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Tomislav Pribanic
10-13-1999, 06:24 PM
Dear All,

three weeks ago I posted a question regarding source codes for 3D
reconstruction, in particular for MDLT (see below original question for more
details). I received two valuable replies, mostly dealing with Tsai
algorithm (camera model), for which I am sincerely grateful about. Since my
primary need is still not satisfied, exchanging and/or just sending my
version of MDLT source code (Matlab) to anyone who is interested (for which
I would like to receive confirmation that it works fine, thus I can not give
any guarantee for it yet) will hopefully encourage someone to do the same.
Nevertheless I am thankful for those replays bringing to my awareness the
existence of Tsai algorithm. Therefore I would like to ask couple questions
about it.

1. Looking at a Tsai camera model and for instance camera model represented
in a paper: Hatze H. HIGH-PRECISION THREE-DIMENSIONAL PHOTOGRAMMETRIC
CALIBRATION AND OBJECT SPACE RECONSTRUCTION USING A MODIFIED DLT-APPROACH.
J. Biomechanics, 1988, 21, 533-538 are quite similar. The only noticeable
difference is Tsai camera model takes into account transformation between
true (distorted) position of the point's image on the sensor plane and its
coordinates in the camera's frame buffer and Hatze model stops right before.
If I am right, does it mean that real improvement of Tsai model upon Hatze
model, if any, lies in the fact that it is really necessary to take into
account errors during digitizing process and is sufficient to incorporate
only one coefficient for lens distortion - radial distortion?

2. Hatze model suggests three coefficients for symmetrical lens distortion
and two for asymmetrical lens distortion. But his paper is from ten years
back. Are today's camera optics so good that there is no need to take
anything more than a coefficient of radial distortion? How many of those
coefficient incorporate today's commercial 3D systems? 3. Is Tsai camera
model the best (or at least one of) optimum for today's reconstruction
algorithms (camera models) or it is just one among many others (which are
they besides traditional DLT) in every day practical use?

Thank you all in advance. Any additional comments concerning specially the
original question or the new ones will be posted.

Sincerely, Tomislav.

ORIGINAL QUESTION****************************************** ***************:

I am post-graduate student in biomechanics. My work is primarily concerned
with algorithms for 3D reconstruction such as DLT and its variations. I
wrote in MATLAB function for DLT and moved on towards the MDLT, accounting
for a fact that we have 10 independent unknown parameters rather than 11,
and also the non-linear (M)DLT taking into account additional parameters due
to optical distortion and decentring distortion (five additional ones).
However I have been experiencing some difficulties with convergence of sets
of solution and a fact that those improved algorithms do not always yield
better (solution) reconstruction accuracy. Rather than going in more details
with a whole list of questions (linearization, Taylor series, local minimum
etc.) I would kindly ask you if you could provide me with (or tell me where
I can find it; Up to this time I have located only one site giving the full
DLT source code from Kinemat) a source code for MDLT and non linear DLT
preferably in MATLAB, but C is all right too. Therefore I can compare it
with mine since I believe I am pretty much clear on theory (Hatze, H.
(1988). High-precision three-dimensional photogrammetric calibration and
object space reconstruction using a modified DLT approach). J. Biomechanics
28,1219-1224; Miller R., Norman et al.(1980). A technique for obtaining
spatial kinematic parameters of segments of biomechanical systems from
cinematographic data J. Biomechanics 13, 535-547 etc.), but I might be doing
something wrong in implementation itself - writing a code.

I would be glad to post summary of replies of all those who can give me some
advice and/or are willing to share their source codes of any variation of
DLT (or any other approach for 3D reconstruction) written in any language
(tool).

END OF ORIGINAL QUESTION
REPLIES******************************************* **************************
*******:

Dear Tomislav,

I can probably save you some time. Here are a number of sites that have the
latest or most developed codes for camera calibration and reconstruction.

Have a look.

Janne Heikkila

University of Oulu, Finland

(MATLAB Toolbox - linearization/calibration very accurate -better than
TSAI!)

email: jth@ee.oulu.fi

web: http://ee.oulu.fi/~jth

Hynek Bakstein

http://terezka.ufa.cas.cz/hynek/toolbox.html

MATLAB toolbox and thesis (see thesis for comparison of methods!)

Peter Corke - CSIRO (Australia) Machine Vision Toolbox (MATLAB) (Tsai
algorithm in matlab)

http://www.cat.csiro.au/cmst/programs/autom/pic/download.html

Tsai Camera Calibration Software (Tsai software in C code)

http://www.cs.cmu.edu/~rgw/TsaiCode.html

Regards,

Alan Morris

Research Engineer - Gait Laboratory

Bloorview MacMillan Centre

350 Rumsey Road

Toronto, Ontario

CANADA

M4G-1R8

Tel (416) 425-6220 x3508Fax (416) 425-1634

ortcam@oise.utoronto.ca

Tomislav,

Just a note... a very handy book for photogrammetric reconstruction

techniques, especially when using non-linear distortion parameters and

multiple images (rather than just 2) is called:

Close range photogrammetry and machine vision. Edited by K.B. Atkinson,
1996. Whittles Publishing, Scotland, UK. ISBN 1-870325-46-X

I think you might find it useful. Sorry, I don't have any code.

Sincerely,

Steve

Steven Boyd, M.Sc., Ph.D. Candidate

Department of Mechanical Engineering

University of Calgary

2500 University Dr., N.W.

Calgary, Alberta, Canada

T2N 1N4

phone: 403-220-2802

fax: 403-284-3553

email: boyd@kin.ucalgary.ca

END OF REPLIES

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