Abstract

The HaiYang-1C coastal zone imager (CZI) consists of two independent cameras with a total image swath of approximately 1000 km. In order to obtain precise imaging parameters of the CZI cameras, a feasible in-orbit geometric calibration approach with multiple fields is presented. First, the master CCD is calibrated with a calibration field. Then, the slave CCDs are respectively calibrated with different fields. Finally, the calibrated internal shift parameters of the slave CCDs are adjusted with tie points between adjacent sub-images. Seven HaiYang-1C CZI images were tested. The experimental results showed that the imaging parameters calibrated with the presented approach could perform as well as those calibrated with the conventional approach with a single field. However, the total swath of the calibration fields could be reduced from approximately 1000 km to 300 km. The application difficulties in collecting satisfactory calibration sub-images could be thereby significantly reduced in the geometric calibration.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The HaiYang-1C satellite is a Chinese ocean remote sensing satellite and was launched on 7th September 2018. A coastal zone imager (CZI) was equipped on the HaiYang-1C satellite. The CZI mainly collects images covering global costal zones and Chinese land. The primary role is to monitor global costal zones, collect quantitative data in estuaries and coasts, and monitor and early warn ocean disasters. The CZI consists of two independent multispectral cameras. Each camera has four multispectral bands. Each band has two linear charge-coupled devices (CCDs), and each CCD has 5450 detectors, as shown in Fig. 1. Four sub-images collected by four CCDs in each band are finally stitched together to generate a complete seamless CZI image. So, like many other optical satellite cameras, in-orbit geometric calibration for the HaiYang-1C CZI is indispensable.

 figure: Fig. 1.

Fig. 1. The imaging sketch map of the HaiYang-1C CZI.

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In-orbit geometric calibration aims to obtain precise imaging parameters of satellite cameras, such as the principle point, principle length, lens distortions, and camera installation angles. Due to the satellite acceleration during the satellite launch, these imaging parameters often differ from those calibrated in laboratory. Additionally, these parameters may change more or less because of the spatial environment changes and the instrument losses during the in-orbit operation. Therefore, in-orbit geometric calibration is an indispensable procedure in the whole life of satellite cameras. With the help of the geometric calibration, the sensor orientation accuracy, the geometric stitching accuracy, the band registration accuracy, and the geometric quality of spatial products derived from satellite images can be guaranteed [17].

Existing in-orbit geometric calibration approaches for optical satellites can be mainly classified into two categories: field-dependent calibration and field-independent calibration. For the field-dependent calibration approach, many ground control points (GCPs) are often surveyed in a calibration field by a global navigation satellite system (GNSS) or extracted from reference data (e.g. digital orthophoto map (DOM) and digital elevation model (DEM)) covering the calibration field. Then, these GCPs are utilized to precisely determine geometric calibration parameters of satellite cameras. This approach has been used by the majority of optical satellites [13,814]. For example, Grodecki and Dial used 33 GCPs surveyed by the GNSS to perform field angle map calibration and interlock calibration of the IKONOS camera [2]. Gachet used many GCPs extracted from the reference data to perform interior calibration of SPOT-5 HRG and HRS cameras [8]. Mulawa performed geometric calibration of OrbView3 cameras with thousands of GCPs extracted from medium-scale aerial images [9]. Wang et al. employed an image matching approach to obtain dense GCPs from the reference DOM and DEM and calibrated external and internal parameters of the ZiYuan-1 02C, ZiYuan-3, and GaoFen-6 satellite cameras [1,4]. In the field-dependent calibration approach, one of the important application requirements is that all sub-images collected by a satellite camera or multiple cameras should cover a calibration field; that is, the swath of the calibration field should be larger than that formed by all sub-images.

For the field-independent calibration approach, it takes full advantage of internal constraints formed by tie points among multiple overlapped satellite images to perform geometric calibration [1520]. For example, Greslou et al. and Lebègue et al. used a couple of images collected in an auto-reverse mode to calibrate the viewing reference frame biases, and used a couple of images collected in a cross mode to calibrate the focal plane of the Pleiades-HR camera [15,16]. Pi et al. employed internal constraints of a cross-image pair and multi-attitude images to perform self-calibration, and a high theoretical accuracy was achieved by the simulated experiments [17,18]. Cheng et al. presented a self-calibration approach for internal parameters of the GaoFen-2 cameras based on three-view stereoscopic images [19]. Yang et al. performed integrated geometric self-calibration of stereo cameras onboard the ZiYuan-3 satellite [20]. With the help of internal geometric constraints in the field-independent calibration approach, the external and internal parameters can be theoretically calibrated without GCPs. In fact, however, the external calibration parameters can only be roughly determined and sparse GCPs are still necessary to achieve an optimal external accuracy [15,19,20]. Additionally, a DEM with higher resolution and accuracy or a flat image-covered area should be selected to reduce the influence of elevation errors on the calibration accuracy [19,21]. Therefore, we can see from previous studies that it is very difficult to achieve real field-independent calibration at present.

For the HaiYang-1C CZI cameras, the ground sample distance (GSD) of the subastral point is approximately 50 m. The globally publicized 15 m resolution Landsat DOM and 90 m resolution shuttle radar topography mission (SRTM) DEM can be thereby used as the reference data. Dense GCPs can be extracted by image matching between the CZI sub-images and the reference DOM and DEM, and the field-dependent calibration can be performed. In this field-dependent approach, only one field is conventionally used, and the field swath should be larger than the total image swath formed by all satellites cameras [5]. Additionally, in order to extract dense GCPs by image matching, each sub-image collected by the CCDs should better be cloud-free, snow-free, land-covered, and texture-rich. However, the total image swath formed by two CZI cameras is approximately 1000 km. Due to so large an image swath, it is very difficult to collect such satisfactory sub-images in a single field. That is to say, although the reference DOM and DEM are available, it is very difficult to perform field-dependent calibration for the HaiYang-1C CZI with a single field.

In this study, we focused on field-dependent calibration and presented an in-orbit geometric calibration approach for the HaiYang-1C CZI with multiple fields. In this approach, the external parameters of the master CCD were first calibrated, and then the internal parameters of each CCD were respectively calibrated with different fields. Finally, the calibrated internal shift parameters of the slave CCDs were adjusted according to tie points between adjacent sub-images. Compared with the conventional calibration approach with a single field, the innovation of the presented approach is that four CCDs can be calibrated with four sub-images covering different fields and each field has a swath of smaller than 300 km. The objective of this study is not to improve the calibration accuracy, but to realize precise multi-field calibration without losing the calibration accuracy. With the presented calibration approach, the application difficulties in collecting satisfactory sub-images with so large a swath in the field-dependent calibration approach could be significantly reduced.

The remainder of this paper is organized as follows. Section 2 details the presented geometric calibration approach, including the establishment of the geometric calibration model, the geometric calibration with a single field, and the geometric calibration with multiple fields. Section 3 describes the use of several HaiYang-1C CZI images to analyze the feasibility and effectiveness of the presented approach. Section 4 gives the conclusions.

2. Methodology

2.1 Geometric calibration model

Like many other optical satellites, each linear CCD of the HaiYang-1C CZI cameras collect images in a push-broom mode. The geometric calibration model of each CCD can be thereby expressed as follows [1,4]:

$$\left[ {\begin{array}{c} {\tan {\phi_x}}\\ {\tan {\phi_y}}\\ 1 \end{array}} \right] = \lambda {\mathbf R}_{\textrm{ADS}}^{\textrm{Camera}}({\varphi ,\omega ,\kappa } ){\mathbf R}_{\textrm{J2000}}^{\textrm{ADS}}({{q_0},{q_1},{q_2},{q_3}} ){\mathbf R}_{\textrm{WGS84}}^{\textrm{J2000}}\left( {{{\left[ {\begin{array}{c} X\\ Y\\ Z \end{array}} \right]}_{\textrm{WGS}84}} - {{\left[ {\begin{array}{c} {{X_S}}\\ {{Y_S}}\\ {{Z_S}} \end{array}} \right]}_{\textrm{WGS84}}}} \right)$$
where $(\tan{\phi _x},\tan{\phi _y})$ are the normalized coordinates of a CCD detector in the camera coordinate system; λ is the scale factor; ${\mathbf R}_{\textrm{Camera}}^{\textrm{ADS}}$ represents the rotation matrix from the camera coordinate system to the attitude determination system (ADS) coordinate system, and it can be constructed by three rotation angles $(\varphi ,\omega ,\kappa )$ as follows:
$${\mathbf R}_{\textrm{ADS}}^{\textrm{Camera}}({\varphi ,\omega ,\kappa } )= \left[ {\begin{array}{ccc} {\cos \varphi }&0&{ - \sin \varphi }\\ 0&1&0\\ {\sin \varphi }&0&{\cos \varphi } \end{array}} \right]\left[ {\begin{array}{ccc} 1&0&0\\ 0&{\cos \omega }&{ - \sin \omega }\\ 0&{\sin \omega }&{\cos \omega } \end{array}} \right]\left[ {\begin{array}{ccc} {\cos \kappa }&{ - \sin \kappa }&0\\ {\sin \kappa }&{\cos \kappa }&0\\ 0&0&1 \end{array}} \right]$$
${\mathbf R}_{\textrm{J2000}}^{\textrm{ADS}}$ is the rotation matrix from the J2000 celestial coordinate system to the ADS coordinate system, and it can be constructed by the measured attitude quaternion $({{q_0},{q_1},{q_2},{q_3}} )$ as follows:
$${\mathbf R}_{\textrm{J2000}}^{\textrm{ADS}}\left( {{q_0},{q_1},{q_2},{q_3}} \right) = \left[ {\begin{array}{ccc} {1 - 2\left( {{q_2}{q_2} + {q_3}{q_3}} \right)}&{2\left( {{q_1}{q_2} - {q_0}{q_3}} \right)}&{2\left( {{q_1}{q_3} + {q_0}{q_2}} \right)}\\ {2\left( {{q_1}{q_2} + {q_0}{q_3}} \right)}&{1 - 2\left( {{q_1}{q_1} + {q_3}{q_3}} \right)}&{2\left( {{q_2}{q_3} - {q_0}{q_1}} \right)}\\ {2\left( {{q_1}{q_3} - {q_0}{q_2}} \right)}&{2\left( {{q_2}{q_3} + {q_0}{q_1}} \right)}&{1 - 2\left( {{q_1}{q_1} + {q_2}{q_2}} \right)} \end{array}} \right]$$

