I have tried asking this in computer science SE, but sadly get no answers. Since this is fundamentally mathematical, I hope someone could give pointers to an answer for this, please.
From a set of 2 similar images taken some small translation distance apart, we can calculate the depth of the a particular point, if we know the distance of a reference object in the frames. This is done by checking the disparity difference in the x pixel coordinates.
My question is about how to calculate depth of a particular point in the image, given 3 randomly translated/rotated/scaled images, without knowing anything about the camera movements?
What is the mathematical principle that allow us to calculate the depth of a particular point just by comparing these 3 normal/uncalibrated camera pictures?
Thank you.
Here you have two problems, the fist is to estimate the parameters of the cameras and then you can use this parameters to get the depht of a particular point.
The problem of estimating the parametes of multiple cameras when you have multiple images in which have been established correspondence between $n$ is called Structure from motion. The principles to solve this problem are epipolar geometry, two interesting books about this problem are "Three dimensional computer vision a geometric viewpoint" by O. Fagueras and "Computer Vision. A modern approach" by D. Forsyth and J. Ponce.
When you have recovered the parameters of the camaras you can just go as if you have two cameras but in this case checking the disparity difference in the x pixel coordinates in three images. Or you can give a different approach like using the third camera to check the correspondences made by the other two cameras.