I've been checking and refining my calculations for the past few days and I'm going to repeat the previous example explaining every step of the way, but this time trying to be more accurate and using
one of the new images suggested by elevenaugust. It would be great if someone tries to follow and verify my reasoning here, as I believe this method to be quite useful as an universal tool for "manual" 3D image analysis.
Here are the basic ingredients:
-
unknown image for analysis, with unknown parameters, but shot at known location
-
calibrated image from the same location, as similar as possible to the previous one
-
physical measurements from the location (laser measured distances)
The calibrated image is simply an image with known parameters from which we can deduce the precise angle of view. For this we can either use EXIF metadata (if present) or calculate it by using an object of known size and at known distance in the image. As final precision of this calculations depends mainly on precision of this image, it should be as good as possible (high resolution, undistorted, high contrast, low noise...), though it doesn't have to be perfect if its flaws are known and corrigible - i.e. if it was shot with the angle-of-view-calibrated camera with known barrel distortion (this calibration can also be done later). Here's one of the suggested calibration images with basic info and illustration of the angle of view concept:
It was resized to 50% of its original size which reduces precision (btw, can I get hold of the original image?), though unlike clipping it doesn't affect the angle of view. As EXIF data survived, I extracted it with
Phil Harvey's EXIFtool which automatically calculates horizontal FoV (48.9°) if the required input data fields (focal length and 35mm scaling factor) are present. The other way to do it would be to ask elevenaugust how far from the camera he was standing and what is the format of images he's holding. Assuming it was plain A4 paper (
0.3m longer size), by measuring it in PS or similar program with a ruler tool (
75px) we can deduce the pixel size for the
image distance plane (another important concept here) containing the paper (75/0.3=
250px/m), and also the width of the whole image (Xres=800px) at the specified distance plane, so 800/250=
3.2m. This seems about right, if you can imagine elevenaugust's full height and rotate him horizontally to measure the width of the image. If we enter this value along with the previously determined HFoV (
48.9°) into the on-line
angular size calculator, it returns the distance of
3.5m from the camera.
The next step is to overlay the image with an unknown object (Chad's image #4 per elevenaugust's numbering notation) onto the known setup of our calibration image and align it by using reference points present in both images
in order to translate objects dimensions into known and measurable environment - this is the basic postulate on which my calculations depend, and if it's not correct I'm sorry for wasting your time. But as I believe that was also the reason why you tried to match the original images, we are probably safe in using this assumption
As you can see in the following image, I used rotation, perspective correction, resizing and whatever else was necessary to achieve as good alignment as possible:
I believe this also answers elevenaugust's question about zooming - as long as unknown image can be precisely aligned with the calibrated one, it doesn't matter what parameters were used for its recording because
by translation into our known setup we are effectively replacing its parameters with known values. Naturally, it would be better if calibration image already matches the unknown without adjustments, but that is not the case with either of images from the location. Even if they were perfectly aligned from the exactly same spot, there's wind, vegetation growth, etc...
But here's another thing, specific for this case: the alignment of images is not even necessary! It will serve as an illustration, but for actual measurement I will use the original image with a line drawn between two selected reference points (marked A and B) identified in both images. I've entered laser distance measurements for these reference points and marked the square that I'm going to use in the next part of my calculations, especially selected because, as you can see, its imaginary diagonal line is passing very close to craft's horizontal axis along the smaller side fins, and it looks as if the craft is very close to the tree canopy - so, hopefully, by calculating the size of this diagonal line we could use it to measure the actual dimensions of the craft.
To be continued...