${\mathbf R}_{\textrm{WGS84}}^{\textrm{J2000}}$ is the rotation matrix from the WGS 84 geocentric coordinate system to the J2000 coordinate system, and it can be constructed by the precession, nutation, pole shift, and rotation of the earth; and $(X,Y,Z)_{\textrm{WGS}\;\textrm{84}}^\textrm{T}$ and $({X_S},{Y_S},{Z_S})_{\textrm{WGS}\;\textrm{84}}^\textrm{T}$ are the coordinates of the ground point and the satellite position, respectively, in the WGS 84 coordinate system.

In Eq. (1), ${\mathbf R}_{\textrm{Camera}}^{\textrm{ADS}}$ represents the relative geometric relationship between the camera and the ADS. The three rotation angles $(\varphi ,\omega ,\kappa )$ constructing ${\mathbf R}_{\textrm{Camera}}^{\textrm{ADS}}$ are often taken as external calibration parameters. Additionally, a look-angle model is often employed to model the normalized detector coordinates $(\tan{\phi _x},\tan{\phi _y})$ as follows [1,5,8,22]:

$$\left\{ {\begin{array}{c} {\tan {\phi_x} = {a_0} + {a_1}n + {a_2}{n^2} + {a_3}{n^3}}\\ {\tan {\phi_y} = {b_0} + {b_1}n + {b_2}{n^2} + {b_3}{n^3}\;} \end{array}} \right.$$
where n is the detector number; and $({a_0},\;{a_1},\;{a_2},\;{a_3},\;{b_0},\;{b_1},\;{b_2},\;{b_3})$ are taken as the internal calibration parameters.

The geometric calibration model expressed by Eqs. (1) and (4) can theoretically describe the rigorous imaging procedure of a satellite camera with linear CCDs. It has been successfully used in the in-orbit geometric calibration of many Chinese optical satellites, such as the ZiYuan-1 02C, ZiYuan-3, and GaoFen-1/2/6 satellites [1,11,19,23].

2.2 Calibration with a single field

The HaiYang-1C CZI cameras has four multispectral bands. In practice, we can first perform geometric calibration of band 2 with the reference DOM and DEM. Then, taking band 2 as the master band, the other bands can be calibrated relative to the master band with the reference DEM. Generally, as long as the master band is precisely calibrated, the other bands can be easily calibrated. In this study, we just focus on the geometric calibration of the master band 2. In the following texts, a CZI image only represents a CZI image of band 2.

As shown in Fig. 2, if four satisfactory field-covered calibration sub-images in a same CZI image are available, we can perform geometric calibration of the CZI with the single field. The major calibration procedures are as follows.

  • (1) Dense GCPs in each sub-image collected by four CZI CCDs are extracted from the reference DOM and DEM by image matching.
  • (2) The middle CCD (i.e., CCD 2 or CCD 3) of four CZI CCDs is taken as the master CCD, and the external and internal calibration parameters of the master CCD in Eqs. (1) and (4) are determined with the extracted GCPs, as performed in [1].
  • (3) The other CCDs are taken as the slave CCDs, and they share the same external calibration parameters with the master CCD. Only the internal parameters of each slave CCD are finally calibrated with the extracted GCPs.

 figure: Fig. 2.

Fig. 2. Geometric calibration of the HaiYang-1C CZI with a single field.

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From the point view of the instrumental structure, two CZI cameras have two sets of different external calibration parameters. In the ground processing, however, we often let different cameras share same external parameters, so that sub-images collected by different cameras could be geometrically stitched, as used in [12,22]. Theoretically, if camera 2 shares the external parameters of camera 1, the normalized coordinates $(\tan{\phi _x},\tan{\phi _y})$ of camera 2 in Eq. (1) are actually calibrated in the camera coordinate system of camera 1 rather than camera 2. Besides, in the geometric calibration model in Eq. (1), the external and internal calibration parameters are highly correlated with the satellite positions and attitudes [24]. It is very difficult or even impossible to separate the satellite position and attitude errors from the calibration parameters. The satellite position and attitude observations are thereby considered to be error free in the above calibration procedures. In fact, however, it is inevitable that they suffer from more or less shift and drift errors. In order to reduce the influence of the drift errors and improve the calibration accuracy, the extracted GCPs should distribute in a narrow image block collected in a small time interval, as shown in Fig. 2. In this case, the shift and drift errors will be inevitably absorbed by the calibrated parameters due to high correlation.

2.3 Calibration with multiple fields

Generally, the in-orbit geometric calibration approach with a single field introduced in section 2.2 is a mature approach. As long as the reference DOM and DEM are available and a satisfactory field-covered image can be collected, the calibration approach can be successfully performed.

In the geometric calibration of the HaiYang-1C CZI cameras, although the Landsat DOM with a 15 m GSD and the SRTM DEM with a 90 m GSD are globally publicized, the satisfactory CZI image cannot be always collected because of the 1000 km image swath. For convenient image matching and GCP extraction, the narrow image block shown in Fig. 2 should be cloud-free, snow-free, land-covered, texture-rich, and collection season-consistent with the Landsat DOM. Within three months after the HaiYang-1C satellite was launched, the CZI cameras collected lots of ground images. From the collected images, we found that it was difficult to find a satisfactory calibration image.

In order to reduce the application difficulties in collecting satisfactory calibration sub-images with so large a swath, we presented a geometric calibration approach for the CZI with multiple fields. In this section, we first analyzed the feasibility of the geometric calibration with multiple fields, and then described the major procedures.

  • 1) Feasibility analysis: In the geometric calibration of the CZI cameras with a single field, the external parameters of the master CCD are firstly calibrated, as described in section 2.2. The satellite position and attitude errors are absorbed by the calibrated external parameters. For the slave CCDs, they share the same external parameters with the master CCD. The geometric influence of the satellite position and attitude errors on four CCDs are same with each other. Therefore, four sub-images collected by four CCDs can be seamlessly stitched together after geometric calibration.

Same external parameters mean that the master and slave CCDs have same external geometric datum. The same external datum is a prerequisite for the geometric stitching of four sub-images. If different CCDs have different external datum, it will be very difficult to geometrically stitch four sub-images. Hence, the master and slave CCDs should also have same external datum in the geometric calibration with multiple fields. That is to say, the slave CCDs should share the same external parameters with the master CCD, just as that with a single field. The difference is that the internal parameters of the slave CCDs are calibrated with different fields. In this case, if the satellite position and attitude errors in different fields are same, the geometric calibration will become very simple. The internal parameters of four CCDs will absorb same errors, and four sub-images can be seamlessly stitched. Unfortunately, due to the randomness of the satellite position and attitude errors, the influence of these errors differs from each other in different fields.

Figure (3 shows the sensor orientation errors of twelve CZI image blocks (shown in Fig. 2) in different fields. Lots of independent check points (ICPs) was extracted from the reference DOM and DEM, and then a rational function model (RFM) was employed to evaluate the orientation errors. It is noted that the rational polynomial coefficients (RPCs) in the RFM were determined with the calibrated camera parameters rather than the initial parameters, so that the satellite position and attitude errors could be analyzed independently from the camera parameter errors. We can see from the orientation errors in different fields that the satellite position and attitude errors are obviously random. These random errors will be absorbed by different CCDs and affect the seamless stitching of four sub-images.

 figure: Fig. 3.

Fig. 3. Sensor orientation errors of twelve CZI image blocks in different fields.

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In order to further analyze the characteristic of the CZI orientation errors, an affine transformation model and a shift model are respectively utilized to eliminate the orientation errors in the RFM-based sensor orientation, as performed in [25]. The achieved orientation accuracies in twelve fields after error compensation are shown in Fig. 4.

 figure: Fig. 4.

Fig. 4. Sensor orientation accuracies of twelve CZI image blocks in different fields.

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We can see from Fig. 4 that the CZI orientation accuracies achieved by the RFM-based affine and shift models are almost the same. The largest difference is only 0.049 pixel that can be neglected. It demonstrates that almost all the CZI orientation errors caused by the satellite position and attitude errors are shift errors. This conclusion is consistent with the expected, because the satellite position and attitude errors are mainly shift errors in an image block collected in a small time interval. Based on this fact, the geometric calibration of the CZI cameras with multiple fields can be performed.

