Solving for the geometry. 

The (u,v) image coordinates need to be transformed into real-world (x,y,z).  Generally, this is an underdertermined equation.  Imagine a standard photo taken horizontally towards the horizon.  Objects at the bottom of the image are nearby, and distant at the top of the image.  For a computer, it's hard to tell the difference between height and distance.  Humans are quite good at this; we recognize a person and register the head at the same distance as the feet.

Granted, we have  stereoscopic vision to help.  The same can be done with cameras, but the physical and processing logistics become much more difficult.

One must also know the 3 orientation angles of the camera in space, and the focal length.  These are traditionally solved for using nonlinear least-squares regression to known image and world control points.  This was always a hassle, and the regression could easily yield bizarre results.  So I wrote an interactive gui to inspect the results and relationship between the parameters.   This helped to limit the parameter's range, otherwise the regression solver would incrementally step it's merry way to infinity.

Look closely at the gui and you'll see the combination of gps track points superimposed with LIDAR bathymetry and the rectified image solution.  These were used to verify the solution was reasonable.

Once the geometry is known, the images can be "rectified", i.e. mapped to a vertical plane in the real world.  Thus they can be used for spatial measurements.

    

This rectified image was overlaid on 30 cm resolution satellite imagery.  Up is true north.