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Peter Sinclair
01-28-2004, 11:48 AM
Dear Biomechanists,

Thank you very much for the useful replies to my question about calibrating
2D images with non-perpendicular camera views?

In brief, it seems that the 2D DLT is a common procedure performed by a
variety of commercial digitising packages (APAS, Motion Analysis Corp,
Peak Performance Technologies, SIMI-Motion, etc) as well as some public
domain software
(http://www.isbweb.org/software/movanal.html
http://www.health.uottawa.ca/biomech/csb/software/ )
that allow accurate reproduction of 2D images without the requirement for
the camera to be perpendicular to the field of view.

Provided a suitable calibration is performed, there should be no problem
with non-perpendicular camera angles, excepting that the errors would be
expected to increase for acute angles to the plane of movement (imagine a
camera parallel to the plane of movement: clearly no meaningful measures
could be taken. Thomas Seeholzer recommends an angle between 60 - 90
degrees to the movement plane). While it was cautioned that errors may be
expected to increase as the angle becomes more acute, there is little
evidence of this for angles close to 90 deg (Brewin and Kerwin. Accuracy of
scaling and DLT reconstruction techniques for planar motion analyses, J
APPL BIOMECH 19 (1): 79-88 FEB 2003). It seems likely that the DLT may be
more susceptible to perspective errors as the angle moves away from 90 deg.
This was tested for perpendicular cameras by Sih,Hubbard and Williams, (J.
Biomechanics., 34, 257-260), but not by Brewin and Kerwin for
non-perpendicular cameras.

Thanks again for all the considered replies

Peter Sinclair





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Original Message

Dear BIOMCH-L members,

Does anyone have any experience with calibrating 2D images with
non-perpendicular camera views? We are using the APAS digitising system
which seems to do be doing a good job. With 18 co-planar calibration
control points spread through the field of view, the APAS calibration
routine accommodates the changing apparent image size to produce a
reasonable calibration. The system will measure a constant distance between
markers on a stick moved across the screen, but we haven't done more
rigorous tests at this stage.

We are only in the preliminary stage of testing the accuracy; needing to
measure (amongst other things) the accuracy's sensitivity to out of plane
movements. Are there theoretical reason's why the calibration of a
non-perpendicular camera position would be less reliable than the usual
perpendicular camera position?

Thanks very much for your assistance,

-----------------------------------------------------------------------------------------------------
From: Thomas Seeholzer

I do not know the specifics of your system.
We use a 2D DLT algorithm to calibrate non-perpendicular planes. This method
requires 4 points with known real world coordinates. SIMI-Motion has also an
extended version (called grid calibration) which allows as many points as
you want. This method is also using 2D DLT to interpolate between the given
points and should be used in cases of heavy lens distortion.
I think that linear interpolation (between the grid points) needs much more
points to be as accurate as the mentioned DLT algorithm.

A non-perpendicular calibration has the same accuracy as the perpendicular
type as long as the angle between your camera and the measurement plane is
not too small (60 to 90) Obviously you will not be able to measure
anything when the camera's view is parallel to the plane.
But its sensitivity to "out-of-plane" points will get worse with each degree
less than 90.

Regards,
Thomas.

Thomas Seeholzer
SIMI Reality Motion Systems GmbH
Tel: +49 89 321459-0
Fax: +49 89 321459-16
Mail: seeholzer@simi.com
Web: http://www.simi.com


-----------------------------------------------------------------------------------------------------
From: "Scheirman, Gary"

The system supplied by our company, Peak Performance Technologies, Inc.,
has a projective scaling algorithm to correct for non-perpendicular views.
Its primary purpose is to free the researcher from accurately level the
video camera. Instead, the plane of motion is determined by the position of
a 4-point rectangular calibration frame. It is much simpler to hold the
frame vertically, which assures that the vertical axis is parallel to the
line of gravity.

There is a potential for the non-perpendicularity to create more errors,
however. Consider that with perpendicular placements there is a one-to-one
correspondence between the image screen pixels and real-world units. When
the camera is non-perpendicular, there is a greater than one-to-one ratio
on the side of the image closer to the camera and a less than one-to-one
ratio on the side farther from the camera. This difference is quite small
when the camera is roughly perpendicular to the plane of motion, but grows
as the optical axis of the camera lens and plane of motion become more
parallel.

I hope this helps and please give my regards to Richard Smith.

Sincerely,

Gary Scheirman
Vice President
Peak Performance Technologies, Inc.
gscheirman@peakperform.com
www.peakperform.com

-----------------------------------------------------------------------------------------------------
From: Aki Salo

My colleagues have tested the accuracy of 2D-DLT for non-perpendilar camera
views. Please see

Brewin MA, Kerwin DG
Accuracy of scaling and DLT reconstruction techniques for planar motion
analyses
J APPL BIOMECH 19 (1): 79-88 FEB 2003

Best regards
Aki

----------------------------------------
Aki Salo, Ph.D.
Lecturer in Sport Biomechanics
Sport and Exercise Science
University of Bath
BATH, BA2 7AY, ENGLAND
Tel. +44-(0)1225-383569
Fax +44-(0)1225-383275
----------------------------------------


-----------------------------------------------------------------------------------------------------
From: "Young-Hoo Kwon, Ph.D."
Dear Peter and all,

I have used the 2-D DLT method for perhaps 15 years or so and it works
well. If you understand how the algorithm works, you will also
understand that there is no reason to question its accuracy. 3-D
recording is basically a space to plane mapping and you can not
reconstruct the 3-D space based on one camera (because it is a plane to
space mapping). However, 2-D recording is a plane to plane mapping and
it guarantees 1 to 1 mapping. 2-D reconstruction, as a result, is OK
with one camera since it is also a plane to plane mapping. Please visit
the DLT Method page at kwon3d.com
(http://kwon3d.com/theory/dlt/dlt.html) for the detailed explanation on
the 2-D DLT.

