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Measuring object length from fixed height with Mavic Air

jtcoastal

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I'm curious if anyone knows specifications on the overall length and width of the video frame (or image frame) of the Mavic Air at different fixed heights. I would like to use this UAV to measure body length in different cetaceans.
 
I'm curious if anyone knows specifications on the overall length and width of the video frame (or image frame) of the Mavic Air at different fixed heights. I would like to use this UAV to measure body length in different cetaceans.

A number of threads have addressed this theoretically, but the simplest solution, guaranteed to work, is just to photograph/video (whichever modes you are interested in using) an object of known size at a known distance. You can do that on the ground, looking horizontally. The ratio of size to distance will be constant for any given mode.
 
Another approach is to use the angle of view which, according to DJI, is 85deg diagonally or 50deg horizontally. After that it's basic trigometry - you have a right-angled triangle with the height provided by your altitude, the base provided by half the width of the frame, and the angle at the top provided by half the AoV.

Assuming we want to calculate the distance along the horizontal (long) edge of the frame to use as our scale for measuring the size of the cetacean:

Length = 2 x Altitude x Tan(25)

Tan 25 is 0.4663...., so as a rough rule of thumb, the length of the horizontal axis will always be around 90% of your altitude, or 93.2% if you want to be more precise.

Note that all that assumes that the camera is pointed straight down, if not then it's stil doable if you know the angle it's at, but there's a lot more trig involved.
 
Another approach is to use the angle of view which, according to DJI, is 85deg diagonally or 50deg horizontally. After that it's basic trigometry - you have a right-angled triangle with the height provided by your altitude, the base provided by half the width of the frame, and the angle at the top provided by half the AoV.

Assuming we want to calculate the distance along the horizontal (long) edge of the frame to use as our scale for measuring the size of the cetacean:

Length = 2 x Altitude x Tan(25)

Tan 25 is 0.4663...., so as a rough rule of thumb, the length of the horizontal axis will always be around 90% of your altitude, or 93.2% if you want to be more precise.

Note that all that assumes that the camera is pointed straight down, if not then it's stil doable if you know the angle it's at, but there's a lot more trig involved.

And it should be as simple as that. But I've proposed that in a number of threads and in at least one case it's been reported that it gives significant (> 25%) errors. I haven't yet got around to direct measurement, but it's pretty easy to do and it will avoid any ambiguity.
 
And it should be as simple as that. But I've proposed that in a number of threads and in at least one case it's been reported that it gives significant (> 25%) errors. I haven't yet got around to direct measurement, but it's pretty easy to do and it will avoid any ambiguity.

The quoted AoV for a lens is often an approximation, but a margin of error of 25% is a lot and I suspect is more likely to be indicative of accuracy problems with the altimeter, or the camera wasn't actually pointing straight down. Direct measurement would correct for the approximate AoV figures, but if you can't reliably set the camera angle or the altimeter isn't up to scratch then your accuracy will suffer.

Another possible wrinkle could arise from the small variances between actual altitude AGL and GPS-reported AGL due to the Earth's uneven magnetic field and equatorial bulge. A quick Google seems to indicate DJI's altitude reporting is somewhat less than perfect in this regard, so any discrepency between the two would throw off the scaling calculation as well.

For OP's use, I'd definitely be looking to test against an object of known length at a number of altitudes and locations to get a feel for what the margin of error mght be, and whether that is acceptable or not.

Or maybe think out of the box... The drone is over water here, a flat terrain, so the operating altitude could be constant. That means you could take off, ascend to your preferred operating altitude, orientate the camera, then take a picture of the boat or some other surface object of known size. You now have an image of something you can use as a rule as long as the drone remains at the same altitude for the duration of the time its surveying the whales.
 
The quoted AoV for a lens is often an approximation, but a margin of error of 25% is a lot and I suspect is more likely to be indicative of accuracy problems with the altimeter, or the camera wasn't actually pointing straight down. Direct measurement would correct for the approximate AoV figures, but if you can't reliably set the camera angle or the altimeter isn't up to scratch then your accuracy will suffer.

