# Locating Geographic Coordinates in an Oblique Photograph

I am trying to determine a formula for locating the pixel coordinates of a geographic location (provided in State Plane) in an oblique aerial photograph with the following variables known:

1. Feature point (State Plane)
2. Photo geographic centroid (State Plane)
3. Photo geographic footprint (Series of state plane coordinates describing the polygon)
4. Camera location at time of photo (State Plane)
5. Pixel coordinates of photo centroid
6. Camera altitude in feet
7. Focal length of lens (50mm)

I tried to use the suggested answers here: Convert coordinates from Cartesian system to non-orthogonal axes

But to no avail. Is this possible or do I need more data to solve this?

• What does “state plane” mean? I guess ground plane. If you have four points which are the corners of the photographed area on the ground, then you should be able to apply this computation to compute a projective transformation between your planes. Adding the projective geoemtry tag might help attract useful answers, I guess. – MvG Jan 31 '17 at 19:31
• State Plane is a flat Cartesian geographic coordinate system measured in feet from a predefined origin. The issue I'm encountering trying to use the footprint to translate is that the footprint is not rectangular nor is it necessarily a quadrilateral (although the shape roughly represents a trapezoid, there are often more than 4 vertices). – Thomas Nourse Jan 31 '17 at 21:26
• Why is it not a quadrilateral? Is it because the real optical lens causes deformation which make a pinhole camera model inappropriate? Or is it because the area covered is so large that the curvature of the earth begins to show? Because if you project from one plane to another plane through a single point (the pinhole of the pinhole camera) you will always map straight lines to straight lines. – MvG Jan 31 '17 at 21:49
• I did not perform the georectification of the photographs so I can't speak to any reasoning behind the results nor the equipment used aside from the focal length of the lens used. If I had to hypothesize as to the irregularity of the geographic footprints, I'd say that adjustments were made due to lens distortions. The "sides" of the footprint are always straight lines while the near and far edges have multiple vertices to approximate a curve. Each image only covers a distance of ~2 miles on the long side so I don't think the curvature of the Earth is being accounted for. – Thomas Nourse Jan 31 '17 at 23:05