Motion Detection from Marker
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How can I calculate both translation and rotation (with respect to a center of motion) y=R*x+t with R is rotation matrix and t is translation vector from a dedicated marker. I have the time-series (x,y,z) coordinates of three rigid markers connected to the object?
Thanks in advance for advices!! Andy
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You can do it using my ABSOR tool ( Download ). So, if you have a matrix of 3 points whose coordinates are known
A=[xa1,ya1,za1;xa2,ya2,za2;xa3,ya3,za3].'
and some target points after rototraslation of A,
B=[xb1,yb1,zb1;xb2,yb2,zb2;xb3,yb3,zb3].'
then you can find the rotation/traslation matching A to B with
params=absor(A,B);
R=params.R;
t=params.t;
6 个评论
Andreas
2015-1-4
Not 100% yet. Is the originate coordinate system preserved? I plotted the translation vector of a 3 marker combination with your code (cumulative) versus the translation of the center of mass (x,y,z spatial coordinates, CMS calculated from same marker data as your code). There is a difference:
Matt J
2015-1-4
Not sure what "preservation" means here. You said you had x,y data related by the equation
y=R*x+t
The code finds the R and t that best fits this equation.
Andreas
2015-1-5
The discussion is getting confusing because you are using the notation x,y for two different things, sometimes a "time-step" and sometimes as 3D cartesian coordinates.
But here is the bottom line, I think. You have an initial set of position vectors pos1 and a final set pos2 arrived at after rotation/translation. Here, pos1 and pos2 as 3xN matrices whos column vectors are corresponding points before and after the rototranslation. Both pos1 and pos2 are measured in the same coordinate system and satisfy
pos2(:,i)=R*pos1(:,i) + t (Eq 1)
where R is a rotation matrix and t is a translation vector. So the R and t that the code gives you will correspond to whatever coordinate system pos1 and pos2 are measured in.
how can I calculate from R and t back translation and rotation in the physical coordinate system?
If pos1 and pos2 are measured in the"physical coordinate system", as you say then R and t are the rotation/translation in that system. R is a rotation about some axis through the origin of that system.
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