experiments presented demonstrate that obtained skeletons match to hand-labeled skeletons provided by human subjects, even in the presence of significant noise and shape variations, cuts and tears, and have the same topology as the original skeletons. In particular, the proposed approach produces no spurious branches without the need of any known skeleton pruning method.