# Formulating relation for calculating distance

Assuming that the person stands parallel to a wall. The person and the wall are at the same ground level. The person takes a picture of the wall (Considering that the person always captures the bottom edge of the wall).

Hypothesis:

It is obvious that when the person is closer to the wall, the bottom edge of the wall tends to be at the bottom in the image. As we move farther, the edge moves more closer towards the center in the image.

So, there exists a relationship between "Distance from wall" and "Position of edge of the wall in the image".

The known parameters are:

-> Height of the camera from which the image is captured

-> Angle(Orientation of the camera)

-> Position of the edge in the image

How can I formulate the distance(depth) based on the above parameters? Are there any other parameters that affect the above relationship?

• Draw a 2D picture of the case. Hint: Trigonometry. – Matti P. May 17 '18 at 10:12

## 1 Answer

From a simple right triangle, the bottom edge of the wall will move up in the frame by an amount $y = x$ tan $\theta$, where y is the increase in height of the edge of the wall, x is the increase in distance from the wall and $\theta$ is the angle of the camera's view (the angle from the aperture to the bottom edge of the viewing window). Of course this is the actual distance of the translation and does not account for dilation onto a photographic screen.