Fryer, John
work on the part of the photogrammetrist must be avoided at all times as
the cross examiner will quickly try to discredit any unscientific
estimates. In the work this author has presented to courts, reconstruction
of the stance of the robber was undertaken by carefully positioning the
feet of an assistant, whose height was similar to that of the robber, and
measuring (and photographing!) him in that stance. See Figure 6. This
technique provided upward estimates of 3 - 5 cm for the court to
consider in conjunction with the actual height determination of the
robber at the time of image capture.
5 ERROR ESTIMATION
Given the above simple physical method of height determination, which
left the defense little room for questioning and the raising of doubts, the
only area where the photogrammetrist should expect strong questioning
will relate to the estimation of likely errors. Courts have been ready to
accept that the mean of several height determinations should provide a
better answer than just one determination from one frame. The
photogrammetrist must behave like the scientist he is and honestly
evaluate his work and place error bounds around his answer. It is pure
folly to claim too high an accuracy for the purpose of self-promotion, as
egos can easily come undone in the tense atmosphere of a court.
The photogrammetrist must realise that while his professional colleagues
are au fait with normal distribution theory, standard errors and the 99%
confidence limit, the court will require something simpler. A simple +
or - bound placed around the height determination is something
acceptable to the court and whether it is at the one, two or three standard
error level is something best left to the photogrammetrist to decide,
based on the merits of each situation and the advice of his attorney.
Figure 6. Estimating an allowance to be
added to height for the stance of a suspect.
Most lay-persons believe that a standard error is a an absolute bound of accuracv, rather than an indicator of precision.
Care should be taken lest the photogrammetrist suddenly finds he must present what amounts to a statistics lecture to
the court. Such a situation would probably confuse and weaken the findings. Error bounds placed at the 3-sigma or
99% confidence level are reasonably easy to defend under oath in the witness box.
6 THE ANHARMONIC RATIO
A fundamental property of a perspective projection is the anharmonic ratio (sometimes known as the ‘cross ratio’ (for
example see Wolf, 1983, 252 ). This ratio can be best described by consideration of Figure 7. The cross product of |
AC.BD divided by AD.BC remains invariant for a particular object through a perspective projection.
In a recent court case involving the author as an expert witness, the objects in question were an M1 Carbine rifle and a
Winchester pump-action shotgun. Both weapons had been shortened in both the barrel and the stock and were therefore
distinctive but not necessarily unique.
The guns, and the accused, had been seized by police at an incident (see
Figure 8) which was quite separate to the bank robbery which occurred
several months earlier and was under prosecution in the court. The
defense attorney claimed that the weapons in the video scenes of the bank
robbery were not the same as those confiscated by the police on the later
occasion. These weapons would provide compelling circumstantial
evidence that the person arrested by police for the latter offence was the
gunman wearing the balaclava in the bank robbery (see Figures 9 and 10).
Figure 8. Shotguns seized by police
250 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.