 Rational
Polynomial Rectification
Papers Cited
QuickBird
… Geometric Correction, Processing and Data.
by Phillip Cheng, Thierry Toutin, Yun Zhang, and Mathew Wood.
EOM, May 2003, pp. 24-30.
Block
Adjustment of High-Resolution Satellite Images Described by Rational
Polynomials. by Jacek
Grodecki and Gene Dial. Photogrammetric
Engineering and Remote Sensing. Vol.
69, No. 1, January 2003, pp. 59-68.
Abstract:
“This paper describes how
to block adjust high-resolution satellite imagery described by Rational
Polynomial Coefficient (RPC) camera models and illustrates the method with
an Ikonos example. By
incorporating a priori constraints into the adjustment model, multiple
independent images can be adjusted with or without ground control.
The RPC black adjustment model presented in this paper is directly
related to the geometric properties of the physical camera model.
Multiple physical camera model parameters having the same net
effect on the object-image relationship are replaced by a single
adjustment parameter. Consequently,
the proposed method is numerically more stable than the traditional
adjustment of exterior and interior orientation parameters.
This method is generally applicable to any photogrammetric camera
with a narrow field of view, calibrated, stable interior orientation, and
accurate a priori exterior orientation data.
As demonstrated in the paper, for Ikonos satellite imagery, the RPC
block adjustment achieves the same accuracy as the ground station block
adjustment with the full physical camera model.”
Bias
Compensation in Rational Functions for Ikonos Satellite Imagery.
Clive S. Fraser and Harry B. Hanley. Photogrammetric Engineering and
Remote Sensing. Vol. 69, No. 1,
January 2003, pp. 53-57.
Abstract:
“A method for the removal
of exterior orientation biases in rational function coefficients (RPC) for
Ikonos imagery is developed. These
biases, which are inherent in RPC’s derived without the aid of ground
control, give rise to geopositioning errors.
The 3D positioning error can subsequently be compensated during
spatial intersection by two additional parameters in image coordinates.
The resulting bias parameters can then be used to correct the
RPC’s supplied with Ikonos Geo imagery such that a practical means is
provided for bias-free ground point determination, nominally to
meter-level absolute accuracy, using entirely standard procedures on any
photogrammetric workstation that supports Ikonos RPCs.
The method requires provision of one or more ground control points.
Aside from developing the bias compensation method, the paper also
summarizes practical testing with bias-corrected RPCs that has
demonstrated sub-meter geopositioning accuracy from Ikonos Geo imagery.”
Error
Tracking in Ikonos Geometric Processing Using a 3D Parametric Model.
Thierry Toutin. Photogrammetric Engineering and Remote Sensing.
Vol. 69, No. 1, January 2003, pp. 43-51.
Abstract:
“Thirteen panchromatic
(Pan) and multiband (XS) Ikonos Geo product images over seven study sites
with various environments and terrain were tested using different
cartographic data and accuracies with a 3D parametric model developed at
the Canada
Center
for
Remote Sensing, Natural Resources Canada.
The objectives of this study were to define the relationship
between the final accuracy and the number and accuracy of input data, to
track error propagation during the full geometric correction process
(bundle adjustment and ortho-rectification), and to advise on the
applicability of the model in operational environments.
“When
ground control points (GCPs) have an accuracy poorer than 3 m, 20 GCPs
over the entire image are a good compromise to obtain a 3- to 4-m accuracy
in the bundle adjustment. When
GCP accuracy is better that 1 m, ten GCPs are enough to decrease bundle
adjustment error of either panchromatic or multiband images to
2
to 3 m.
Because GCP residuals reflect the input data errors (map and/or
plotting), these errors did not propagate through the 3D parametric model,
and the internal accuracy of the geometric models is thus better (around a
pixel or less).
“Quantitative
and qualitative evaluations of ortho-images were thus performed with
either independent check points or overlaid digital vector files.
