How to estimate the disparity/depth map limits from stereo geometry parameters?

Question

i'm trying to estimate an upper limit for the disparity between some points in a stereo pair. I know the following parameters:

converge angle: 2.2°

baseline: 77 mm

focal length: 6.3 mm

Xresolution: 72

Yresolution: 72

resolution unit: 0x2 (inch)

i know that the distance between corrispondent points in x direction (along the epipolar line) varies up to about 120 pixel... i've seen that for points in foreground this distance is little, for points in background is greater and i want a method to establish an upper limit for this distance automatically... my question is if i could estimate this upperlimit using these parameters (without estimate the disparity/depth map).. i don't need the exact values of disparity but just an approximation for vary my upper limit safety.

notice i've not the sensor size :(

thanks for all responses!

Answer 1

Some clarification first - the question seems to confuse disparity with distance, whereas they are (roughly) the inverse of each other. The disparity is large in absolute value for close points, small for far away ones. E.g., for cameras with parallel focal axes, a point at infinity in the direction of the same axis would have exactly zero disparity.

As for the sensor resolution, if you have the EXIF headers, see if it's actually there. The keys of interest are "FocalPlaneXResolution" etc. The one you quote, XResolution, is the print resolution, which is something else (and completely useless). See this page for details.

The distance resolution and bounds are easier to work out for parallel cameras. See, for example this article. For toed-in cameras the geometry is a little more complicated, especially if you cannot assume that the focal axes are convergent (so that baseline and both focal axes lie in the same plane). Either way, you compute them as follows:

• For the closest distance, you consider one plane and two rays:

  • The plane is the back-projection of the right edge of the left image, i.e. the plane containing the left of optical center and the right edge of the left image.
  • The rays are the back-projections of the top-left and bottom-left corners of the right image.
  • The closest of the two points of intersection between the plane and the rays is the closest point that's visible and measurable by the stereo pair.

  -

• For the farthest distance, you consider:
  • The ray Rf in the right camera that's parallel to the focal axis F of the left camera. Backproject Rf to find its corresponding pixel. The disparity at this pixel is, of course, exactly zero, since it is the disparity of two parallel rays.
  • Now move one pixel toward the left in the same plane Rf-F, and find the ray Rd that backprojects this second pixel. Rd must intersect F, since it's in the same plane and is not parallel to F. The intersection is at the farthest distance that can be measured units of disparity of one pixel.