  • 2) Geometric calibration: When four CZI CCDs are calibrated with different fields, the internal parameters of different CCDs will absorb different satellite position and attitude errors. Fortunately, these absorbed errors are different shift errors. We can thereby adjust the internal shift parameters to eliminate the influence of the shift errors, so that the geometric consistence between the adjacent sub-images can be guaranteed. The major calibration procedures with multiple fields are follows.
  • (1) Dense GCPs in a sub-image collected by the master CCD are extracted from the reference DOM and DEM in a small image block (e.g., 300 to 500 image lines), as shown in Fig. 5, and then the external and internal parameters are successively determined. Here, the field used to calibrate the master CCD is named master field.
  • (2) Dense GCPs in sub-images collected by three slave CCDs are extracted, as shown in Fig. 6. Then, the slave CCDs share the same external parameters with the master CCD, and the internal parameters of each slave CCD are respectively determined. Here, the fields covered by three sub-images can differ from each other and from the master field.
  • (3) Several tie points are matched between the adjacent sub-images covering the master field, as shown in Fig. 5. From the master CCD to the two side slave CCDs, the internal shift parameters of the slave CCDs are successively adjusted.

 figure: Fig. 5.

Fig. 5. Four CZI sub-images covering the master field.

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 figure: Fig. 6.

Fig. 6. (a) Sub-image 1, (b) sum-image 3, and (c) sub-image 4 covering different fields.

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In this section, we just take sub-image 1 collected by CCD 1 and sub-image 2 collected by CCD 2 in Fig. 5 as an example to introduce the adjustment procedures of the internal shift parameters of CCD 1. The adjustment procedures of CCD 3 and CCD 4 are similar as CCD 1. The main procedures are as follows.

  • (1) With the calibrated external and internal parameters of CCD 2, each tie point p(x2, y2) in sub-image 2 is projected onto the reference DEM according to Eqs. (1) and (4). The projected object point P(X, Y, Z) is then obtained.
  • (2) With the shared external parameters of CCD 1, each object point P(X, Y, Z) is projected onto sub-image 1 according to Eq. (1), and then the projected normalized detector coordinates $(\tan{\phi _{xp}},\tan{\phi _{yp}})$ are obtained.
  • (3) With the calibrated internal parameters of CCD 1, the normalized detector coordinates $(\tan{\phi _{xt}},\tan{\phi _{yt}})$ for each tie point p(x1, y1) in sub-image 1 corresponding to the point p(x2, y2) in sub-image 2 are calculated according to Eq. (4).
  • (4) The shift errors caused by the satellite position and attitude errors in different fields are calculated as follows:
    $$\left\{ \begin{array}{l} \Delta {a_0} = \frac{1}{m}\sum\limits_{i = 1}^m {{{({\tan{\phi_{xp}}\textrm{ - }\tan{\phi_{xt}}} )}_i}} \\ \Delta {b_0} = \frac{1}{m}\sum\limits_{i = 1}^m {{{({\tan{\phi_{yp}}\textrm{ - }\tan{\phi_{yt}}} )}_i}} \end{array} \right.$$
    where m is the number of tie points.
  • (5) The look-angle model of CCD 1 is changed as follows:
    $$\left\{ {\begin{array}{c} {\tan {\phi_x} = {{a^{\prime}}_0} + {a_1}n + {a_2}{n^2} + {a_3}{n^3}}\\ {\tan {\phi_y} = {{b^{\prime}}_0} + {b_1}n + {b_2}{n^2} + {b_3}{n^3}\;} \end{array}} \right.$$
where $({a^{\prime}_0},{b^{\prime}_0})$ are adjusted internal shift parameters, and they can be adjusted as follows:
$$\left\{ {\begin{array}{c} {{{a^{\prime}}_0} = {a_0} + \Delta {a_0}}\\ {{{b^{\prime}}_0} = {b_0} + \Delta {b_0}} \end{array}} \right.$$

In the above geometric calibration procedures, four CCDs can be calibrated with different fields. Four satisfactory sub-images covering a single calibration field with a total image swath of approximately 1000 km are not necessary. Instead, four sub-images covering different fields with a swath of approximately 295 km, 245 km, 245 km, and 295 km are sufficient. The application difficulties in collecting satisfactory calibration sub-images can be thereby significantly reduced. In the presented approach, only several tie points between the adjacent sub-images covering the master field are required to adjust the internal shift parameters of the slave CCDs. For the HaiYang-1C CZI cameras, four CCDs were physically designed to be geometrically collinear. The shift errors between the adjacent sub-images are theoretically caused by the calibrated internal parameters; that is, the shift errors in different image blocks are theoretically same. Therefore, several tie points distributed in a small image block, as shown in Fig. 5, are sufficient to determine the shift errors. Such a requirement of tie points is easily satisfied in practice.

After geometric calibration with the presented approach, the calibration parameters of two CZI cameras can be directly used to generate standard CZI image products. It is unnecessary for each image to perform geometric calibration. Of course, in order to achieve an optimal orientation accuracy of a standard image product, GCPs are necessary to eliminate the orientation errors shown in Fig. 3, as performed in [25].

3. Results and discussion

3.1 Experimental datasets

In this study, seven HaiYang-1C CZI images were tested. The general characteristics of the seven images are listed in Table 1. The size of all sub-images in each image is 5450×8000 pixels. The roll and pitch angles of each image are approximately 0 degree. Considering that the GSD of CZI images is approximately 50 m, the globally publicized 15 m resolution Landsat DOM and 90 m resolution SRTM DEM are used as the reference data in both geometric calibration and accuracy evaluation. The planimetric accuracy of the Landsat DOM is 12 m [24], and the height accuracy of the SRTM DEM is 16 m [26]. The calibration and evaluation error of the CZI images caused by the reference DOM and DEM is theoretically smaller than 0.3 pixel, which is acceptable for the geometric calibration of the CZI cameras.

Tables Icon

Table 1. General characteristics of the HaiYang-1C CZI images

In order to comparatively evaluate the feasibility of the presented geometric calibration approach, we designed three experiments as follows:

  • 1) Experiment E1: Image 1 was used to perform geometric calibration with a single field, as described in section 2.2; that is, four sub-images of image 1 were respectively used to calibrate four CCDs.
  • 2) Experiment E2: Image 1 to image 4 were used to perform geometric calibration with multiple fields, as described in section 2.3; that is, sub-image 2 of image 1, sub-image 1 of image 2, sub-image 3 of image 3, and sub-image 4 of image 4 were respectively used to calibrate CCD 2, CCD 1, CCD 3, and CCD 4. It was noted that the internal shift parameters of the slave CCDs were not adjusted in this experiment.
  • 3) Experiment E3: On basis of experiment E2, the internal shift parameters of the slave CCDs were adjusted with image 1, as described in section 2.3.

After geometric calibration, image 5 to image 7 were used to evaluate the external and internal parameters calibrated with a single field and those calibrated with multiple fields.

3.2 Calibration accuracy analysis

The geometric calibration accuracy is a very important indicator to judge whether the external and internal parameters are precisely determined. In this section, we mainly focused on the geometric calibration accuracy analysis.

In experiments E1 and E2, dense GCPs in each sub-image were first extracted from the reference DOM and DEM, as shown in Fig. 7 and Fig. 8. The geometric calibration accuracy of each CCD achieved with dense GCPs is listed in Table 2.

 figure: Fig. 7.

Fig. 7. GCP distribution in (a) sub-image 1, (b) sub-image 2, (c) sub-image 3, and (d) sub-image 4 of image 1.

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 figure: Fig. 8.

Fig. 8. GCP distribution in (a) sub-image 1 of image 1, (b) sub-image 3 of image 3, and (c) sub-image 4 of image 4.

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Tables Icon

Table 2. Geometric calibration accuracies of four CZI CCDs.a

Based on the results in Table 2, we could draw the following conclusions.

  • (1) In experiment E1, the geometric calibration accuracies of all the CZI CCDs achieved with a single field reached better than 1.0 pixel. It demonstrated that the calibration parameters of each CCD were precisely determined. It was consistent with the expected, since the geometric calibration with a single field was actually a mature approach. In general, as long as a satisfactory field-covered CZI image and the reference DOM and DEM are available, the geometric calibration can be successfully performed.
  • (2) In experiment E2, four CCDs were respectively calibrated with different fields. The geometric calibration accuracies of four CCDs also reached better than 1.0 pixel and were almost the same with those achieved in experiment E1. It was also consistent with the expected. Although the satellite position and attitude errors in different fields differed from each other, they were fully absorbed by the calibrated parameters due to high correlation. Specially, they were absorbed by the external parameters for the master CCD and by the internal parameters for the slave CCDs. In fact, we could not judge whether the geometric calibration was successful or not simply from the calibration accuracy. The geometric stitching accuracy between the adjacent sub-images was another very important indicator that we should take into account.

3.3 Stitching accuracy analysis

In the ground processing of the HaiYang-1C CZI images, four sub-images collected by four CCDs should be stitched together into a complete seamless image. The stitching accuracy of adjacent sub-images directly determines the geometric quality of the stitched image.

In this section, many tie points between the adjacent sub-images in image 1 were matched. Each tie point in the right sub-image was first projected onto the reference DEM, and then the projected object point was further projected onto the left sub-image. The maximum errors and the RMSE of the image-space coordinate residual errors between the projected image points and the corresponding matched points in the left sub-image were calculated and listed in Table 3.

