Question

Simple Stereo: Consider the typical “simple stereo” camera system where the orientations of the coordinate axes of the two cameras are the same, but the right camera is shifted 40 cm to the right along the positive X axis.

*ALL ANSWERS WILL BE INTEGERS.*

4a. (3 points) For a focal length of 50 pixels, and stereo baseline of 40 cm, what is the depth of a surface point that has a disparity value of 25 pixels?    Answer in cm

4b. (3 points) For a focal length of 50 pixels and stereo baseline of 40 cm, what is the disparity of a point that has depth (Z value) of 80 cm? Answer in pixels

4c. (3 points) For a focal length of 50 pixels, and stereo baseline of 40 cm, if I know that the closest surface in my scene is no less than 50 cm away, what is the maximum integer disparity value I can expect to see? Answer in pixels

4d. (3 points) For a focal length of 50 pixels and a stereo baseline of 40 cm, what is the farthest finite depth that can be measured if disparity d is constrained to be an integer (i.e. d=0,1,2,3,4,... that is, we cannot computed d to subpixel precision)? Hint: we are looking for the farthest Z value beyond which we have to say the point is “at infinity” Answer in cm

4e. (3 points) For ANY non-zero focal length and stereo baseline, if disparity d is constrained to be an integer in the range 0 <= d <= 16, how many finite depths can be computed in the scene? (finite means it evaluates to a number less than infinity)

Answer 1

Answer:

4a.

As per the method of triangulation, depth Z is related to focal length f, baseline b and disparity d by

Z = (f*b)/d

Or, Z = (50 pixel * 40 cm) / 25 pixel

Now, 1 pixel = 0.026 cm

Thus, Z = (50*0.026*40) / (25*0.026) cm

Or, Z = 80 cm

Thus, depth = 80 cm

4b.

Z = 80cm

F = 50 pixel

b = 40 cm = 1511 Pixel

Thus, disparity d = f*b/z

Or, d = (50*1511)/3023 Pixel

Or, d = 25 pixel

Thus disparity = 25 pixel

4c.

Z = 50 cm = 1889 pixel

F = 50 pixel

B = 40 cm = 1511 pixel

Thus, d = f*b/z

Or, d = 50*1511/1889

Or, d = 40 Pixel

Thus, maximum integer disparity value = 40 pixel

4d.

Z = F*b/d

As Z and d are inversely proportional, for Z to be maximum, the value of D should be minimum.

We cannot put the value of d as 0. Thus, the value of d must be equal to 1 (as it can be an integer only)

On substituting the values, we have

Z=50*.026*40 cm

Or Z = 52 cm

Thus, the farthest finite depth that can be measured if disparity is constrained to be an integer is 52 cm.