♻️ Distance Transfer

Distance transfer is concerned with measuring lengths in the world using a reference measurement and an image. That is, given an image and a world measurement of a line in the image, our goal is to find the world length of another line.

First, we need to find the horizon. This can be done either with orthogonal parallel lines, assuming horizontal horizon and finding one vanishing point, or using Cross Ratios.

Then, we connect one end of the lines together and find their intersection with the horizon. This gives us a vanishing point .

Connecting with the top of the known line and shooting it to the unknown line, we intersect at . Note that and are parallel in the world. Thus, is the same length as in the world.

Then, let be the vertical vanishing point. We can now apply cross ratios,

In the world, with at infinity, we have

We can measure with the image, and we’re given . Thus, we can solve for to get the length of the unknown line in the world.