Dear Biomch-L readers,

Phil Cheetham was asking advice regarding calibration of a 2-D
filming setup. I am not familiar with Jim Walton's 2D DLT
algorithm, but it seems to be exactly what is needed. I once
used a 2D DLT to solve a similar problem (analyzing a photograph
of a horse's hoof on a force plate). The DLT can deal with
an arbitrary camera position and orientation, and is therefore a
general and very elegant solution.

If you substitute Z=0 (defining the sagittal plane) into the
classical 3D DLT equations, three out of eleven DLT coefficients
are eliminated. The remaining eight can be determined using four
(or more) calibration points in the Z=0 plane. I have developed
two simple Fortran subroutines to do the calibration, and
(subsequently) to calculate XY coordinates from raw camera data.
One limitation of my software is, that the calibration routine
uses exactly four calibration points. It may be possible to
increase the reliability by using more than four, and solving the
DLT parameters from an overdetermined system of equations.

So, my advice is to use a 2D DLT approach. If you do not want to
start from scratch, my Fortran code is available. One final
warning: any 2D analysis will depend on the assumption that all
landmarks remain in the sagittal plane. The results become more
sensitive to this assumption with a non-perpendicular camera
view, which increases the parallax errors. From Phil's
description of the actual situation, it would seem that this is
not a major problem here.

-- Ton van den Bogert
Human Performance Laboratory
University of Calgary, Canada