Analyzing Shape Context Using the Hamiltonian Cycle,"

Abstract. 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

Analyzing Shape Context Using the Hamiltonian Cycle

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.

Perceptually Motivated Shape Context Which Uses Shape Interiors

In this paper, we identify some of the limitations of current-day shape matching techniques. We provide examples of how contour-based shape matching techniques cannot provide a good match for certain visually similar shapes. To overcome this limitation, we propose a perceptually motivated variant of the well-known shape context descriptor. We identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties. We show that our method can easily be augmented with any other shape matching algorithm. We also show from our experiments that the use of our descriptor can significantly improve the retrieval rates

Rotationally invariant 3D shape contexts using asymmetry patterns

This paper presents an approach to resolve the azimuth ambiguity of 3D Shape Contexts (3DSC) based on asymmetry patterns. We show that it is possible to provide rotational invariance to 3DSC at the expense of a marginal increase in computational load, outperforming previous algorithms dealing with the azimuth ambiguity. We build on a recently presented measure of approximate rotational symmetry in 2D defined as the overlapping area between a shape and rotated versions of itself to extract asymmetry patterns from a 3DSC in a variety of ways, depending on the spatial relationships that need to be highlighted or disabled. Thus, we define Asymmetry Patterns Shape Contexts (APSC) from a subset of the possible spatial relations present in the spherical grid of 3DSC; hence they can be thought of as a family of descriptors that depend on the subset that is selected. This provides great flexibility to derive different descriptors. We show that choosing the appropriate spatial patterns can considerably reduce the errors obtained with 3DSC when targeting specific types of points