Shape matching plays important roles in many fields such as object recognition, image retrieval,etc. Belongie, et.al.recently 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. .
Abrams, Carl E.; Tappert, Charles C.; and Cha, Sung-Hyuk, "Analyzing Shape Context Using the Hamiltonian Cycle" (2006). CSIS Technical Reports. Paper 23.