Another possible wrinkle could arise from the small variances between actual altitude AGL and GPS-reported AGL due to the Earth's uneven magnetic field and equatorial bulge. A quick Google seems to indicate DJI's altitude reporting is somewhat less than perfect in this regard, so any discrepency between the two would throw off the scaling calculation as well.

For OP's use, I'd definitely be looking to test against an object of known length at a number of altitudes and locations to get a feel for what the margin of error mght be, and whether that is acceptable or not.

Or maybe think out of the box... The drone is over water here, a flat terrain, so the operating altitude could be constant. That means you could take off, ascend to your preferred operating altitude, orientate the camera, then take a picture of the boat or some other surface object of known size. You now have an image of something you can use as a rule as long as the drone remains at the same altitude for the duration of the time its surveying the whales.

The tests were apparently done just using the barometric relative altitude which should have been reasonably accurate. Either way - there is really no need to test in the air or at multiple distances. Simply photographing a known length at a known distance is enough to determine the scale factor, provided that the image is free of distortion - i.e. is the scale factor in the center of the image the same as the scale factor towards the edges. That might be worth characterizing separately.
 
This is really helpful. Thank you. Ground-truthing the data on each flight by recording an object of known size (boat) from a fixed height is really wise. Ideally, I would not have to do it but if the altimeter data is not always reliable then it should be done. I'd like to fly at a fixed height with the camera straight down for all measurements as suggested but may try and find a way to create a table of different lengths and widths of the frame at different heights so I can make some kind of grid to overlay the images to help measure the animals.
 
Maybe make a segmented 50' chalk line in a parking lot and photograph it at 20', 30', 40', etc, elevation.
 
Let it hover at a given altitude, walk into the camera view, mark the corners on the frame looking at your display with a rock or something, change altitude and repeat. Then measure the rock placements.
ETA; That is for the frame size I think you desire. PLUS if you already have photos, and you know the altitude they were taken from, it would help size existing photos.
 
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I used to be a cartography tech and often had to calculate scale and distance on aerial photos. As suggested previously, if you know the relative size of other things seen in the photos, the easiest way to roughly calculate approximate measurements of other unknown objects is to divide the length you are viewing the known object at on your monitor by the actual length of the known object to get a ratio. Then simply divide the measured length of what your unknown object is as seen in your monitor (without zooming in to it) by the same ratio.

1.Lets say you see a RV in the photo that you know is 10m long for real (convert it to cm first) = 1000 cm

2. Measure the RV on your photo - say 1cm

3. Your object of interest is a fenceline- say it is 5cm long as seen in the photo.

4. To get the ratio, divide measured RV length by its actual length (both in the same units). 1cm/1000cm= 0.001

5. To get the calculated length of the unknown object seen in the photo, divide measured fenceline by ratio
5cm/.001 = 5000cm or 50m

Your fenceline is appropriately 50m long.

This method is rough and assumes you are using a photo looking straight down (nadir shot), and works best with objects closest to center of the image.

If you want higher accuracy or don’t see anything else with known lengths in the photo, you have to use focal length and AGL and some math in to calculate the image scale. Again, its only an estimate as lens quality, topography and tilt all cause errors in this, that’s why cartographers use othophotos that have been corrected to do this.

To calculate image scale, first convert all measurements to the same units (m and mm, etc.) and divide AGL by FL : Example:

AGL = 100m or 100,000mm

(Mavic 2 Pro) Fixed FL= 28mm

(MP2Z) variable FL= 24 - 48mm (you will have to use EXIF data from image to see which it used)

AGL 100,000mm/FL 28mm = 1:3571 photoscale

Using the same M2P at 50m would give you: AGL 50,000mm/ FL 28mm = 1:1786 photoscale.

Using the photoscale, simply measure something in the image that was taken at a certain AGL and multiply the number by the scale- such as with the 100m AGL photo, photoscale = 1:3571, so a 1 inch wide field in the photo taken at 100m is really 3571 inches wide.

The nice thing about photoscale is that no matter which measurement units (metric or English) you use, it will be the same units x the scale on the ground.

Here’s a couple good links explaining how to calculate it and to get object height and other measurements from your aerials:

Aerial image scale calculation

Photogrammetry
 
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