Dear all

This is rather a late contribution. In an earlier email I quoted the
standards used by the American Society for Photogrammetry (ASP) - that
is "the z axis coincides with the optical axis of the camera
and is positive along the direction towards the image plane
of the camera. The x axis is paralell to the x axis on the plane of
the photograph and is positive towards the direction of flight (or
along the camera baseline). The y axis is paralell to the y axis on
the photographic plane " (that is perpendicular to the x axis). Using
an upright camera for example the x-axis would be horizontal,
increasing to the left, the y axis vertical and the z axis increasing
positively toward one.

>From Dr. Hatze's summary, I realise that my earlier message was in
some ways rather ambiguos and that the assumption that he made that
the we were using a single camera could easily be made. I was
originally going to send this message personally to Dr. Hatze, but
felt that I would like to state my opinion more clearly were

The main reason for making the statement of the ASP conventions that
when using upright cameras, which is often the case when viewing
human movement, the Y axis is the vertical axis, which is contrary to
the recommended ISB standards. We are presently making use of two
cameras mounted on a base of variable length - the normal camera
separation is approximately 2 meters. As stated by Dr.Hatze's summary
obviously one cannot have a 3D coordinate system were the optical
axes of both cameras are coincident especially as the cameras have to
view the same object and therefore their axes converge. As with many
systems using photogrammetric techniques for analysis, the DLT
(direct linear transformation) is often used to solve for camera
parameters. For this a control frame with points that have known 3D
coordinate values is required. As the cameras are mounted on a fixed
base, I surveyed our control using tradional survey methods with the
x axis paralell to the base line, the y axis vertical and the z axis
increasing towards the cameras. Obviously when using multiple camera
setups, there is no baseline on which all three cameras would be
situated, but when using the DLT the actual control frame determines
the coordinate system. Furthermore in what manner the subject is
placed in the area that the control frame occupied, in my experience,
depends very much on where the markers are placed. The obvious
overriding factor is that they are clearly visible to the cameras. As
long as the data is obtained in 3D, it can be manipulated in any
manner to suite the user of the data.

So after this long email - what is my opinion on the whole matter. I
agree with the people who have suggested that the coordinate system
should not be defined to any specific system, especially as different
applications such as force plate systems and motion analysis systems
often use different coordinate conventions. When using a 3D
coordinate system the orientation of the axes should be clearly
defined.

Barbara

Barbara van Geems
Department of Biomedical Engineering
University of Cape Town Medical School
Observatory 7925
South Africa
Tel: (021) 406-6547
Fax: (021) 448-3291
Pmail: GTSBAR@ANAT.UCT.AC.ZA