On Aligning Curves

Thomas B. Sebastian,  Philip N. Klein,  Benjamin B. Kimia

Brown University, Providence RI, USA

Abstract

We present a novel  approach to finding a correspondence (alignment) between two curves. The correspondence is based on a notion of an alignment curve which treats both curves symmetrically. We define a metric of  similarity based on the alignment using two intrinsic properties of the  curve, namely, length and curvature. The optimal correspondence is found by an efficient dynamic-programming method both for aligning pairs of curve segments and pairs of closed curves, and is effective in the presence of a variety of transformations of the curve. We then show how the alignment can be used to ``average'' a set of curves. Finally, the correspondence is shown to serve as a key element in a number of applications including handwritten character recognition, prototype formation, shape morphing, comparing medical structures and object recognition. These applications depict the usefulness of the curve alignment framework which is potentially useful in other applications such as registration and tracking.
 

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