Curve matching for open 2D curves

We present a curve matching framework for planar open curves under similarity transform1Similarity transform is defined as a 2D transform that is limited to translation, rotation and uniform scaling.¹ based on a new scale invariant signature. The signature is derived from the concept of integral of unsigned curvatures. If one input curve as a whole can be aligned with some part in the second curve then the algorithm will find the requisite starting and end positions and will estimate the similarity transform in O (N log (N)) time. We extend our frame work to a more general case where some part of the first input curve can be aligned with some part of the second input curve. This is a more difficult problem that we solve in O (N³) time. The contributions of the paper are the new signature as well as faster algorithms for matching open 2D curves. We present examples from diverse application set to show that our algorithm can work across several domains.