Generally, the measured errors and a 2- to 4-m positioning accuracy
was achieved for the ortho-images depending upon the elevation accuracy
(DEM and grid spacing). To
achieve a better final positioning accuracy, such as 1 m, a DEM with an
accuracy of 1 to 2 m and with a fine grid spacing is required, in addition
to well-defined GCPs with an accuracy of 1 m.”
Rational
Functions and Potential for Rigorous Sensor Model Recovery.
Kalchang Di, Ruijin Ma, and Rong Xing U. Photogrammetric Engineering
and Remote Sensing. Vol. 69,
No. 1, January 2003, pp. 33-41.
Abstract:
“Rational functions (RFs)
have been applied to photogrammetry and remote sensing to represent the
transformation between the image space and object space whenever the
rigorous model is made unavailable intentionally or unintentionally.
It attracts more attention now because Ikonos
high-resolution images are being released to users with only RF
coefficients. This paper
briefly introduces the RF for photogrammetric processing.
Equations of space intersection with upward RF are derived.
The computational experimental result with one-meter resolution
Ikonos Geo stereo images and other airborne data verified the accuracy of
the upward RF-based space intersection.
We demonstrated different ways to improve the geopositioning
accuracy of Ikonos Geo stereo imagery with ground control points by either
refining the vendor-provided Ikonos RF coefficients or refining the RF-derived
ground coordinates. The
accuracy of 3D ground point determination was improved to 1 to 2 meters
after refinement. Finally we
showed the potential for recovering sensor models of a frame image and
linear array image from the RF.”
3D
Reconstruction Methods Based on the Rational Function Model.
C. Vincent Tao and Yong Hu.
Photogrammetric Engineering and Remote Sensing.
Vol. 68, No. 7, July 2002, pp. 705-714.
Abstract:
“The rational function
model (RFM) is an alternative sensor model allowing users to perform
photogrammetric processing. The
RFM has been used as a replacement sensor
model in some commercial photogrammetric systems due to its capability of
maintaining the accuracy of the physical sensor models and its generic
characteristic of supporting sensor-independent photogrammetric
processing. With RFM
parameters provided, end users are able to perform photogrammetric
processing including orthorectification, 3D reconstruction, and DEM
generation with an absence of the physical sensor model.
In this research, we investigate two methods for RFM-based 3D
reconstruction, the inverse RFM method and the forward RFM method.
Detailed derivations of the algorithmic procedure are described.
The emphasis is placed on the comparison of these two
reconstruction methods. Experimental
results show that the forward RFM can achieve a better reconstruction
accuracy. Finally, real
Ikonos stereo pairs were employed to verify the applicability and the
performance of the reconstruction method.”
Updating
Solutions of the Rational Function Model Using Additional Control
Information.
Yong Hu and C. Vincent Tao. Photogrammetric
Engineering and Remote Sensing. Vol.
68, No. 7, July 2002, pp. 715-723.
Abstract:
“The rational function
model (RFM) is a sensor model that allows users to perform ortho-rectification
and 3D feature extraction from imagery without knowledge of the physical
sensor model. It is a fact
that the RFM is determined by the vendor using a proprietary physical
sensor model. The accuracy of
the RFM solution is dependent on the availability and usage of ground
control points (GCP). In
order to obtain a more accurate RFM solution, the user may be asked to
supply GCPs to the data vendor. However,
control information may not be available at the time of data processing or
cannot be supplied due to some reasons (e.g., politics or
confidentiality). This paper
addresses a means to update or improve the existing RFM solutions when
additional GCPs are available, without knowing the physical sensor model.
From a linear estimation perspective, the above issue can be
tackled using a phased estimation theory.
In this paper, two methods are proposed: a batch iterative
least-squares (BILS) method and an incremental discrete Karman filtering (IDKF)
method. Detailed descriptions
of both methods are given. The
feasibility of these two methods is validated and their performances are
evaluated. Some results
concerning the updating of Ikonos imagery are also discussed.”
A
Study on the Generation of the Komsat-1 RPC Model.
