Patent Document ID: 8768101
Application ID: 13174723
Patent Flag: 1

Claim One:
1. A method for determining an optimal rotational matrix R Ti and an optimal translation vector TR Ti for registering and calibrating a target image I Ti with a reference image I R , wherein reference image I R is characterized as a two dimensional set of points labeled p i , and target image I Ti is characterized as a two dimensional set of points labeled p i ′, such that: p i ′=R Ti p i +TR Ti + N i , where R Ti is a 3×3 rotation matrix; TR Ti is a 3×1 translation vector, and N i represents noise; comprising finding an R Ti and TR Ti to minimize: Σ 2 = ∑ i = 1 N ⁢  p i ′ - ( R Ti ⁢ p i + TR Ti )  2 by the steps of: (a) defining mean values p and p ′ of, respectively, p and p′ as: p _ = 1 N ⁢ ∑ i = 1 N ⁢ ⁢ p i ⁢ ⁢ ⁢ and p _ ′ = 1 N ⁢ ∑ i = 1 N ⁢ ⁢ p i ′ ; (b) defining two error measures representing variability about mean values p and p ′ as: 
 q i =p i − p 
 q i ′=p i ′− p i ; (c) from p i and p i ′, calculating mean values p and p ′ according to step (a) and calculating the two error measures q i and q i ′ according to step (b); (d) calculating a 3×3 matrix H defined as: H := ∑ i = 1 N ⁢ q i ⁢ q i ′ ⁢ ⁢ T ; (e) finding the singular value decomposition of H as: 
 H=UδV T ; (f) calculating the optimum R Ti to minimize the value of the equation in step (a) as: 
 R Ti =VU T , and; (g) calculating the optimal TR Ti as: 
 TR Ti =p′− R Ti p.