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# Absolute Orientation - Horn's method 1.0

Date Added: September 15, 2013  |  Visits: 217

As input data, one has A: a 2xN or 3xN matrix whos columns are the coordinates of N source points. B: a 2xN or 3xN matrix whos columns are the coordinates of N target points. The syntax [regParams,Bfit,ErrorStats]=absor(A,B) solves the unweighted/unscaled registration problem min. sum_i ||R*A(:,i) + t - B(:,i)||^2 for unknown rotation matrix R and unknown translation vector t. This is a special case of the more general problem min. sum_i w(i)*||s*R*A(:,i) + t - B(:,i)||^2 where s>=0 is an unknown global scale factor, to be estimated along with R and t, and w is a user-supplied length N vector of weights. One can include either s or w or both in the problem formulation using the syntax, [regParams,Bfit,ErrorStats]=absor(A,B,'param1',value1,'param2',value2,...) with parameter/value pair options 'doScale' - Boolean flag. If TRUE, the global scale factor, s, is included. Default=FALSE. 'weights' - the length N vector of weights, w. Default, no weighting. OUTPUT: regParams: structure output with estimated registration parameters, regParams.R: The estimated rotation matrix, R regParams.t: The estimated translation vector, t regParams.s: The estimated scale factor (set to 1 if doScale=false). regParams.M: Homogenous coordinate transform matrix [s*R,t;[0 0 ... 1]]. For 3D problems, the structure includes regParams.q: A unit quaternion [q0 qx qy qz] corresponding to R and signed to satisfy max(q)=max(abs(q))>0 For 2D problems, it includes regParams.theta: the counter-clockwise rotation angle about the 2D origin Bfit: The rotation, translation, and scaling (as applicable) of A that best matches B. ErrorStats: structure output with error statistics. In particular, defining err(i)=sqrt(w(i))*norm( Bfit(:,i)-B(:,i) ), it contains ErrorStats.errlsq = norm(err) ErrorStats.errmax = max(err)

 Requirements: No special requirements Platforms: Matlab Keyword: Coordinate,  Homogenous,  Output,  Parameters,  Regparams,  Regparamsm,  Regparamsr,  Regparamst,  Structure Users rating: 0/10