Dear Biomch-L readers:

I am just beginning to catch up with my E-mail after a two week
vacation, and I have just encountered Ton van den Bogert's recent
discussion of the DLT--and it's origins. Although Ton's statements
are generally correct, the DLT was in use in photogrammetry long
before Abdel-Aziz and Karara gave it a name ("The Direct Linear
Transformation') in 1971.

As some of you may know, I have worked on 3-D tracking algorithms
since 1968. My first paper on the topic was prepared in 1970--
a Master's Thesis for Michigan State University entitled
"Photographic and Computational Techniques for Three-Dimensional
Location of Trampolinists."

In the 1970's, while Karara and his students were developing the DLT
at tne University of Illinois, I worked at Penn State and at
Stanford on algorithms I described as the generalized
three-dimensional model, and the generalized two-dimensional model.
Some of this work was presented during the International Congress of
Sport Sciences, which was held in Edmonton, Alberta, in 1978. A
more complete reference is my doctoral dissertation, "Close-Range
Cine-Photogrammetry: A Generalized Technique for Quantifying Gross
Human Motion" (Penn State, 1981).

Since 1981, I have continued my interest in image-based motion
measurement, but I have chosen to pursue the technology in a more
commercial/industrial setting, while others have investigated
the topic in academic environments. I have applied the technology
in a wide variety of military, industrial, academic, biomedical,
legal and life science environments.

The purpose of this note is to point out that the DLT has a variety
of origins that extend back beyond the work of Abdel-Aziz and
Karara. This is not to negate their excellent contribution, but to
let the biomechanics community know that they were not the first to
use this algorithm.

Over the last twenty years I have developed an extensive
bibliography on the topic. Although I don't have the time at the
present to trace all the references I have on DLT-like algorithms,
I can cite one in particular, in the photogrammetric literature,
which provides an explicit description of the DLT ...

Das, G.B. "A Mathematical Approach to Problems in Photogrammetry,"
Empire Survey Review, Vol X, No. 73, July 1949.

This was written 22 years before Abdel-Aziz and Karara--by a Brit.

Frankly, I believe that the reason the DLT did not take-off until
the 1970's was the lack of computing power. The algorithm had been
around for a while, but the ability to exploit it did not
exist until practical computer software had been developed.
However, the people needing the capability (Abdel-Aziz and Karara,
myself, and others) were apparently unaware of the algorithm and so
we 'reinvented the wheel' and then wrote the software. Likewise,
in other disciplines, the same 'wheel' has been reinvented.

I hope this has provided food for thought.


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