Tables Icon

Table 3. Geometric stitching accuracies of the HaiYang-1C CZI sub-images.

We can see from the results in Table 3 that the geometric stitching accuracies of three couples of adjacent sub-images in image 1 reached better than 0.2 pixel in experiment E1. It demonstrated that the adjacent sub-images could be stitched very well, as shown in Fig. 9(a). Three main reasons could account for this. One reason was that the look-angle model in Eq. (4) could precisely describe the internal errors of the CZI CCDs. The second reason was that the internal parameters of four CCDs were precisely determined. The last reason was that four CCDs were physically designed to be geometrically collinear. In the geometric calibration with a single field, four small image blocks containing dense GCPs in Fig. 7 were collected at the same imaging time. The geometric influences of the satellite position and attitude errors on four CCDs were thereby same.

 figure: Fig. 9.

Fig. 9. Geometric stitching results in (a) experiment E1, (b) experiment E2, and (c) experiment E3.

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In experiment E2, four CZI CCDs were calibrated with multiple fields. All the geometric calibration accuracies reached better than 1.0 pixel, as listed in Table 2. In fact, however, the satellite position and attitude errors in different fields differed from each other, as shown in Fig. 3. Unlike experiment E1, the calibrated parameters of four CCDs in experiment E2 absorbed different errors. Consequently, the geometric stitching accuracies between the adjacent sub-images reached approximately 1.0 pixel to 2.0 pixels. The adjacent sub-images could not be seamlessly stitched, as shown in Fig. 9(b).

In experiment E3, the internal shift parameters of the slave CCDs were adjusted with tie points between adjacent sub-images in image 1. The objective of the parameter adjustment was to eliminate the influence of different satellite position and attitude errors in different fields, so that the calibration parameters of four CCDs could absorb the same errors, just as that in experiment E1. After the parameter adjustment, the geometric stitching accuracies reached better than 0.2 pixel, which were almost the same with those achieved in experiment E1. The adjacent sub-images could then be seamlessly stitched, as shown in Fig. 9(c).

3.4 Evaluation of calibrated parameters

In-orbit geometric calibration aims to provide precise external and internal parameters of satellite cameras for the ground processing of satellite images. In order to further demonstrate the feasibility of the presented approach, image 5 to image 7 were used to evaluate the performance of the calibrated parameters.

For convenient comparison, we designed two evaluation scenarios as follows:

  • 1) Scenario S1: The calibrated parameters in experiment E1 were used for evaluation.
  • 2) Scenario S2: The calibrated parameters in experiment E3 were used for evaluation.

In general, satellite image users mainly concern two geometric accuracies: external (absolute) accuracy and internal (relative) accuracy. The 15 m resolution Landsat DOM and 90 m resolution SRTM DEM are globally publicized, and GCPs in CZI images are generally available. Hence, we mainly focused on the internal accuracy of CZI images in this section.

An optimal geometric stitching accuracy of the adjacent sub-images is a prerequisite to achieve a better internal accuracy of the stitched image. In both scenarios, the calibrated parameters were first used to evaluate the geometric stitching accuracies. The achieved stitching accuracies were listed in Table 4. We could see from Table 4 that the stitching accuracies achieved in scenario S2 were almost the same with those achieved in scenario S1. The largest difference was only approximately 0.08 pixel that could be neglected. In addition, the stitching accuracies achieved here were also almost the same with those in Table 3. It demonstrated that the calibrated parameters in both experiment E1 and experiment E3 could precisely describe the relative geometric relationship between the adjacent CCDs.

Tables Icon

Table 4. Geometric stitching accuracies of the HaiYang-1C CZI sub-images.

In order to further evaluate the internal accuracy, four sub-images in image 5 to image 7 were respectively stitched together, as performed in [12]. Many GCPs in each stitched image were first extracted from the reference DOM and DEM. The extracted GCPs in image 5 were taken as an example and shown in Fig. 10. Then, the RFM-based bias compensation in [25] was performed, and the achieved internal accuracies were listed in Table 5.

 figure: Fig. 10.

Fig. 10. GCP distribution in image 5 in (a) scenario S1 and (b) scenario S2.

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Tables Icon

Table 5. Internal accuracies of the HaiYang-1C CZI images.

We could see from Table 5 that the internal accuracies of three CZI images achieved in scenario S2 reached better than 1.0 pixel. Such a better accuracy was almost the same with that in Table 2. No obvious geometric accuracy was lost in the geometric stitching of four sub-images. Additionally, the largest accuracy difference achieved between scenarios S2 and S1 was smaller than 0.04 pixel. We could thereby conclude that the calibrated parameters in experiment E3 performed as well as those in experiment E1. The presented geometric calibration approach with multiple fields was demonstrated to be feasible.

4. Conclusion

The HaiYang-1C CZI consists of two independent cameras with a total image swath of approximately 1000 km. In the geometric calibration of the CZI cameras, a cloud-free, snow-free, land-covered, and texture-rich CZI image covering a calibration field should be conventionally collected in order to extract dense GCPs from the reference DOM and DEM. In practice, however, it is very different to collect such a satisfactory CZI image with so large an image swath. In this study, a feasible in-orbit geometric calibration approach for the CZI cameras with multiple fields is presented. In the presented approach, four satisfactory sub-images covering a single calibration field with a total image swath of approximately 1000 km are not necessary. Instead, different CCDs can be calibrated with different fields. Four sub-images covering different fields with a swath of approximately 295 km, 245 km, 245 km, and 295 km are sufficient. Hence, the application difficulties in collecting satisfactory calibration sub-images can be significantly reduced.

The presented geometric calibration approach was tested on seven HaiYang-1C CZI images. The experimental results showed that the presented approach achieved almost the same calibration accuracy with the conventional calibration approach with a single field. Meanwhile, the geometric stitching accuracy of adjacent sub-images and the internal accuracy of the stitched images achieved with the presented and the conventional approaches almost had no difference. The imaging parameters calibrated with the presented approach performed as well as those calibrated with the conventional approach. As such, the experimental results demonstrated the feasibility and effectiveness of the presented approach.

It is noted that the satellite position and attitude errors of the HaiYang-1C satellite are mainly shift errors in an image block. Based on this fact, the presented approach can perform well. Of course, many more datasets of other optical satellite cameras are needed to further validate the feasibility of the presented approach. Theoretically, the presented approach is suitable for the geometric calibration of other optical satellite cameras, as long as the satellite position and attitude errors are mainly shift errors in an image block.

Funding

National Natural Science Foundation of China (61801331); Scientific Research Foundation of Hubei University of Technology (BSQD2020055); Northwest Engineerring Corporation Limited Major Science and Technology Projects (XBY-ZDKJ-2020-08).

Acknowledgments

The authors would like to thank the anonymous reviewers and members of the editorial team for their comments and contributions and National Satellite Ocean Application Service for providing the test datasets.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. M. Wang, B. Yang, F. Hu, and X. Zang, “On-orbit geometric calibration model and its applications for high-resolution optical satellite imagery,” Remote Sens. 6(5), 4391–4408 (2014). [CrossRef]  

2. J. Grodecki and G Dial., “IKONOS geometric accuracy validation,” Proceedings of ISPRS Commission I Mid-Term Symposium, Denver, Colorado, USA. 6 pages (on CD-ROM), 2002.

3. J. Cao, X. Yuan, and J. Gong, “In-orbit geometric calibration and validation of ZY-3 three-line cameras based on CCD-detector look angles,” Photogramm. Rec. 30(150), 211–226 (2015). [CrossRef]  

4. M. Wang, Y. Cheng, B. Guo, and S. Jin, “Parameters determination and sensor correction method based on virtual CMOS with distortion for the GaoFen6 WFV camera,” ISPRS J. Photogramm. Remote Sens. 156, 51–62 (2019). [CrossRef]  

5. S. Liu, C. S. Fraser, C. Zhang, M. Ravanbakhsh, and X. Tong, “Georeferencing performance of THEOS satellite imagery,” Photogramm. Rec. 26(134), 250–262 (2011). [CrossRef]  

6. S. Kocaman and A. Gruen, “Orientation and self-calibration of ALOS PRISM imagery,” Photogramm. Rec. 23(123), 323–340 (2008). [CrossRef]  

7. J. Takaku and T. Tadono, “PRISM on-orbit geometric calibration and DSM performance,” IEEE Trans. Geosci. Remote Sens. 47(12), 4060–4073 (2009). [CrossRef]  

8. R. Gachet, “SPOT5 in-flight commission: inner orientation of HRG and HRS instruments,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 35(B1), 535–539 (2004).

9. D. Mulawa, “On-orbit geometric calibration of the OrbView-3 high resolution imaging satellite,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 35(B1), 1–6 (2004).

