# Creating 3d coordinates from stereoscopic images

1. Jul 16, 2014

### steven77723

Hi, I'm working on a project that would take a 3d image using stereocopic camera and would record the depth and the 2d (x1,y1) , (x2,y2) coordinates of a single point in the image. The depth is found using the focal point, disparity, and the distance between the difference the camera sees on the point.

I was wondering if there is a formula that would convert this point into a (x,y,z) coordinate. I'm stuck because even if the physical location of the point may be different, the camera would reply with a different depth, but same x,y values.

Thanks,

2. Jul 16, 2014

### elegysix

isn't the depth the z coordinate? Could you be more specific about what you are imaging, and maybe include some kind of illustration?

3. Jul 18, 2014

### Baluncore

Is this a correct description of the problem ?

You have two identical cameras. The pinholes of those cameras are positioned on the x-axis, the first at the origin, looking along the z-axis, with the second camera, at x = s, with camera 2 optical axis parallel to that of camera 1.

The images from the two cameras each have a cardinal reference point, defined by the intersection of the image and the optical axis. A point object, visible on both images is located relative to the reference point; on image #1 at (x1, y1), and on image #2 at (x2, y2).

Find the position of the point object(x, y, z), given s, and the (x1, y1) and (x2, y2) offsets.

Do you have the distance of the pinhole from the image plane?

4. Jul 18, 2014

### blainiac

Last edited: Jul 18, 2014
5. Jul 21, 2014

### steven77723

Baluncore, Thats exactly how I should've worded it.
The distance from the pinhole to image plane is roughly about 50cm, but I want it to work for any value.

6. Jul 21, 2014

### Baluncore

The x-coordinate is a function of s.

The z-coordinate is a function of the image plane to pinhole distance.
With a lens, that is the focal length only when focussed at infinity.
Let's be slack and just call it f.

So you must be able to somehow measure or calibrate f, against your camera separation, s.

Draw a view of the object and image placement in the x-z plane and you will see it is ratiometric.
x = s * x1 / (x1+x2), I will let you sort out the sign of the x values.
z = f * ?, and the y = ? values.

See the post#4 references from blainiac.