International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
T
E.
Figure 11. A patch of the calibrated data set.
All the three models presented above are applied to this
calibration data set. The vector plot of the residual errors for
GCPs and the check points for all mathematical models are
displayed in Figure 12.
15 micron
3D Affine Transformation
RMSE- on. control points 5.
= X int kp" iz i
RMSE on check points 2.51 is micron
Rational Function (Order 3 with full terms)
Figure 12. Vector plot of residual errors of the different
mathematical models.
These graphs indicate that:
1. Projective transformation is stable as regards the error
fluctuations. However, it seems not to be flexible
enough to take care of the inherent non-linearity of
the image distortions.
2. The 3D affine transformation has the same limitation
as the projective transformation.
3. The rational functions show a good performance in
particular if the coefficients for the denominators are
selected to be the same for the X and Y components.
4. Although quite flexible, polynomials and rational
functions main shortcomings are their non-stability
for the position of the points.located between GCPs.
The error can be drastically amplified for those points
that are far from the GCPs. That is, GCPs distribution
plays a decisive rule in retaining the model stability.
5. Apart from polynomials, increasing the number of
GCPs increases the fitting and absolute accuracy.
However, the accuracy figures do not show a clear
improvement if the number of GCPs are increased
beyond certain levels.
4. CONCLUSION REMARKS
In this study the following experiments have been conducted to
analyze the radiometric and geometric performance of Canon
EOS-1Ds high resolution CMOS camera.
To evaluate the radiometric potential of CMOS, the point
spread function (PSF) of the imaging system was estimated.
This was done by using the smallest detectable symmetric
feature with a uniform grey scale background that could be
found in the image. The sigma of the PSF was determined by
assuming a Gaussian model for it. The pictorial restoration
operations were then performed by modified inverse and
Wiener filters respectively.
Geometric correction of the CMOS camera has been examined
based on an evaluation of three mathematical models based on
Rational functions, 3D Affine and 2D Projective
transformation. For the accuracy evaluation vector plots of the
residual errors for control points and check points are prepared.
Further experiments with other Canon EOS-IDs images
confirm the high capability of this CMOS camera.
5. REFERENCES
Atkinson, K.B., 1996. Close Range Photogrammetry and
Computer Vision, Whittles Publishing Bristol.
Castleman, K.R., 1996. Digital Image Processing, Prentice-
Hall, Simon&Schuster.
Cannon, 2004: http://www.canon.co.uk/For_Home/
Product_Finder/Cameras/Digital_SLR/EOS_1Ds/
Dowman, L, and J.T. Dolloff, 2000. An evaluation of rational
functions for photogrammetric restitution. Int'l Archive of
photogrammetry and Remote Sensing, 33(Part B3): 254-266.
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