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kwon3d
01-22-2004, 03:11 AM
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
------------------------------------------------------

-----Original Message-----
From: Biomechanics and Movement Science listserver
[mailto:BIOMCH-L@NIC.SURFNET.NL] On Behalf Of Peter Sinclair
Sent: Wednesday, January 21, 2004 11:31 PM
To: BIOMCH-L@NIC.SURFNET.NL
Subject: [BIOMCH-L] 2D digitising with non-perpendicular camera

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,

Peter Sinclair
Lecturer in Biomechanics
School of Exercise and Sport Science
The University of Sydney
p.sinclair@fhs.usyd.edu.au

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