Registering perspective contours with 3-D objects without correspondence, using orthogonal polynomials

The paper proposes aligning perspective contours with 3D objects without knowledge of the correspondence between 2D image points and a projected 3D model, by matching some global image characteristics from the images. It was found that simply using image moments was not sufficient for registration, but converting the image with orthogonal polynomials gave good results. The proposed approach only requires computational complexity of O(n), where n is the number of image contour points to be aligned, and provides the flexibility of not requiring the same number of 2D and 3D points. Furthermore, convergence regions for finding numerical solutions are enlarged significantly by using central moments. Global convergence is achieved using 64 different initial guesses. Experiments with Monte Carlo analysis of three different objects with different movements have been conducted to show the effectiveness of the proposed approach. The results of using three different orthogonal polynomials: Chebyshev, Gram and Legendre polynomials at three different noise levels are also compared.