# Absolute Orientation - Horn's method (Scripts) 1.0

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• Last update: 5 years ago
• Operating system: Linux, Mac OS X, Win All, BSD, Solaris
• Publisher: Matt J (15 other programs)
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## Absolute Orientation - Horn's method (Scripts) Publisher's description

### ABSOR - a tool for solving the absolute orientation problem using Horn's

ABSOR - a tool for solving the absolute orientation problem using Horn's
quaternion-based method, that is, for finding the rotation, translation, and
optionally also the scaling, that best maps one collection of point coordinates
to another in a least squares sense. 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 to maximize speed.

DESCRIPTION:

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)

#### System Requirements:

MATLAB 7.9 (2009b)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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