A new Chebyshev polynomials descriptor applicable to open curves

Effective and efficient representation of open curves is a challenging problem in statistical shape analysis. In this paper, we propose a novel shape descriptor, called Chebyshev polynomial descriptor (CPD) for representing open curves. Firstly, a general formula for the computation of CPDs and parametric equations of reconstructed curves are given; secondly, we investigate properties of CPDs, including its stability, similarity-invariant and invariance under different starting points. Finally, the reconstructed curve from CPDs is used to compute the curvature of an original open curve. Experimental results demonstrate the effectiveness of both representation of handwriting and computation of curvatures.