Absolute Orientation - Horn's method
ABSOR is a tool for least squares estimation of the rotation -- and optionally also the
scaling and translation -- that maps one collection of point coordinates to
another. It is based on Horn's quaternion-based algorithm. The function works for both 2D and 3D coordinates, and also gives the option of weighting the coordinates non-uniformly. The code avoids for-loops so as to maximize speed.
DESCRIPTION:
As input data, one has
答:2 xn或3 xn矩阵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 basic 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.
ABSOR can also solve 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 N-vector of weights. One can include/exclude any
combination of s, w, and translation t in the problem formulation. Which
parameters participate is controlled 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.
Otherwise, it is assumed that s=1. Default=FALSE.
'doTrans' - Boolean flag. If TRUE, the translation, t, is included. Otherwise,
zero translation is assumed. Default=TRUE.
'weights' - The length N-vector of weights, w. Default, no weighting.
OUTPUTS:
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.
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
最佳匹配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)
Cite As
Matt J (2022).Absolute Orientation - Horn's method(//www.tianjin-qmedu.com/matlabcentral/fileexchange/26186-absolute-orientation-horn-s-method), MATLAB Central File Exchange. Retrieved.
MATLAB Release Compatibility
Platform Compatibility
Windows macOS LinuxCategories
Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!Discover Live Editor
Create scripts with code, output, and formatted text in a single executable document.