Monday, January 11, 2016

Mini-drone Photogrammetry Test

Behold, my new Parrot Rolling Spider Minidrone:

The Minidrone takes its new rightful place next to the other little aircraft. Good grad office flair.

This neat little bugger has some built-in sensors and instruments which allows for some very stable flight. Combining the use of a pressure altimeter, sonic altimeter, and downward facing camera, it can hover essentially hands-free. The downward facing camera can also take meh-resolution photos, which I thought had some potential for a fun photogrammetry demo, instead of the not-so-subtly spying on my roommates that it's mostly been used for so far.

Incoming foot! Warning! Warning!

I wanted to calculate the height of something using photogrammetric principles. This is possible using geometry; the image of an object is distorted based on how far away from the center of the photo it is (the farther an object is away from the center of the photograph, or Principle Point, the greater the apparent displacement between the top and bottom of the object. Directly overhead, there is no displacement, so you can only see the top).

Using a single photograph to measure the height of an object, from "Remote Sensing of the Environment: An Earth Resource Perspective, Second Edition, by J. R. Jensen).

In the grad lab, I set up a small box, simulating a building, and had the drone fly over it (at eye-level with myself) and take a photo, simulating a low-flying aircraft. 

Building. Not to scale.

Below is the resulting photo. Notice how the box is distorted, and the distortion radiates away from the center of the photograph. Also, the distortion is greater with greater distance from the centerpoint.

Raw aerial photo from the minidrone of the study area from a breathtaking altitude of 5.5 feet.

Next, the math! Using the equation above, the height (h) of the box is equal to the lateral displacement of the top and bottom of the box (d) times how high up the photograph was taken (H) divided by the lateral distance from the center of the photograph (principle point) to the top of the box (r). 

h = (dH)/r

I was able to try this for two spots, as more than one edge of the box was in the photograph.

Aerial photo with annotations. Altitude: 5.5 feet.

Using a ruler and my computer screen, I got the following values:
r1 = 18.0 mm
d1 = 4.5 mm

r2 = 13.2 mm
d2 = 3.2 mm

H = 5.5 feet (my height)

This results in calculated box heights (h) of 1.38 feet and 1.33 feet. Let's call it 1.35 feet. So I went over to the box and measured its height as 1 foot 4.5 inches, or 1.375 feet.

In other words, an error of only about 2%. Not bad! I'll have to find some more fun ways to play with the little drone.

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