10. P. V. Radhadevi and S. S. Solanki, “In-flight geometric calibration of different cameras of IRS-P6 using a physical sensor model,” Photogramm. Rec. 23(121), 69–89 (2008). [CrossRef]  

11. M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020). [CrossRef]  

12. J. Cao, Z. Zhang, S. Jin, and X. Chang, “Geometric stitching of a HaiYang-1C ultra violet imager with a distorted virtual camera,” Opt. Express 28(9), 14109–14126 (2020). [CrossRef]  

13. S. Leprince, P. Musé, and J. P. Avouac, “In-flight CCD distortion calibration for pushbroom satellites based on subpixel correlation,” IEEE Trans. Geosci. Remote Sens. 46(9), 2675–2683 (2008). [CrossRef]  

14. S. Lee and D. Shin, “On-orbit camera misalignment estimation framework and its application to earth observation satellite,” Remote Sens. 7(3), 3320–3346 (2015). [CrossRef]  

15. D. Greslou, F. de Lussy, J. M. Delvit, C. Dechoz, and V. Amberg, “Pleiades-HR innovative techniques for geometric image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 543–547 (2012). [CrossRef]  

16. L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012). [CrossRef]  

17. Y. Pi, B. Yang, M. Wang, X. Li, Y. Cheng, and W. Tang, “On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite,” IEEE Geosci. Remote Sens. Lett. 14(7), 1176–1180 (2017). [CrossRef]  

18. Y. Pi, B. Yang, X. Li, and M. Wang, “Study of full-link on-orbit geometric calibration using multi-attitude imaging with linear agile optical satellite,” Opt. Express 27(2), 980–998 (2019). [CrossRef]  

19. Y. Cheng, M. Wang, S. Jin, L. He, and Y. Tian, “New on-orbit geometric interior parameters self-calibration approach based on three-view stereoscopic images from high-resolution multi-TDI-CCD optical satellites,” Opt. Express 26(6), 7475–7493 (2018). [CrossRef]  

20. B. Yang, Y. Pi, X. Li, and Y. Yang, “Integrated geometric self-calibration of stereo cameras onboard the ZiYuan-3 satellite,” ISPRS J. Photogramm. Remote Sens. 162, 173–183 (2020). [CrossRef]  

21. Y. Pi, X. Li, and B. Yang, “Global Iterative Geometric Calibration of a Linear Optical Satellite Based on Sparse GCPs,” IEEE Trans. Geosci. Remote Sens. 58(1), 436–446 (2020). [CrossRef]  

22. Y. Jiang, K. Xu, R. Zhao, G. Zhang, K. Cheng, and P. Zhou, “Stitching images of dual-cameras onboard satellite,” ISPRS J. Photogramm. Remote Sens. 128, 274–286 (2017). [CrossRef]  

23. Y. Cheng, S. Jin, M. Wang, Y. Zhu, and Z. Dong, “A new image mosaicking approach for the multiple camera system of the optical remote sensing satellite GaoFen1,” Remote Sens. Lett. 8(11), 1042–1051 (2017). [CrossRef]  

24. M. Wang, Y. Cheng, Y. Tian, L. He, and Y. Wang, “A new on-orbit geometric self-calibration approach for the high-resolution geostationary optical satellite GaoFen4,” IEEE J. Sel. Top. Appl. Earth Observations and Remote Sensing. 11(5), 1670–1683 (2018). [CrossRef]  

25. C. S. Fraser and H. B. Hanley, “Bias-compensated RPCs for sensor orientation of high-resolution satellite imagery,” Photogramm. Eng. Remote Sens. 71(8), 909–915 (2005). [CrossRef]  

26. CGIAR. SRTM 90 m DEM Digital Elevation Database. https://srtm.csi.cgiar.org/ [accessed on 14th April 2021].

References

  • View by:
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  • |

  1. M. Wang, B. Yang, F. Hu, and X. Zang, “On-orbit geometric calibration model and its applications for high-resolution optical satellite imagery,” Remote Sens. 6(5), 4391–4408 (2014).
    [Crossref]
  2. J. Grodecki and G Dial., “IKONOS geometric accuracy validation,” Proceedings of ISPRS Commission I Mid-Term Symposium, Denver, Colorado, USA. 6 pages (on CD-ROM), 2002.
  3. J. Cao, X. Yuan, and J. Gong, “In-orbit geometric calibration and validation of ZY-3 three-line cameras based on CCD-detector look angles,” Photogramm. Rec. 30(150), 211–226 (2015).
    [Crossref]
  4. M. Wang, Y. Cheng, B. Guo, and S. Jin, “Parameters determination and sensor correction method based on virtual CMOS with distortion for the GaoFen6 WFV camera,” ISPRS J. Photogramm. Remote Sens. 156, 51–62 (2019).
    [Crossref]
  5. S. Liu, C. S. Fraser, C. Zhang, M. Ravanbakhsh, and X. Tong, “Georeferencing performance of THEOS satellite imagery,” Photogramm. Rec. 26(134), 250–262 (2011).
    [Crossref]
  6. S. Kocaman and A. Gruen, “Orientation and self-calibration of ALOS PRISM imagery,” Photogramm. Rec. 23(123), 323–340 (2008).
    [Crossref]
  7. J. Takaku and T. Tadono, “PRISM on-orbit geometric calibration and DSM performance,” IEEE Trans. Geosci. Remote Sens. 47(12), 4060–4073 (2009).
    [Crossref]
  8. R. Gachet, “SPOT5 in-flight commission: inner orientation of HRG and HRS instruments,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 35(B1), 535–539 (2004).
  9. D. Mulawa, “On-orbit geometric calibration of the OrbView-3 high resolution imaging satellite,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 35(B1), 1–6 (2004).
  10. P. V. Radhadevi and S. S. Solanki, “In-flight geometric calibration of different cameras of IRS-P6 using a physical sensor model,” Photogramm. Rec. 23(121), 69–89 (2008).
    [Crossref]
  11. M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020).
    [Crossref]
  12. J. Cao, Z. Zhang, S. Jin, and X. Chang, “Geometric stitching of a HaiYang-1C ultra violet imager with a distorted virtual camera,” Opt. Express 28(9), 14109–14126 (2020).
    [Crossref]
  13. S. Leprince, P. Musé, and J. P. Avouac, “In-flight CCD distortion calibration for pushbroom satellites based on subpixel correlation,” IEEE Trans. Geosci. Remote Sens. 46(9), 2675–2683 (2008).
    [Crossref]
  14. S. Lee and D. Shin, “On-orbit camera misalignment estimation framework and its application to earth observation satellite,” Remote Sens. 7(3), 3320–3346 (2015).
    [Crossref]
  15. D. Greslou, F. de Lussy, J. M. Delvit, C. Dechoz, and V. Amberg, “Pleiades-HR innovative techniques for geometric image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 543–547 (2012).
    [Crossref]
  16. L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
    [Crossref]
  17. Y. Pi, B. Yang, M. Wang, X. Li, Y. Cheng, and W. Tang, “On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite,” IEEE Geosci. Remote Sens. Lett. 14(7), 1176–1180 (2017).
    [Crossref]
  18. Y. Pi, B. Yang, X. Li, and M. Wang, “Study of full-link on-orbit geometric calibration using multi-attitude imaging with linear agile optical satellite,” Opt. Express 27(2), 980–998 (2019).
    [Crossref]
  19. Y. Cheng, M. Wang, S. Jin, L. He, and Y. Tian, “New on-orbit geometric interior parameters self-calibration approach based on three-view stereoscopic images from high-resolution multi-TDI-CCD optical satellites,” Opt. Express 26(6), 7475–7493 (2018).
    [Crossref]
  20. B. Yang, Y. Pi, X. Li, and Y. Yang, “Integrated geometric self-calibration of stereo cameras onboard the ZiYuan-3 satellite,” ISPRS J. Photogramm. Remote Sens. 162, 173–183 (2020).
    [Crossref]
  21. Y. Pi, X. Li, and B. Yang, “Global Iterative Geometric Calibration of a Linear Optical Satellite Based on Sparse GCPs,” IEEE Trans. Geosci. Remote Sens. 58(1), 436–446 (2020).
    [Crossref]
  22. Y. Jiang, K. Xu, R. Zhao, G. Zhang, K. Cheng, and P. Zhou, “Stitching images of dual-cameras onboard satellite,” ISPRS J. Photogramm. Remote Sens. 128, 274–286 (2017).
    [Crossref]
  23. Y. Cheng, S. Jin, M. Wang, Y. Zhu, and Z. Dong, “A new image mosaicking approach for the multiple camera system of the optical remote sensing satellite GaoFen1,” Remote Sens. Lett. 8(11), 1042–1051 (2017).
    [Crossref]
  24. M. Wang, Y. Cheng, Y. Tian, L. He, and Y. Wang, “A new on-orbit geometric self-calibration approach for the high-resolution geostationary optical satellite GaoFen4,” IEEE J. Sel. Top. Appl. Earth Observations and Remote Sensing. 11(5), 1670–1683 (2018).
    [Crossref]
  25. C. S. Fraser and H. B. Hanley, “Bias-compensated RPCs for sensor orientation of high-resolution satellite imagery,” Photogramm. Eng. Remote Sens. 71(8), 909–915 (2005).
    [Crossref]
  26. CGIAR. SRTM 90 m DEM Digital Elevation Database. https://srtm.csi.cgiar.org/ [accessed on 14th April 2021].

