motion capture using only one marker and one camera

[Sina Mehdizadeh]

Hello everyone,
I am going to record the motion of subjects while performing shuttle test. Due to some considerations I want to attach only one marker on the head of the subjects. The camera will be attached to the roof in a way that its lens is parallel to the ground and it will record the 2D horizontal motion of the performer.
I wish to know is this setup, a marker on the head and one camera, suitable for recording? Are data acquired reliable? Otherwise, what is the other similar reliable setup regarding marker placement and camera positioning?

Regards,

Sina

Tehran

[Ton van den Bogert]

Re: motion capture using only one marker and one camera

Dear Sina,

The setup you propose should work well in certain conditions.

If the camera on the ceiling is high enough, with image plane oriented parallel to the floor, a simple scaling of the image data will give you actual horizontal displacement.

If the celing is not very high, you will need to assume that the marker will stay in the same horizontal plane.

If the camera image plane is not oriented parallel to the floor, a relatively simple 2D DLT calibration can help transform from image coordinates to real XY coordinates. See here for an old Biomch-L thread on this topic. A minimum of four calibration points, placed in the same plane as the marker will be, are required. I think DLT calibration is always a good idea. It will take care of the scaling and you will not have to worry about camera placement and orientation.

The camera calibration and 2D coordinate calculation are relatively easy to do in Matlab. Some code with the 3D DLT can be found in the Kinemat software. The 2D DLT is done in a very similar way, only with a simpler camera model. And the 2D coordinate calculation from image coordinates involves 2 equations with 2 unknowns, so there is no least-squares method needed.

If you are using a wide angle lens that introduces distortion, you may need a nonlinear camera model which is similar to DLT but has additional terms such as X^2, Y^2, and XY in the camera model. Then you will also need more than 4 calibration points to determine the camera parameters. Solving the X and Y from the image coordinates (u,v) is no longer a linear problem, so you would need some sort of iterative method such Matlab's fsolve or your own implementation of the Newton-Raphson algorithm.

More information can be found by searching Biomch-L with the keywords "camera calibration" or "lens distortion".

Ton van den Bogert

[Sina Mehdizadeh]

Re: motion capture using only one marker and one camera

Dear professor Bogert

Thank you for your valuable reply. It was so comprehensive and helpful. I will implement the method and I will ask if I had any further questions.

Sina