Hye-jin Kim, Dae-sung Kim, Hyo-sung Lee, Young-il Kim. no date. 4
pages. see http://www.isprs.org/commission3/
proceedings/papers/paper129.pdf
Abstract:
“The rational polynomial
coefficients (RPC) model is a generalized sensor model that is used as an
alternative solution for the physical sensor model for IKONOS of the Space
Imaging. As the number of
sensors increases along with greater complexity, and the standard sensor
model is needed the applicability of the RPC model is increasing.
The RPC model has the advantages in being able to substitute for
all sensor models, such as the projective, the linear pushbroom and the
SAR.
“This
report aimed to generate a RPC model from the physical sensor model of the
KOMPSAT-1 (Korean Multi-Purpose Satellite) and aerial photography.
The KOMPSAT-1 collects 510~730 nm panchromatic imagery with a
ground sample distance (GSD) of 6.6 m and a swath width of 17 km by
pushbroom scanning. The
iterative least square solution was used to estimate the RPC.
In addition, data normalization and regularization were applied to
improve the accuracy and minimize noise.
This study found that the RPC model is suitable for both KOMPSAT-1
and aerial photography.”
Rational
Mapper: A Software Tool for Photogrammetric Exploitation of High Resolution
Satellite Imagery.
C. Vincent Tao, Yong Hu, Wanshou Jiang.
no date. 6 pages.
see http://www.geoict.yorku.ca/project/rationalmapper/rationalmapper.htm
Background:
“The Rational Function
Model (RFM) has gained considerable interest recently in the
photogrammetry and remote sensing community.
This is mainly due to the fact that some satellite data vendors,
for example, Space Imaging, Thornton, CO, USA,
have adopted the RFM as a replacement sensor model for image exploitation.
The data vendor will supply users with the parameters of the RFM
instead of the rigorous sensor models.
Such a strategy may help keep the confidential information about
the sensors and on the other hand, facilitate the use of high-resolution
satellite imagery for general public uses (non-photogrammetrists) since
the RFM is easy to use and easy to understand.”
Continues
on with a easily understood description of the general idea.
An
Update on the Use of Rational Functions for Photogrammetric Restitution.
Ian Dowman and Vincent Tao. ISPRS.
September 2002, Vol. 1, No. 3. pp.
22-29.
Extraction:
“During the past four or
five years the photogrammetric community at large has become aware of the
use of rational functions for photogrammetric restitution.
This has been due largely to the need to use these for setting up
Ikonos data, as Space Imaging does not provide a physical sensor model
with the image data. Rational
functions have been used for some time for military use and their
widespread acceptance in that area has led to the proposal to the OGC for
a standard for image restitution based on rational functions on the basis
of its universality: it can be used with any sensor.”
For
the complete article see: http://www.isprs.org/publications/highlights/highlights0703/
22_HL_09_02_Article_Dowman.pdf
Geometric
Information from IKONOS. Zhigu
Hu. GIM International.
Vol. 17, No. 9, September 2003.
pp. 42-45.
“Since
pixel size of panchromatic IKONOS imagery is one meter it is
desirable that the planimetric and height error after georeferencing be
smaller. Which method
provides the high accuracy requirement?
The author tested three processing methods: (1) IKONOS RPC
parameters only, (2) an associated adjustment of RPC parameters with
control points and (3) a strict geometric model based on affine
transformation. The
adjustment of RPC coefficients with one or two control points improves
accuracy significantly, especially in elevation.
Using only five control points, the strict
model yields very high accuracy of 5 to 12 cm in X, Y, and Z with
one pair of stereo images covering. The
method does not need RPC coefficients, whilst the coordinate system can be
any independent one. The
strict model represents a new step forward, both in theory and
application, for high-resolution IKONOS imagery processing.”
[In
the first sentence of this paper the author states: “The
stereo pair of panchromatic IKONOS images with 1-meter spatial resolution
used in the test covers over 20 square kilometers of a quite
flat Beijing
suburb.”
It is possible that a DEM was not even used and the solution was
performed using an average elevation.
How well will these results extend to areas with typical
topographic relief?]
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25 March 2009 |
page update:
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