2020 (4)

M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020).
[Crossref]

Y. Pi, X. Li, and B. Yang, “Global Iterative Geometric Calibration of a Linear Optical Satellite Based on Sparse GCPs,” IEEE Trans. Geosci. Remote Sens. 58(1), 436–446 (2020).
[Crossref]

J. Cao, Z. Zhang, S. Jin, and X. Chang, “Geometric stitching of a HaiYang-1C ultra violet imager with a distorted virtual camera,” Opt. Express 28(9), 14109–14126 (2020).
[Crossref]

B. Yang, Y. Pi, X. Li, and Y. Yang, “Integrated geometric self-calibration of stereo cameras onboard the ZiYuan-3 satellite,” ISPRS J. Photogramm. Remote Sens. 162, 173–183 (2020).
[Crossref]

2019 (2)

Y. Pi, B. Yang, X. Li, and M. Wang, “Study of full-link on-orbit geometric calibration using multi-attitude imaging with linear agile optical satellite,” Opt. Express 27(2), 980–998 (2019).
[Crossref]

M. Wang, Y. Cheng, B. Guo, and S. Jin, “Parameters determination and sensor correction method based on virtual CMOS with distortion for the GaoFen6 WFV camera,” ISPRS J. Photogramm. Remote Sens. 156, 51–62 (2019).
[Crossref]

2018 (2)

Y. Cheng, M. Wang, S. Jin, L. He, and Y. Tian, “New on-orbit geometric interior parameters self-calibration approach based on three-view stereoscopic images from high-resolution multi-TDI-CCD optical satellites,” Opt. Express 26(6), 7475–7493 (2018).
[Crossref]

M. Wang, Y. Cheng, Y. Tian, L. He, and Y. Wang, “A new on-orbit geometric self-calibration approach for the high-resolution geostationary optical satellite GaoFen4,” IEEE J. Sel. Top. Appl. Earth Observations and Remote Sensing. 11(5), 1670–1683 (2018).
[Crossref]

2017 (3)

Y. Jiang, K. Xu, R. Zhao, G. Zhang, K. Cheng, and P. Zhou, “Stitching images of dual-cameras onboard satellite,” ISPRS J. Photogramm. Remote Sens. 128, 274–286 (2017).
[Crossref]

Y. Cheng, S. Jin, M. Wang, Y. Zhu, and Z. Dong, “A new image mosaicking approach for the multiple camera system of the optical remote sensing satellite GaoFen1,” Remote Sens. Lett. 8(11), 1042–1051 (2017).
[Crossref]

Y. Pi, B. Yang, M. Wang, X. Li, Y. Cheng, and W. Tang, “On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite,” IEEE Geosci. Remote Sens. Lett. 14(7), 1176–1180 (2017).
[Crossref]

2015 (2)

S. Lee and D. Shin, “On-orbit camera misalignment estimation framework and its application to earth observation satellite,” Remote Sens. 7(3), 3320–3346 (2015).
[Crossref]

J. Cao, X. Yuan, and J. Gong, “In-orbit geometric calibration and validation of ZY-3 three-line cameras based on CCD-detector look angles,” Photogramm. Rec. 30(150), 211–226 (2015).
[Crossref]

2014 (1)

M. Wang, B. Yang, F. Hu, and X. Zang, “On-orbit geometric calibration model and its applications for high-resolution optical satellite imagery,” Remote Sens. 6(5), 4391–4408 (2014).
[Crossref]

2012 (2)

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

D. Greslou, F. de Lussy, J. M. Delvit, C. Dechoz, and V. Amberg, “Pleiades-HR innovative techniques for geometric image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 543–547 (2012).
[Crossref]

2011 (1)

S. Liu, C. S. Fraser, C. Zhang, M. Ravanbakhsh, and X. Tong, “Georeferencing performance of THEOS satellite imagery,” Photogramm. Rec. 26(134), 250–262 (2011).
[Crossref]

2009 (1)

J. Takaku and T. Tadono, “PRISM on-orbit geometric calibration and DSM performance,” IEEE Trans. Geosci. Remote Sens. 47(12), 4060–4073 (2009).
[Crossref]

2008 (3)

P. V. Radhadevi and S. S. Solanki, “In-flight geometric calibration of different cameras of IRS-P6 using a physical sensor model,” Photogramm. Rec. 23(121), 69–89 (2008).
[Crossref]

S. Kocaman and A. Gruen, “Orientation and self-calibration of ALOS PRISM imagery,” Photogramm. Rec. 23(123), 323–340 (2008).
[Crossref]

S. Leprince, P. Musé, and J. P. Avouac, “In-flight CCD distortion calibration for pushbroom satellites based on subpixel correlation,” IEEE Trans. Geosci. Remote Sens. 46(9), 2675–2683 (2008).
[Crossref]

2005 (1)

C. S. Fraser and H. B. Hanley, “Bias-compensated RPCs for sensor orientation of high-resolution satellite imagery,” Photogramm. Eng. Remote Sens. 71(8), 909–915 (2005).
[Crossref]

2004 (2)

R. Gachet, “SPOT5 in-flight commission: inner orientation of HRG and HRS instruments,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 35(B1), 535–539 (2004).

D. Mulawa, “On-orbit geometric calibration of the OrbView-3 high resolution imaging satellite,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 35(B1), 1–6 (2004).

Amberg, V.

D. Greslou, F. de Lussy, J. M. Delvit, C. Dechoz, and V. Amberg, “Pleiades-HR innovative techniques for geometric image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 543–547 (2012).
[Crossref]

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

Avouac, J. P.

S. Leprince, P. Musé, and J. P. Avouac, “In-flight CCD distortion calibration for pushbroom satellites based on subpixel correlation,” IEEE Trans. Geosci. Remote Sens. 46(9), 2675–2683 (2008).
[Crossref]

Blanchet, G.

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

Cao, J.

J. Cao, Z. Zhang, S. Jin, and X. Chang, “Geometric stitching of a HaiYang-1C ultra violet imager with a distorted virtual camera,” Opt. Express 28(9), 14109–14126 (2020).
[Crossref]

J. Cao, X. Yuan, and J. Gong, “In-orbit geometric calibration and validation of ZY-3 three-line cameras based on CCD-detector look angles,” Photogramm. Rec. 30(150), 211–226 (2015).
[Crossref]

Chang, X.

Cheng, K.

Y. Jiang, K. Xu, R. Zhao, G. Zhang, K. Cheng, and P. Zhou, “Stitching images of dual-cameras onboard satellite,” ISPRS J. Photogramm. Remote Sens. 128, 274–286 (2017).
[Crossref]

Cheng, Y.

M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020).
[Crossref]

M. Wang, Y. Cheng, B. Guo, and S. Jin, “Parameters determination and sensor correction method based on virtual CMOS with distortion for the GaoFen6 WFV camera,” ISPRS J. Photogramm. Remote Sens. 156, 51–62 (2019).
[Crossref]

Y. Cheng, M. Wang, S. Jin, L. He, and Y. Tian, “New on-orbit geometric interior parameters self-calibration approach based on three-view stereoscopic images from high-resolution multi-TDI-CCD optical satellites,” Opt. Express 26(6), 7475–7493 (2018).
[Crossref]

M. Wang, Y. Cheng, Y. Tian, L. He, and Y. Wang, “A new on-orbit geometric self-calibration approach for the high-resolution geostationary optical satellite GaoFen4,” IEEE J. Sel. Top. Appl. Earth Observations and Remote Sensing. 11(5), 1670–1683 (2018).
[Crossref]

Y. Cheng, S. Jin, M. Wang, Y. Zhu, and Z. Dong, “A new image mosaicking approach for the multiple camera system of the optical remote sensing satellite GaoFen1,” Remote Sens. Lett. 8(11), 1042–1051 (2017).
[Crossref]

Y. Pi, B. Yang, M. Wang, X. Li, Y. Cheng, and W. Tang, “On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite,” IEEE Geosci. Remote Sens. Lett. 14(7), 1176–1180 (2017).
[Crossref]

de Lussy, F.

D. Greslou, F. de Lussy, J. M. Delvit, C. Dechoz, and V. Amberg, “Pleiades-HR innovative techniques for geometric image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 543–547 (2012).
[Crossref]

Dechoz, C.

D. Greslou, F. de Lussy, J. M. Delvit, C. Dechoz, and V. Amberg, “Pleiades-HR innovative techniques for geometric image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 543–547 (2012).
[Crossref]

Déchoz, C.

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

deLussy, F.

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

Delvit, J. M.

D. Greslou, F. de Lussy, J. M. Delvit, C. Dechoz, and V. Amberg, “Pleiades-HR innovative techniques for geometric image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 543–547 (2012).
[Crossref]

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

Dial, G

J. Grodecki and G Dial., “IKONOS geometric accuracy validation,” Proceedings of ISPRS Commission I Mid-Term Symposium, Denver, Colorado, USA. 6 pages (on CD-ROM), 2002.

Dong, Z.

Y. Cheng, S. Jin, M. Wang, Y. Zhu, and Z. Dong, “A new image mosaicking approach for the multiple camera system of the optical remote sensing satellite GaoFen1,” Remote Sens. Lett. 8(11), 1042–1051 (2017).
[Crossref]

Fourest, S.

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

Fraser, C. S.

S. Liu, C. S. Fraser, C. Zhang, M. Ravanbakhsh, and X. Tong, “Georeferencing performance of THEOS satellite imagery,” Photogramm. Rec. 26(134), 250–262 (2011).
[Crossref]

C. S. Fraser and H. B. Hanley, “Bias-compensated RPCs for sensor orientation of high-resolution satellite imagery,” Photogramm. Eng. Remote Sens. 71(8), 909–915 (2005).
[Crossref]

Gachet, R.

R. Gachet, “SPOT5 in-flight commission: inner orientation of HRG and HRS instruments,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 35(B1), 535–539 (2004).

