Dear DAVID Community,

As you are probably aware, the entire DAVID company, team and product range has been integrated into HP Inc.
This forum is now read-only. Relevant content has been migrated to HP and merged into HP's Support Forums on November 1, 2016.

To start new discussions for 3D Scanning, please register and post your new topic at the HP Support Forums

Help RE: Tsai Calibration

The place for questions, problems, comments and tips regarding the camera calibration.

Help RE: Tsai Calibration

Postby poojit » Thu Jun 04, 2009 1:22 pm

Hi,

I was hoping someone who has a good knowledge of how DAVID works could explain how it uses Tsai Calibration

Ive read the Tsai paper and tried computing the rotational matrix R and translational matrix T followed by principal point (x0,y0) and focal distance f.

Tsai requires the foll parameters :-

Xi,Yi - image coordinates
Xc,Yc,Zc - camera coordinates
Xs,Ys,Zs - scence coordinates
f- principal focus
X0,Y0 - principal point

Ive taken Xs,Ys,Zs as the points given in Calibpoints.dat in the DAVID folder.

Xi,Yi as the coordinates of the red markers after DAVID has calibrated. (I as of now havent tried detecting the points from the image using any algorithm so just fed them manually).

Now i have 25 scene coordinates (i.e. Xs,Ys,Zs) and 25 corresponding image coordinates (i.e. Xi,Yi). Using the equation on page 6 in the Tsai pdf, I have set Ty=1 and converted the homogenous system to non-homogenous system and solved for sr11,sr12,sr13,stx,r21,r22,r23 using 7 points (points 0,4,10,12,14,20,24 as marked by the DAVID calibpoints).
I havent done that least squares method for overdeterministic set of equations as of now.

I then find out the scale factor c and also s.

I then multiplied sr11,sr12,sr13,stx,r21,r22,r23 by c and divided sr11,sr12,sr13 by s.

Now i have r11,r12,r13
r21,r22,r23
NOTE: the above are after multiplying by c

To find last row of rotation vector r31,r32,r33 , i normalized the first two rows and did their cross product as told.
Finally to find ‘f’ and ‘tz’ i used one of the 25 points in calibpoints.dat and solved the two equations.

-----------------------------------------

Here is my problem

When i use point 0 (i.e 147.00000 20.00000 0.00000)
i got principal focus f = 0 and tz = around 69 approx.

f=0 didnt make sense to me. possibly ive interpreted the Tsai paper wrongly or gone wrong along the way .

If someone could help me out, it would be greatly appreciated.

I have attached the paper i referred to.

Following are the Xi and Yi(found manually from the DAVID window) that i fed to corresponding calibpoints

0 610 474
1 613 322
2 591 206
3 572 110
4 557 28
5 513 516
6 500 381
7 488 268
8 480 172
9 470 91
10 405 561
11 402 431
12 400 323
13 397 229
14 395 149
15 275 560
16 286 430
17 293 321
18 299 228
19 302 147
20 167 517
21 186 378
22 201 265
23 214 169
24 226 89

Calibpoints.dat :-

0 147.00000 20.00000 0.00000
1 160.00000 80.00000 0.00000
2 160.00000 140.00000 0.00000
3 160.00000 200.00000 0.00000
4 160.00000 260.00000 0.00000
5 100.00000 20.00000 0.00000
6 100.00000 80.00000 0.00000
7 100.00000 140.00000 0.00000
8 100.00000 200.00000 0.00000
9 100.00000 260.00000 0.00000
10 40.00000 20.00000 0.00000
11 40.00000 80.00000 0.00000
12 40.00000 140.00000 0.00000
13 40.00000 200.00000 0.00000
14 40.00000 260.00000 0.00000
15 0.00000 20.00000 40.00000
16 0.00000 80.00000 40.00000
17 0.00000 140.00000 40.00000
18 0.00000 200.00000 40.00000
19 0.00000 260.00000 40.00000
20 0.00000 20.00000 100.00000
21 0.00000 80.00000 100.00000
22 0.00000 140.00000 100.00000
23 0.00000 200.00000 100.00000
24 0.00000 260.00000 100.00000
Attachments
Tsai_Revisited.pdf
(90.78 KiB) Downloaded 203 times
xiyi.jpg
poojit
 
Posts: 1
Joined: Thu Jun 04, 2009 10:33 am

Return to Camera Calibration

Who is online

Users browsing this forum: No registered users and 2 guests