Curve Parameterization and Curvature via Method of Hurwitz-Radon Matrices

Parametric representation of the curve is more appropriate in computer vision applications then explicit form y = f(x) or implicit representation f(x, y) = 0. Proposed method of Hurwitz-Radon Matrices (MHR) can be used in parameterization and interpolation of curves in the plane. Suitable parameterization leads to curvature calculations. Points with local maximum curvature are treated as feature points in object recognition and image analysis. This paper contains the way of curve parameterization and computing the curvature in the range of two successive interpolation nodes via MHR method. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurwitz-Radon (OHR), built from these matrices, is described. It is shown how to create the orthogonal OHR and how to use it in a process of curve parameterization and curvature calculation.