Need help determining height above ground of aircraft

[bulgin]

Thanks for accepting me into the forum.

I am involved in a study which is attempting to determine the height above ground of aircraft that pass over our urban area.

Given that we know the wingspan in feet of a given photograph of an aircraft and given that we know the camera focal length and angle from which the photograph is taken (usually directly overhead, or 90 degrees), is there is way to reliably determine the height above ground of that aircraft?

Someone in another forum who could not provide details, said something about counting pixels, but I am not a mathematician and could use what ever help there is to determine the height above ground of this aircraft.

Thank you.

[eliscio]

Hi Bulgin,

I am going to be out of touch for a couple of days, but here is something to get you started....I am quite certain you should have the following:

Camera Focal Length  (you can get this from the jpg image, header information.  Look for EXIF data if you don't already know.)
Wingspan of aircraft or length (whatever is the greater distance will be best).
Pixel size of the unaltered jpg image that is taken.  Ideally, you take this at the maximum resolution possible.
Size of the CCD sensor on your camera (physical dimensions...Width x Height)

You need to understand the relationship between the image sensor, lens, focal length and then the distance to the object.  They are all related and with a bit of simple math (and some Google help), you should be able to get it.

Cheers,

Eugene

[bulgin]

thank you for your reply.  Here is some information I have obtained.  I have looked at the jpeg images with a hex editor but cannot find any EXIF information contained therein.  I did google with that information but could not find any formulas based on that information.  Any help would be greatly appreciated.

Here, from the specifications manual:

Panasonic DMC-FX33
Official specs:

Camera Effective Pixels    8.1 Megapixels

Optical Zoom    3.6x
Image Sensor    1/2.5", 8.32 Total Megapixels CCD, Primary Color Filter
Extra Optical Zoom    4:3 Aspect Ratio: 4.6x for 5 Mega, 5.7x for 3 Mega, 2 Mega, 0.3 Mega
3:2 Aspect Ratio: 4.6x for 4.5 Mega, 5.7x for 2.5 Mega
16:9 Aspect Ratio: 4.6x for 4.5 Mega, 5.7x for 2 Mega
Digital Zoom 1    4x (Max. 14.3x combined with Optical Zoom without Extra Optical Zoom)
(Max. 22.7x combined with Extra Optical Zoom)
Focal Length    f=4.6-16.4mm (35mm equiv: 28-100mm)
Aperture Range    Wide: F2.8/F8.0 (2 steps)
Tele: F5.6/F16.0 (2 steps)

(Pixels)      .
4:3 Aspect Ratio (Still Image)    3264 x 2448
2560 x 1920
2048 x 1536
1600 x 1200
640 x 480
3:2 Aspect Ratio (Still Image)    3264 x 2176
2560 x 1712
2048 x 1360
16:9 Aspect Ratio (Still Image)    3264 x 1840
2560 x 1440
1920 x 1080
Motion Image (4:3 Aspect Ratio)    640 x 480, 320 x 240
30 fps, 10fps
Motion Image (16:9 Aspect Ratio)    

[eliscio]

For the EXIF data, you can download a free program like Irfanview and it will give you the data for each image...it's a free program too.

Also, have a look at my article...look at the section on Focal Length.  The images will give you some idea of what you need to do.

http://www.ai2-3d.com/ForumExternalLinks/Photogrammetry%20and%20Forensics%20Primer.pdf

When I have more time, I'll try to post a detailed example, but you can always try to test the concept yourself by using anything as airiplane like a stick or ruler.

Eugene

[bulgin]

On another forum I was told to take the product of wingspan and focal length and divide that by the width of the wingspan as seen in the image.

So:

wingspan: 508mm (it's a small model airplane)
focal length: 28mm
wingspan as perceived in photo: 6 mm

so:

508 * 28 = 14,224, then divide that by 6 mm = 2,370mm or 93" distance model airplane is from camera.  but in fact I measure it and the plane was 140 inches so I don't know what I'm getting wrong.

[eliscio]

Think of things in terms of what happens outside of the camera as being represented more or less the same internally in the camera.  So the actual distance the aircraft is away from the lens and the size that it shows up in the viewfinder will be the same, except at a much smaller scale "inside" the camera.

You know the image sensor size (w x h)
You know the image size in pixels (w x h)
The focal length you have in the EXIF information of the jpg image

The size of the aircraft in the digital photo is a scaled result of the image as it was projected on the sensor.  So, let's take some numbers...

If your sensor size is 5.75 x 4.31 mm and the image size is 3264 x 2448 pixels, measure the length of the aircraft in pixels.  Notice that if you divide 5.75/4.31 = 1.33.  Also, if you take 3264/2448 = 1.33.  (I am going to assume that the aircraft is going to be aligned straight up and down and not on angle).

So, if the aircraft shows up as 1000 pixels from nose to tail, then take the ratio of 1000/3264 (assuming that's the way it's oriented in the photograph).  The result would be 0.30637.  So, this ratio will be reflected in the actual sensor as well.  i.e, the aircraft will show up as approximately 30.637% of the width of the sensor. 

So, 0.30637 x 5.75 mm = 1.7616 mm  (The aircraft shows up as 1.76 mm as projected on the camera sensor)

Now, this is where we take some ratios....

The actual aircraft length divided by the distance away from the camera is the same as 1.7616 mm divided by the focal length (5.8 mm) in our case.

So, the Distance the aircraft is away from the camera = (length of aircraft x focal length) / 1.7616 mm

Make sure all your units are the same, but hopefully this will make sense.

Try a test with a painting or something on the wall where you are a known distance away from the wall.

Regards,

Eugene

[bulgin]

Thank you for the precise and useful information.  I think I can make it work now.  My only question that remains is that when I look at a photograph through the Irfanview information window, it gives me two focal length sets of information -- the one which would be the equivalent in a 35mm camera and another one which is just 1 number.

Which one should I use?

Thank you.

[eliscio]

Don't use the 35mm equivalent.  It's just a way of relating the focal length on a newer digital camera (that has a smaller sensor size) to the the larger 35mm film format.

Best of luck.

Eugene

[bulgin]

thank you for all your help.  It has been educational AND useful.

I think I'm set now.