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Brian Davis wrote:
> Following on from Rich Hinrich's posting: If one uses 16 or 50 points,
> presumably some are more accurately known than others. I've often
> wondered whether one should (i) calculate the residuals (i.e., differences
> between "known" and predicted locations of the markers on the calibration
> object), (ii) exclude those marker(s) with a large residual, and (iii) recalibrate
> the cameras. This procedure would entail starting off with 16 (or 50)
> markers and ending up with slightly fewer (e.g., 15 or 49) points that would be
> used in the final calibration process.
>
> I suspect that this would offer the advantage that a single, incorrectly
> defined, point on the calibration cube would not degrade the calibration
> procedure. I also suspect that this method would yield equivalent results
> when using 16 or 50 points since you would land up using only the best
> subset of the "known" calibration points.
>
> Regards, Brian Davis
> Cleveland Clinic Foundation
>
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Indeed, this can be done and I have experimented (rather extensively) with user
interactive
iterative adjustment methods of this type for DLT parameter estimation. However,
there is an important aspect of these methods that one should
always keep in mind -- the residuals are composed of errors in: 1) measured position,
2) calculated position, and 3) the camera model. Thus, when removing a point
using "residual reducing" , the source of the error is often unclear. It could be that
the "known" or measured measured position was the culprit, not the
calculated (or predicted) position.
The importance of this can be better understood by the following
simple experiment. Perform a normal DLT calibration. Then adjust the measured
position of the control point with the largest residual (without actually moving the
control point!) so that the overall residual errors are reduced. Note, the condition
number for the overdetermined system of equations (in the DLT matrix formulation)
could also be used as the objective function to be minimized). It is usually possible
to reduce the residual errors (differences between measured and predicted values) by
making these numerical adjustments to the measured position. But, the obvious
question to ask is -- Does this improve the accuracy in the reconstruction?
Answer -- sometimes. Why? Because sometimes the residual error may be
strongly influenced by a measured position error, while at other times it may be
dominated by errors in the camera model (e.g. lens distortion) or calculated position
errors.
Comment. Often there is a tendency to fill the view plane (in each camera) with
the control points; i.e. position the cameras such that several control points are
near the boundaries of the image planes in each camera. This is almost surely not
a good idea when using the DLT method (esp. the linear DLT method); since image
points at the boundaries of the image plane will nearly always dominate
the errors (mainly due to greater distortion along the boundaries). And thus,
control point images along the boundaries will tend to degrade the overall
accuracy of the DLT parameters (and 3D reconstruction). Improved
accuracy (overall) can usually be obtained by using control points that lie closer
to the center of the image. Again, I suggest that you perform some simple
experiment to test this claim.
A more provocative question is -- Do we really need calibration parameters to obtain
the 3D position of a marker from its 2D camera images? This question should not be
dismissed so quickly since it gets at the very heart of geometrical transformations --
more
specifically, the foundations of perspective geometry. For the more curious, take a
look at:
http://www.inria.fr/
You might be surprised!
-- VPS
************************************************** *
V. Stokes, Ph.D. ---------> Quality Has No Fear
BMC, Neuroscience of Time
Karolinska Institute
SWEDEN
************************************************** *
> Following on from Rich Hinrich's posting: If one uses 16 or 50 points,
> presumably some are more accurately known than others. I've often
> wondered whether one should (i) calculate the residuals (i.e., differences
> between "known" and predicted locations of the markers on the calibration
> object), (ii) exclude those marker(s) with a large residual, and (iii) recalibrate
> the cameras. This procedure would entail starting off with 16 (or 50)
> markers and ending up with slightly fewer (e.g., 15 or 49) points that would be
> used in the final calibration process.
>
> I suspect that this would offer the advantage that a single, incorrectly
> defined, point on the calibration cube would not degrade the calibration
> procedure. I also suspect that this method would yield equivalent results
> when using 16 or 50 points since you would land up using only the best
> subset of the "known" calibration points.
>
> Regards, Brian Davis
> Cleveland Clinic Foundation
>
> -------------------------------------------------------------------
> To unsubscribe send UNSUBSCRIBE BIOMCH-L to LISTSERV@nic.surfnet.nl
> For more information: http://www.kin.ucalgary.ca/isb/biomch-l.html
> -------------------------------------------------------------------
Indeed, this can be done and I have experimented (rather extensively) with user
interactive
iterative adjustment methods of this type for DLT parameter estimation. However,
there is an important aspect of these methods that one should
always keep in mind -- the residuals are composed of errors in: 1) measured position,
2) calculated position, and 3) the camera model. Thus, when removing a point
using "residual reducing" , the source of the error is often unclear. It could be that
the "known" or measured measured position was the culprit, not the
calculated (or predicted) position.
The importance of this can be better understood by the following
simple experiment. Perform a normal DLT calibration. Then adjust the measured
position of the control point with the largest residual (without actually moving the
control point!) so that the overall residual errors are reduced. Note, the condition
number for the overdetermined system of equations (in the DLT matrix formulation)
could also be used as the objective function to be minimized). It is usually possible
to reduce the residual errors (differences between measured and predicted values) by
making these numerical adjustments to the measured position. But, the obvious
question to ask is -- Does this improve the accuracy in the reconstruction?
Answer -- sometimes. Why? Because sometimes the residual error may be
strongly influenced by a measured position error, while at other times it may be
dominated by errors in the camera model (e.g. lens distortion) or calculated position
errors.
Comment. Often there is a tendency to fill the view plane (in each camera) with
the control points; i.e. position the cameras such that several control points are
near the boundaries of the image planes in each camera. This is almost surely not
a good idea when using the DLT method (esp. the linear DLT method); since image
points at the boundaries of the image plane will nearly always dominate
the errors (mainly due to greater distortion along the boundaries). And thus,
control point images along the boundaries will tend to degrade the overall
accuracy of the DLT parameters (and 3D reconstruction). Improved
accuracy (overall) can usually be obtained by using control points that lie closer
to the center of the image. Again, I suggest that you perform some simple
experiment to test this claim.
A more provocative question is -- Do we really need calibration parameters to obtain
the 3D position of a marker from its 2D camera images? This question should not be
dismissed so quickly since it gets at the very heart of geometrical transformations --
more
specifically, the foundations of perspective geometry. For the more curious, take a
look at:
http://www.inria.fr/
You might be surprised!
-- VPS
************************************************** *
V. Stokes, Ph.D. ---------> Quality Has No Fear
BMC, Neuroscience of Time
Karolinska Institute
SWEDEN
************************************************** *