Understanding Disparity Map in Opencv

Question

Can somebody explain me what exactly does a disparity map return. Because there is not much given in the documentation and I have a few questions related to it.

1. Does it return difference values of pixels with respect to both images?

2. How to use disparity values in the formula for depth estimation i.e.

   Depth = focalLength*Baseline/Disparity

3. I have read somewhere that disparity map gives a function of depth f(z)

Please explain what it means. If depth is purely an absolute value how can it be generated as a function or is it a function with respect to the pixels?

Answer 1

The difference d = pl − pr of two corresponding image points is called disparity.

Here, pl is the position of the point in the left stereo image and pr is the position of the point in the right stereo image.

For parallel optical axes, the disparity is d = xl − xr

⇒ search for depth information is equivalent to search for disparity, i.e. corresponding pixel the distance is inversely proportional to disparity

The disparity values are visualized in a so-called disparity map, each disparity value for each pixel in the reference image (here: left) is coded as a grayscale value. Also for pixel that do not have any correspondences, a grayscale value (here: black) is defined. The so-called groundtruth-map is a disparity map that contains the ideal solution of the correspondence problem.

Relation between Disparity and Depth information:

The following image represent two cameras (left and right) and then tries to find the depth of a point p(x_w, z_x).

The result of depth is given my:

so, it can be seen that the depth is inversely proportional to disparity.

UPDATE:

To calculate the disparity, you need two image (1) Left image and (2) Right image. Lets say that there is a pixel at position (60,30) in left image and that same pixel is present at position (40,30) in right image then your disparity will be: 60 - 40 = 20. So, disparity map gives you the difference between the position of pixels between left image and right image. If a pixel is present in left image but absent in right image then then value at that position in disparity map will be zero. Once you get the disparity value for each pixel of left image then we can easily calculate the depth using the formula given at the end of my answer.