1
\$\begingroup\$

I've been working on an application that, given an aerial picture taken by a drone and the coordinates of an object of interest, tries to determine whether the object is located within the ground footprint of the picture.

In order to achieve this, I'm trying to figure out what the most accurate way to compute the ground footprint of an aerial picture is.

My understanding is that the image is nadir, the footprint can be calculated as follows:

footprint_width = sensor_width * altitude / focal_length

footprint_height = sensor_height * altitude / focal_length

Is this correct?

If the picture wasn't taken perpendicularly, how do pitch, yaw, and roll factor into this calculation?

\$\endgroup\$
5
  • \$\begingroup\$ Yes for first question (within reasonable altitude limits), rest is fodder for math.stackexchange.com (spherical trigonometry). \$\endgroup\$
    – xenoid
    Apr 23 at 7:40
  • \$\begingroup\$ Does this answer your question? How do I calculate the ground footprint of an aerial camera? \$\endgroup\$ Apr 23 at 12:27
  • \$\begingroup\$ @SaaruLindestøkke some have commented on that question explaining that the accepted answer is incorrect, so that doesn't answer my question yet \$\endgroup\$
    – Samuele B.
    Apr 23 at 12:39
  • \$\begingroup\$ That's a pity, the comments also mention "This answer is incorrect and only works with a 0º gimbal pitch and roll (x, y)". Your case is when the pitch and roll is 0, right? There's also this other question, does that help? \$\endgroup\$ Apr 23 at 14:01
  • \$\begingroup\$ I’m voting to close this question because it is about using the camera as a measurement device, and not about the art, science, or business photography. \$\endgroup\$
    – scottbb
    Apr 24 at 16:13

1 Answer 1

0
\$\begingroup\$

We can trace the path of the image forming light rays, inside the camera, after they traverse lens and play on the image sensor. The borders of this trace, from the axis of the lens to the boundaries of the sensor, form a triangle. Likewise, a trace can be made of the path of the incoming light rays from the vista being images, its boundaries also form a triangle. The image triangle and the object triangle are similar triangles, their angles are identical, their sides are proportional.

Suppose the dimensions of the sensor are 20mm length 14mm width. Also, suppose the focal length of the mounted lens is 25mm.

Suppose the drone is at an altitude of 40 feet. Convert this value to millimeter which works out to 12,192mm.

The height of the image triangle is 12,192mm. The height of the image trainable is the focal length which is 25mm.

The ratio of these similar triangles is found by division. Thus 12192 ÷ 25 = 487.7. Using this ratio as a multiplier. Multiplying the actual sensor dimensions by this ratio computes the footprint of the vista being images. Thus 20 X 487.7 = 9,754mm length = 384 inches length = 32 feet. Width of the imaged area is 14 X 487.7 = 6,828mm = 2689 inches = 22.4 feet.

Note: if the drone is low to the ground, its lens will likely need to be adjusted to focus. This act elongates the lens to sensor distance. Should this occur, this revised back-focus distance replaces the focal length.

\$\endgroup\$

Not the answer you're looking for? Browse other questions tagged or ask your own question.