Gong, J.

J. Cao, X. Yuan, and J. Gong, “In-orbit geometric calibration and validation of ZY-3 three-line cameras based on CCD-detector look angles,” Photogramm. Rec. 30(150), 211–226 (2015).
[Crossref]

Greslou, D.

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

D. Greslou, F. de Lussy, J. M. Delvit, C. Dechoz, and V. Amberg, “Pleiades-HR innovative techniques for geometric image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 543–547 (2012).
[Crossref]

Grodecki, J.

J. Grodecki and G Dial., “IKONOS geometric accuracy validation,” Proceedings of ISPRS Commission I Mid-Term Symposium, Denver, Colorado, USA. 6 pages (on CD-ROM), 2002.

Gruen, A.

S. Kocaman and A. Gruen, “Orientation and self-calibration of ALOS PRISM imagery,” Photogramm. Rec. 23(123), 323–340 (2008).
[Crossref]

Guo, B.

M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020).
[Crossref]

M. Wang, Y. Cheng, B. Guo, and S. Jin, “Parameters determination and sensor correction method based on virtual CMOS with distortion for the GaoFen6 WFV camera,” ISPRS J. Photogramm. Remote Sens. 156, 51–62 (2019).
[Crossref]

Hanley, H. B.

C. S. Fraser and H. B. Hanley, “Bias-compensated RPCs for sensor orientation of high-resolution satellite imagery,” Photogramm. Eng. Remote Sens. 71(8), 909–915 (2005).
[Crossref]

He, L.

M. Wang, Y. Cheng, Y. Tian, L. He, and Y. Wang, “A new on-orbit geometric self-calibration approach for the high-resolution geostationary optical satellite GaoFen4,” IEEE J. Sel. Top. Appl. Earth Observations and Remote Sensing. 11(5), 1670–1683 (2018).
[Crossref]

Y. Cheng, M. Wang, S. Jin, L. He, and Y. Tian, “New on-orbit geometric interior parameters self-calibration approach based on three-view stereoscopic images from high-resolution multi-TDI-CCD optical satellites,” Opt. Express 26(6), 7475–7493 (2018).
[Crossref]

Hu, F.

M. Wang, B. Yang, F. Hu, and X. Zang, “On-orbit geometric calibration model and its applications for high-resolution optical satellite imagery,” Remote Sens. 6(5), 4391–4408 (2014).
[Crossref]

Jiang, Y.

Y. Jiang, K. Xu, R. Zhao, G. Zhang, K. Cheng, and P. Zhou, “Stitching images of dual-cameras onboard satellite,” ISPRS J. Photogramm. Remote Sens. 128, 274–286 (2017).
[Crossref]

Jin, S.

M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020).
[Crossref]

J. Cao, Z. Zhang, S. Jin, and X. Chang, “Geometric stitching of a HaiYang-1C ultra violet imager with a distorted virtual camera,” Opt. Express 28(9), 14109–14126 (2020).
[Crossref]

M. Wang, Y. Cheng, B. Guo, and S. Jin, “Parameters determination and sensor correction method based on virtual CMOS with distortion for the GaoFen6 WFV camera,” ISPRS J. Photogramm. Remote Sens. 156, 51–62 (2019).
[Crossref]

Y. Cheng, M. Wang, S. Jin, L. He, and Y. Tian, “New on-orbit geometric interior parameters self-calibration approach based on three-view stereoscopic images from high-resolution multi-TDI-CCD optical satellites,” Opt. Express 26(6), 7475–7493 (2018).
[Crossref]

Y. Cheng, S. Jin, M. Wang, Y. Zhu, and Z. Dong, “A new image mosaicking approach for the multiple camera system of the optical remote sensing satellite GaoFen1,” Remote Sens. Lett. 8(11), 1042–1051 (2017).
[Crossref]

Kocaman, S.

S. Kocaman and A. Gruen, “Orientation and self-calibration of ALOS PRISM imagery,” Photogramm. Rec. 23(123), 323–340 (2008).
[Crossref]

Kubik, P.

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

Lachérade, S.

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

Latry, C.

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

Lebègue, L.

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

Lee, S.

S. Lee and D. Shin, “On-orbit camera misalignment estimation framework and its application to earth observation satellite,” Remote Sens. 7(3), 3320–3346 (2015).
[Crossref]

Leprince, S.

S. Leprince, P. Musé, and J. P. Avouac, “In-flight CCD distortion calibration for pushbroom satellites based on subpixel correlation,” IEEE Trans. Geosci. Remote Sens. 46(9), 2675–2683 (2008).
[Crossref]

Li, X.

B. Yang, Y. Pi, X. Li, and Y. Yang, “Integrated geometric self-calibration of stereo cameras onboard the ZiYuan-3 satellite,” ISPRS J. Photogramm. Remote Sens. 162, 173–183 (2020).
[Crossref]

Y. Pi, X. Li, and B. Yang, “Global Iterative Geometric Calibration of a Linear Optical Satellite Based on Sparse GCPs,” IEEE Trans. Geosci. Remote Sens. 58(1), 436–446 (2020).
[Crossref]

Y. Pi, B. Yang, X. Li, and M. Wang, “Study of full-link on-orbit geometric calibration using multi-attitude imaging with linear agile optical satellite,” Opt. Express 27(2), 980–998 (2019).
[Crossref]

Y. Pi, B. Yang, M. Wang, X. Li, Y. Cheng, and W. Tang, “On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite,” IEEE Geosci. Remote Sens. Lett. 14(7), 1176–1180 (2017).
[Crossref]

Liu, S.

S. Liu, C. S. Fraser, C. Zhang, M. Ravanbakhsh, and X. Tong, “Georeferencing performance of THEOS satellite imagery,” Photogramm. Rec. 26(134), 250–262 (2011).
[Crossref]

Long, X.

M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020).
[Crossref]

Mulawa, D.

D. Mulawa, “On-orbit geometric calibration of the OrbView-3 high resolution imaging satellite,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 35(B1), 1–6 (2004).

Musé, P.

S. Leprince, P. Musé, and J. P. Avouac, “In-flight CCD distortion calibration for pushbroom satellites based on subpixel correlation,” IEEE Trans. Geosci. Remote Sens. 46(9), 2675–2683 (2008).
[Crossref]

Pi, Y.

Y. Pi, X. Li, and B. Yang, “Global Iterative Geometric Calibration of a Linear Optical Satellite Based on Sparse GCPs,” IEEE Trans. Geosci. Remote Sens. 58(1), 436–446 (2020).
[Crossref]

B. Yang, Y. Pi, X. Li, and Y. Yang, “Integrated geometric self-calibration of stereo cameras onboard the ZiYuan-3 satellite,” ISPRS J. Photogramm. Remote Sens. 162, 173–183 (2020).
[Crossref]

Y. Pi, B. Yang, X. Li, and M. Wang, “Study of full-link on-orbit geometric calibration using multi-attitude imaging with linear agile optical satellite,” Opt. Express 27(2), 980–998 (2019).
[Crossref]

Y. Pi, B. Yang, M. Wang, X. Li, Y. Cheng, and W. Tang, “On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite,” IEEE Geosci. Remote Sens. Lett. 14(7), 1176–1180 (2017).
[Crossref]

Porez-Nadal, F.

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

Radhadevi, P. V.

P. V. Radhadevi and S. S. Solanki, “In-flight geometric calibration of different cameras of IRS-P6 using a physical sensor model,” Photogramm. Rec. 23(121), 69–89 (2008).
[Crossref]

Ravanbakhsh, M.

S. Liu, C. S. Fraser, C. Zhang, M. Ravanbakhsh, and X. Tong, “Georeferencing performance of THEOS satellite imagery,” Photogramm. Rec. 26(134), 250–262 (2011).
[Crossref]

Shin, D.

S. Lee and D. Shin, “On-orbit camera misalignment estimation framework and its application to earth observation satellite,” Remote Sens. 7(3), 3320–3346 (2015).
[Crossref]

Solanki, S. S.

P. V. Radhadevi and S. S. Solanki, “In-flight geometric calibration of different cameras of IRS-P6 using a physical sensor model,” Photogramm. Rec. 23(121), 69–89 (2008).
[Crossref]

Tadono, T.

J. Takaku and T. Tadono, “PRISM on-orbit geometric calibration and DSM performance,” IEEE Trans. Geosci. Remote Sens. 47(12), 4060–4073 (2009).
[Crossref]

Takaku, J.

J. Takaku and T. Tadono, “PRISM on-orbit geometric calibration and DSM performance,” IEEE Trans. Geosci. Remote Sens. 47(12), 4060–4073 (2009).
[Crossref]

Tang, W.

Y. Pi, B. Yang, M. Wang, X. Li, Y. Cheng, and W. Tang, “On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite,” IEEE Geosci. Remote Sens. Lett. 14(7), 1176–1180 (2017).
[Crossref]

Tian, Y.

Y. Cheng, M. Wang, S. Jin, L. He, and Y. Tian, “New on-orbit geometric interior parameters self-calibration approach based on three-view stereoscopic images from high-resolution multi-TDI-CCD optical satellites,” Opt. Express 26(6), 7475–7493 (2018).
[Crossref]

M. Wang, Y. Cheng, Y. Tian, L. He, and Y. Wang, “A new on-orbit geometric self-calibration approach for the high-resolution geostationary optical satellite GaoFen4,” IEEE J. Sel. Top. Appl. Earth Observations and Remote Sensing. 11(5), 1670–1683 (2018).
[Crossref]

Tong, X.

