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Based on the aforementioned internal accuracy evaluation
method, the internal relative accuracy statistics are shown in
Table 10. After calibration, a relative positioning error of less
than 1.0 pixel was achieved when a small number of GCPs was
used to eliminate the influence of system error.
Discussion
Based on the results in the experiments, we can see that the
significant advantage of the self-calibration strategy for WFV
cameras of GF1 is the use of partial coverage of the refer-
ence calibration data. This approach allows highly accurate
calibration of the whole WFV image, significantly reducing the
demand for a calibration field with large coverage, and thus it
is much more labor- and cost-saving.
Based on the principle of the self-calibration model,
we know that the same internal distortion is the important
precondition. Though the light aberration and atmospheric re-
fraction errors of different images would probably be different
because of the different imaging attitudes, because the geo-
metric resolution of WFV camera is relatively low these errors
can be taken as systematic errors for each pixels in one image
and compensated by the installation angles in the first two
steps of the self-calibration process. The internal distortion of
images is relatively consistent, and thusthe effectiveness of
the proposed self-calibration process for WFV1 can be guaran-
teed. The model based on paired stereoscopic images confers
a significant time advantage compared to that based on three
stereoscopic images, which depends less on the reference DEM
and makes this approach adaptable to complex terrain.
The overlapping relationship of the stereoscopic images
has a direct influence on the coverage required for the calibra-
tion field, and an appropriate overlapping relationship is im-
portant to the effectiveness of the approach. In the application
of the calculated a0 and b0 in the stepwise estimation method,
stereoscopic images have different horizontal directions based
on whether the right or left CCD is selected as the primary CCD.
The relative positioning accuracy between the adjacent
WFV cameras is also important, because it will directly affect
the mosaicking accuracy of the adjacent WFV images. As we
can see in Figure 10, the selected small-range geometric cali-
bration fields have nearly the same imaging times, and thus
the negative effect of the attitude measurement error can be
reduced (Wang et al. 2016; Cheng et al. 2017). The selected
small-range geometric calibration fields can also provide the
geometric constraints in the stitching areas. After the geo-
metric self-calibration, the gaps between the adjacent WFV
cameras were removed and the mosaicking accuracy based
on the geometric information of the data set 1 in Table 2 was
decreased to less than 1.0 pixel (as shown in Table 11). This
benefits from the internal parameters’ stepwise estimation
method and the reasonable distribution of the small-range
geometric calibration fields.
Conclusions
Using partial calibration-field coverage, we developed the
self-calibration scheme for WFV cameras on GF1, which will
reduce the dependence on a large-scale calibration field. Our
work focused on four aspects:
• We provided a detailed introduction to the flow of the
proposed calibration approach for WFV cameras, based on
partial reference calibration data coverage.
• Two self-calibration models for WFV cameras on GF1 were
verified—based on paired stereoscopic images and on three
stereoscopic images, respectively—along with the corre-
sponding stepwise internal-parameter estimation methods.
• The application conditions of the self-calibration of GF1
WFV cameras were fully discussed.
• Detailed and comprehensive experiments were performed
to verify the effectiveness of the proposed calibration
approach. The different overlapping relationships of the
stereoscopic images obtained by four WFV cameras on GF1
were fully analyzed and validated.
This article provides a new usable approach for GF1 and other
large-field-of-view optical satellites to overcome the stringent
requirements for high resolution and the use of large refer-
ence data sets in traditional calibration methods.
Acknowledgments
The authors would like to thank the editors and anonymous
reviewers for their valuable comments, which helped im-
prove this article. This work was substantially supported
by the National Key Research and Development Program of
China (2016YFB0501402) and the National Science Fund
for Distinguished Young Scholars (61825103). GF1 data were
provided by the China Center for Resources Satellite Data and
Application. This support was valuable.
Table 9. Positioning accuracy (root-mean-square; pixels) before and after calibration of internal distortion (WFV1 and WFV2).
Camera
Before Traditional Calibration Self-Calibration
Sample Line Plane Sample Line Plane Sample Line Plane
WFV1 35.462 4.435 35.738 0.409 0.422 0.587 0.461 0.488 0.671
WFV2 35.564 4.783 35.884 0.428 0.417 0.597 0.554 0.470 0.727
Table 10. Relative positioning accuracy (root-mean-square error; pixels) of WFV1 and WFV2 cameras.
Location (Longitude and Latitude) Imaging Time
WFV1 Accuracy WFV2 Accuracy
Sample Line Plane Sample Line Plane
E104.3_N39.7/E106.6_N39.3 6 Jan 2018 0.498 0.523 0.722 0.524 0.482 0.711
E109.8_N36.3/E112.0_N36.0 4 Feb 2018 0.523 0.489 0.716 0.576 0.509 0.795
E110.1_N34.9/E112.4_N34.5 28 Feb 2018 0.517 0.539 0.747 0.535 0.577 0.787
Table 11. Mosaicking accuracy (root-mean-square; pixels)
after calibration between adjacent images.
Between
WFV1 and WFV2
Between
WFV2 and WFV3
Between
WFV3 and WFV4
Sample Line Sample Line Sample Line
0.423 0.409 0.327 0.315 0.411 0.428
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