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In this paper, we propose a numerical algorithm for extracting the topology of a three-dimensional object (2 dimensional surface) embedded in a three-dimensional space R3. The method is based on capturing the topology of a modified Reeb graph by tracking the critical points of a distance function. As such, the approach employs Morse theory in the study of translation, rotation, and scale invariant skeletal graphs. The latter are useful in the representation and classification of objects in R3.