# Shape Matching and Object Recognition Using Shape Contexts

### Serge J. Belongie, Jitendra Malik and Jan Puzicha

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-01-1128

2001

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2001/CSD-01-1128.pdf

We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solving for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context 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 flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits and the COIL dataset.

BibTeX citation:

@techreport{Belongie:CSD-01-1128, Author = {Belongie, Serge J. and Malik, Jitendra and Puzicha, Jan}, Title = {Shape Matching and Object Recognition Using Shape Contexts}, Institution = {EECS Department, University of California, Berkeley}, Year = {2001}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2001/6435.html}, Number = {UCB/CSD-01-1128}, Abstract = {We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solving for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context 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 flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits and the COIL dataset.} }

EndNote citation:

%0 Report %A Belongie, Serge J. %A Malik, Jitendra %A Puzicha, Jan %T Shape Matching and Object Recognition Using Shape Contexts %I EECS Department, University of California, Berkeley %D 2001 %@ UCB/CSD-01-1128 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2001/6435.html %F Belongie:CSD-01-1128