Matching shapes

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Abstract
We present a novel approach to measuring similar- ity between shapes and exploit it for object recogni- tion. In our framework, the measurement of similar- ity is preceded by (1) solving for correspondences be- tween points on the two shapes, (2) using the correspon- dences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descrip- tor, the shape context, to each point. The shape con- text at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thin-plate splines provide a fle xi- ble class of transformation maps for this purpose. Dis- similarity between two shapes is computed as a sum of matching errors between correspondingpoints, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework. Results are presented for sil- houettes, trademarks, handwritten digits and the COIL dataset.

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