Using Parallax to Measure Height

on a Single Aerial Photo

heights can be measured using parallax on a single photo if:

1. you know that the height you are measuring is straight and vertical

2. you can find the center of the photograph (the principal point)

3. you know the flying height of the photo

4. the object is far enough from the center to have a measurable displacement between the top and bottom of the object.

To use parallax on a single photo to measure height

1. Find the principal point on the image the point directly below the airplane. This will usually be the center of the photograph and can be found by drawing lines between corresponding fiducial marks on the sides of the photo. You may also be able to find this point by noting that the parallax displacement on all vertical objects will cause them to appear to point to the principal point.

2. Measure the distance from the principal point to the top of the object, r. Remember this technique only works for measuring a vertical straight line that you can top to bottom, so if you are measuring the height of a building, you are really measuring the height of a wall and r is to the top of the wall, not the center of the building (you can’t see the bottom of a line running through the middle of the building, though you might be able to estimate it’s position if you really needed to…)

3. Measure the length of the object on the image, d. Again, you are measuring a straight, vertical line such as one wall of a building, not the distance from the front door to the back of the roof. This is often a very small distance, so measure it carefully! Measure to 1/64” or 0.5mm if you can. You are just measuring the object whose height you wish to find, not its shadow. The shadow length will change every hour, and we don’t have any information about the sun in this technique!

4. Use the formula h = H x d/r to find the height, h. Since d/r is a ratio of lengths on the photo, as long as they are both in the same units it doesn’t matter what units you use cm or in or mm. d cm/ r cm = d in/ r in = d mm/r mm. H does NOT have to be in the same units as d and r. the units of h will be the same as the units of H, usually feet or meters.

5. Note. The ratio of d/r will stay the same if you change the image size, so you can blow up to picture to make r and d easier to measure, as long as you keep the principal point in your enlarged picture.

Example:

the principal point is indicated by the +.

r = 10.35 cm

d= .40 cm

H = 3000 ft

r/d = 0.40 cm/10.35 cm = 0.0386

h= 116 ft