The calibration error in the 2-D DLT method mainly comes from the
perspective error, not from the algorithm itself. The perspective error
is intrinsic to any 2-D method. Human or animal body is a 3-dimensional
entity and it can not move within a plane. If a marker is off the plane
of motion, the perspective error occurs. The perspective error exists
regardless of the angle between the camera axis and the plane of motion.
The only problem is that if the camera angle deviates from 90 deg quite
a bit, it can enlarge the magnitude of the perspective error
substantially.

The main advantages of the 2-D DLT method include:

1. The camera angle does not have to be 90 deg;
2. Multiple cameras can be employed in a single project. This is an
important advantage often overlooked. As long as one uses a single
(large) calibration frame, different cameras can aim the same area or
different areas of the control area. Use of multiple cameras will simply
increase the redundancy in the reconstruction. The reconstructed
coordinates of the markers can be combined since they are all based on
the same calibration frame. For example, in gait analysis one can place
two cameras (right & left) facing to each other. The subject moves
through the cameras. The right-side camera will pick up all the markers
placed on the right side of the body, vice versa. Or in long jump, one
or two cameras may aim the run way while another camera aim the pit.
This is helpful because one can increase the size of the image
substantially.

Unfortunately, the 2-D DLT does not have the capability to correct the
optical errors (optical distortion and de-centering distortion). One
solution to this problem is to use the so called pseudo 3D approach: 3-D
calibration w/ optical error correction + 2-D reconstruction w/ one
known coordinate. One camera will be enough since we are not doing the
3-D reconstruction.

I hope it helped.

Young-Hoo
------------------------------------------------------
- Young-Hoo Kwon, Ph.D.
- Biomechanics Lab, Texas Woman's University
- kwon3d@kwon3d.com
- http://kwon3d.com
------------------------------------------------------


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From: Mont Hubbard

See

CORRECTING OUT-OF-PLANE ERRORS IN TWO DIMENSIONAL IMAGING USING
NON-IMAGE-RELATED INFORMATION,
B. L. Sih, M. Hubbard and K. R. Williams, J. Biomechanics., 34, 257-260.

which may be of help.

Mont Hubbard



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From: "Jim WALTON"

You will find a complete description of the "2-D DLT" in my
Doctoral Dissertation, published in 1981 ...

Walton, James S. "Close-Range Cine-Photogrammetry: A Generalized
Technique for Quantifying Gross human Motion." Penn State University,
1981.

You can get copies from University Microfilms. Their reference
(order number) is 8120471. The technique is derived from the full
3-D algorithm ... which is also dervived in the dissertation. I
think it is reasonable to state that this was the first description
of the "2D-DLT" and the source of most subsequent implementations
of the algorithm in commercial products.

4DVideo has been in business for just over 15 years. We have used
the technique to solve a wide variety of industrial problems. It
works well.

Sincerely,

Jim Walton

BTW, we are developing a commercial product that should be
available in mid-year.

************************************************** ************
* JAMES (Jim) S. WALTON, Ph.D., President, 4DVIDEO *
* Fellow, Society of Photo-Optical Instrumentation Engineers *
* 825 Gravenstein Highway North, Suite 4 *
* SEBASTOPOL, California 95472 USA *
************************************************** ************
* PHONE: (707) 829-8883 FAX: (707) 829-3527 *
* INTERNET: Jim@4DVideo.com *
************************************************** ************


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From: "D. Gordon E. Robertson, Ph.D."

We regularly do this. We use an algorithm developed by Herman Woltring
that is called a Fractional Linear Transform. The algorithm is built into our
Biomech Motion Analysis System which is capable of processing APAS files
plus other ASCII formats. It is available from the CSB website at:
http://www.health.uottawa.ca/biomech/csb/software/

The system permits up to 100 control points but APAS limits you to 31. These
points can be randomly distributed in the calibration plane or arranged as
a grid.
It can handle any kind of linear distortion and is similar to how the DLT.


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From: Ton van den Bogert

The ISB website has some Matlab code that may be useful. See
http://www.isbweb.org/software/movanal.html Look for
"2D-DLT".

Ton van den Bogert
Department of Biomedical Engineering
Cleveland Clinic Foundation
9500 Euclid Avenue (ND-20)
Cleveland, OH 44195, USA
Phone: (216)444-5566
Fax: (501)665-1506

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From: "Daniel India"

Dan India with Motion Analysis. If you are working with Richard Smith, I
believe his 3D Motion Analysis system (with EVa 6.0) has a 2D
non-perpendicular calibration method using the 8 point cube as used with the
3D system.

The Camera can be at any angle to the feild of view for calibration and for
data collection.

Let me know if you need any more information.


Dan.India@motionanalysis.com


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Peter Sinclair
Lecturer in Biomechanics
School of Exercise and Sport Science
The University of Sydney
East St Lidcombe NSW 1825
Phone 61 2 9351 9137
p.sinclair@fhs.usyd.edu.au

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