Effective curve registration using a novel solution method for overdetermined systems of polynomial equations

Ji Zhang; Shanshan Huang; Mireille Boutin

doi:10.1117/12.816527

2 February 2009 Effective curve registration using a novel solution method for overdetermined systems of polynomial equations

Ji Zhang, Shanshan Huang, Mireille Boutin

Author Affiliations +

Proceedings Volume 7246, Computational Imaging VII; 72460O (2009) https://doi.org/10.1117/12.816527
Event: IS&T/SPIE Electronic Imaging, 2009, San Jose, California, United States

Abstract

We propose a new method for registering a cloud of points in 2D onto a planar curve. This method does not require the knowledge of an initial guess for the position of the point cloud and proceeds without having to order, smooth out or otherwise process the points of the query point cloud in any way. The method consists in representing the planar curve by an algebraic curve, and in fitting the algebraic curve to the points of the point cloud by solving a corresponding over-constrained system of polynomial equations. The solution of this system is obtained using a new solution method for polynomial systems of equations, which we introduce in this paper. This solution method, which can be seen as an extension of the pseudo-inverse approach to solving linear systems of equations, naturally handles over-contrained systems of equations in a robust fashion.

Citation Download Citation

Ji Zhang, Shanshan Huang, and Mireille Boutin "Effective curve registration using a novel solution method for overdetermined systems of polynomial equations", Proc. SPIE 7246, Computational Imaging VII, 72460O (2 February 2009); https://doi.org/10.1117/12.816527

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available