This paper was originally published as a Technical Report No.228 in July 2006 for the Ivan E. Seidenberg School of Computer Science and Information Systems (ISSCSIS), Pace University.

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Shape matching plays important roles in many fields such as object recognition, image retrieval,etc. Belongie, proposed a novel shape matching algorithm utilizing the shape context as a shape descriptor and the magnitude of the aligning two shape contexts as a distance measure. It was claimed to be an information rich descriptor that is invariant to translation, scale and rotation. We examine the limitation of the algorithm using graph theory and present several geometrically different shapes that are considered identical by the shape context algorithm. Theoretical contributions pertain to linking shape context and the Hamiltonian cycle. .