# Multi-camera calibration wand

I am master student, and I work on project with camera tracking based on sphered Infrared (IR) markers.

Now I have to implement multi-camera calibration system with a wand like this one:

And I want to find out the details of each step, understand it.

My cameras has IR filter, and it helps to discard another information (example of image, it is not a calibration wand on a photo):

To find a center of sphere (actually, the projection of sphere will be ellipse in general case):

1. Find countours;
2. Fit the ellipse to contour;
3. Calculated weighted center of fitted ellipse

$\bar{u}=\frac{\sum_{i=1}^{n}\sum_{j=1}^{m} u_iw_{i,j}}{\sum_{i=1}^{n}\sum_{j=1}^{m} w_{i,j}};$

$\bar{v}=\frac{\sum_{i=1}^{n}\sum_{j=1}^{m} v_jw_{i,j}}{\sum_{i=1}^{n}\sum_{j=1}^{m} w_{i,j}};$

where $u_i$ - x coordinate of pixel, $v_i$ - y coordinate of pixel, $w_{i,j}$ - gray-scale value of pixel.

But what do I have to do after that? I just don't know how to connect pinhole camera matrix with this centers. I know that:

$\lambda m_1=K_1[R_1T_1]M$ and $\lambda m_2=K_2[R_2T_2]M$,

where $m_i=[u_i,v_i,1]$ - coordinate on pixel map, $K%$ - intrinsic parameters of camera, $R$ - rotation matrix, $T$ - translation matrix, $M=[X,Y,Z,1]$ - coordinate in 3D world.

Also I have to include distortion model, but I miss the chain, which connect general matrix model with these centers of spheres.

I also can let, that these 3 IR markers have $Y=0, Z=0$, because they are situated on the line. Is it true assumption?

If you refer me to any book, paper or something, I will be very glad of it.

• So what exactly is your question? "I also can let, that these 3 IR markers have Y=0,Z=0, because they are situated on the line. Is it true assumption?" No. – Evil Jul 27 '17 at 4:40
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