Disparity Angle

[bohemian]

Hi Bob,

Would you please explain, what is "disparity angle" and why it can be
used to estimate obstacle distance?

Cheers

[Bob Mottram]

Suppose that two points in a pair of camera images have been found to correspond.  Unless the point is far away there will be a difference in the horizontal position of the point in both images of typically a few pixels.  We know the number of horizontal pixels across the image (usually 320 or 640) and we also know the field of view of the camera (for webcams its usually around 40 degrees from the far left of the image to the far right).  So we can turn the difference in position of the point from pixels into an angle, called the disparity angle.  Usually all angles are represented as radians within computer programs.

Knowing the disparity angle, the baseline distance between the two cameras and the focal length the range can then be computed with a simple formula given here http://code.google.com/p/sentience/wiki/StereoRanging

However, this range value should not be taken as the absolute truth.  When detecting corresponding points in two images there will always be some uncertainty about exactly where the point is, mainly due to the quantizing effect of pixelation.  So, instead of a completely certain range value what we really need to do is represent the range as a probability distribution in space - something called a probability density function, like this http://code.google.com/p/sentience/wiki/StereoUncertainty