Shape matching and object recognition using shape contexts

www.cs.berkeley.edu/~malik/papers/BMP-shape.pdf

This paper suggests its unique shape context descriptor by which you can do shape matching and object recognition. 

In fact, I couldn't understand the logic which this paper suggests but I could know the background knowledge about recognition technology roughly. So, I want to cite some impressive statements. 

1. Introduction

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Our primary contribution in this work is a robust and simple algorithm for findning correspondences between shapes. 

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We introduce a shape descriptor, the shape context, to describe the coarse distribution of the rest of the shape with respect to a given point on the shape.

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The dissimilarity between the two shapes can now be computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. 

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2. Prior work on shape matching

Mathematicians typically define shape as an equivalence class under a group of transformations. This definition is imcomplete in the context of visual analysis. This only tells us when two shapes are exactly the same. We need more than that for a theory of shape similarity or shape distance. 

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2.1 Feature-based methods

A great deal of research on shape similarity has been done using the boundaries of silhouette images. 

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Silhouettes are fundamentally limited as shape descriptors for general objects; they ignore internal contours and are difficult to extract from real images. More promising are approaches that treat the shape as a set of points in the 2D image. Extracting these from an image is less of a problem-e.g., one can just use an edge detector. Huttenlocher et al. developed methods in this category based on the Hausdorff distance; this can be extended to deal with partial matching and clutter. 

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3. Matching with shape contexts

In our approach, we treat an object as a (possible infinite) point set and we assume that the shape of an object is essentially captured by a finite subset of its points.

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3.3 Invariance and Robustness

A matching approach should be 1) invariant under scaling and translation, and 2) robust under small geometrical distortions, occlusion and presence of outliers. 

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