S. Liu, C. S. Fraser, C. Zhang, M. Ravanbakhsh, and X. Tong, “Georeferencing performance of THEOS satellite imagery,” Photogramm. Rec. 26(134), 250–262 (2011).
[Crossref]

Wang, M.

M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020).
[Crossref]

M. Wang, Y. Cheng, B. Guo, and S. Jin, “Parameters determination and sensor correction method based on virtual CMOS with distortion for the GaoFen6 WFV camera,” ISPRS J. Photogramm. Remote Sens. 156, 51–62 (2019).
[Crossref]

Y. Pi, B. Yang, X. Li, and M. Wang, “Study of full-link on-orbit geometric calibration using multi-attitude imaging with linear agile optical satellite,” Opt. Express 27(2), 980–998 (2019).
[Crossref]

M. Wang, Y. Cheng, Y. Tian, L. He, and Y. Wang, “A new on-orbit geometric self-calibration approach for the high-resolution geostationary optical satellite GaoFen4,” IEEE J. Sel. Top. Appl. Earth Observations and Remote Sensing. 11(5), 1670–1683 (2018).
[Crossref]

Y. Cheng, M. Wang, S. Jin, L. He, and Y. Tian, “New on-orbit geometric interior parameters self-calibration approach based on three-view stereoscopic images from high-resolution multi-TDI-CCD optical satellites,” Opt. Express 26(6), 7475–7493 (2018).
[Crossref]

Y. Cheng, S. Jin, M. Wang, Y. Zhu, and Z. Dong, “A new image mosaicking approach for the multiple camera system of the optical remote sensing satellite GaoFen1,” Remote Sens. Lett. 8(11), 1042–1051 (2017).
[Crossref]

Y. Pi, B. Yang, M. Wang, X. Li, Y. Cheng, and W. Tang, “On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite,” IEEE Geosci. Remote Sens. Lett. 14(7), 1176–1180 (2017).
[Crossref]

M. Wang, B. Yang, F. Hu, and X. Zang, “On-orbit geometric calibration model and its applications for high-resolution optical satellite imagery,” Remote Sens. 6(5), 4391–4408 (2014).
[Crossref]

Wang, Y.

M. Wang, Y. Cheng, Y. Tian, L. He, and Y. Wang, “A new on-orbit geometric self-calibration approach for the high-resolution geostationary optical satellite GaoFen4,” IEEE J. Sel. Top. Appl. Earth Observations and Remote Sensing. 11(5), 1670–1683 (2018).
[Crossref]

Xu, K.

Y. Jiang, K. Xu, R. Zhao, G. Zhang, K. Cheng, and P. Zhou, “Stitching images of dual-cameras onboard satellite,” ISPRS J. Photogramm. Remote Sens. 128, 274–286 (2017).
[Crossref]

Xue, L.

M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020).
[Crossref]

Yang, B.

Y. Pi, X. Li, and B. Yang, “Global Iterative Geometric Calibration of a Linear Optical Satellite Based on Sparse GCPs,” IEEE Trans. Geosci. Remote Sens. 58(1), 436–446 (2020).
[Crossref]

B. Yang, Y. Pi, X. Li, and Y. Yang, “Integrated geometric self-calibration of stereo cameras onboard the ZiYuan-3 satellite,” ISPRS J. Photogramm. Remote Sens. 162, 173–183 (2020).
[Crossref]

Y. Pi, B. Yang, X. Li, and M. Wang, “Study of full-link on-orbit geometric calibration using multi-attitude imaging with linear agile optical satellite,” Opt. Express 27(2), 980–998 (2019).
[Crossref]

Y. Pi, B. Yang, M. Wang, X. Li, Y. Cheng, and W. Tang, “On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite,” IEEE Geosci. Remote Sens. Lett. 14(7), 1176–1180 (2017).
[Crossref]

M. Wang, B. Yang, F. Hu, and X. Zang, “On-orbit geometric calibration model and its applications for high-resolution optical satellite imagery,” Remote Sens. 6(5), 4391–4408 (2014).
[Crossref]

Yang, Y.

B. Yang, Y. Pi, X. Li, and Y. Yang, “Integrated geometric self-calibration of stereo cameras onboard the ZiYuan-3 satellite,” ISPRS J. Photogramm. Remote Sens. 162, 173–183 (2020).
[Crossref]

Yuan, X.

J. Cao, X. Yuan, and J. Gong, “In-orbit geometric calibration and validation of ZY-3 three-line cameras based on CCD-detector look angles,” Photogramm. Rec. 30(150), 211–226 (2015).
[Crossref]

Zang, X.

M. Wang, B. Yang, F. Hu, and X. Zang, “On-orbit geometric calibration model and its applications for high-resolution optical satellite imagery,” Remote Sens. 6(5), 4391–4408 (2014).
[Crossref]

Zhang, C.

S. Liu, C. S. Fraser, C. Zhang, M. Ravanbakhsh, and X. Tong, “Georeferencing performance of THEOS satellite imagery,” Photogramm. Rec. 26(134), 250–262 (2011).
[Crossref]

Zhang, G.

Y. Jiang, K. Xu, R. Zhao, G. Zhang, K. Cheng, and P. Zhou, “Stitching images of dual-cameras onboard satellite,” ISPRS J. Photogramm. Remote Sens. 128, 274–286 (2017).
[Crossref]

Zhang, Z.

Zhao, R.

Y. Jiang, K. Xu, R. Zhao, G. Zhang, K. Cheng, and P. Zhou, “Stitching images of dual-cameras onboard satellite,” ISPRS J. Photogramm. Remote Sens. 128, 274–286 (2017).
[Crossref]

Zhou, P.

Y. Jiang, K. Xu, R. Zhao, G. Zhang, K. Cheng, and P. Zhou, “Stitching images of dual-cameras onboard satellite,” ISPRS J. Photogramm. Remote Sens. 128, 274–286 (2017).
[Crossref]

Zhou, X.

M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020).
[Crossref]

Zhu, Y.

Y. Cheng, S. Jin, M. Wang, Y. Zhu, and Z. Dong, “A new image mosaicking approach for the multiple camera system of the optical remote sensing satellite GaoFen1,” Remote Sens. Lett. 8(11), 1042–1051 (2017).
[Crossref]

Acta Geod. Cartogr. Sin. (1)

M. Wang, B. Guo, X. Long, L. Xue, Y. Cheng, S. Jin, and X. Zhou, “On-orbit geometric calibration and accuracy verification of GF-6 WFV camera,” Acta Geod. Cartogr. Sin. 49(2), 171–180 (2020).
[Crossref]

IEEE Geosci. Remote Sens. Lett. (1)

Y. Pi, B. Yang, M. Wang, X. Li, Y. Cheng, and W. Tang, “On-orbit geometric calibration using a cross-image pair for the linear sensor aboard the agile optical satellite,” IEEE Geosci. Remote Sens. Lett. 14(7), 1176–1180 (2017).
[Crossref]

IEEE J. Sel. Top. Appl. Earth Observations and Remote Sensing. (1)

M. Wang, Y. Cheng, Y. Tian, L. He, and Y. Wang, “A new on-orbit geometric self-calibration approach for the high-resolution geostationary optical satellite GaoFen4,” IEEE J. Sel. Top. Appl. Earth Observations and Remote Sensing. 11(5), 1670–1683 (2018).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (3)

Y. Pi, X. Li, and B. Yang, “Global Iterative Geometric Calibration of a Linear Optical Satellite Based on Sparse GCPs,” IEEE Trans. Geosci. Remote Sens. 58(1), 436–446 (2020).
[Crossref]

S. Leprince, P. Musé, and J. P. Avouac, “In-flight CCD distortion calibration for pushbroom satellites based on subpixel correlation,” IEEE Trans. Geosci. Remote Sens. 46(9), 2675–2683 (2008).
[Crossref]

J. Takaku and T. Tadono, “PRISM on-orbit geometric calibration and DSM performance,” IEEE Trans. Geosci. Remote Sens. 47(12), 4060–4073 (2009).
[Crossref]

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. (4)

R. Gachet, “SPOT5 in-flight commission: inner orientation of HRG and HRS instruments,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 35(B1), 535–539 (2004).

D. Mulawa, “On-orbit geometric calibration of the OrbView-3 high resolution imaging satellite,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. 35(B1), 1–6 (2004).

D. Greslou, F. de Lussy, J. M. Delvit, C. Dechoz, and V. Amberg, “Pleiades-HR innovative techniques for geometric image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 543–547 (2012).
[Crossref]

L. Lebègue, D. Greslou, F. deLussy, S. Fourest, G. Blanchet, C. Latry, S. Lachérade, J. M. Delvit, P. Kubik, C. Déchoz, V. Amberg, and F. Porez-Nadal, “Pleiades-HR image quality commissioning,” Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXIX-B1(B1), 561–566 (2012).
[Crossref]

ISPRS J. Photogramm. Remote Sens. (3)

M. Wang, Y. Cheng, B. Guo, and S. Jin, “Parameters determination and sensor correction method based on virtual CMOS with distortion for the GaoFen6 WFV camera,” ISPRS J. Photogramm. Remote Sens. 156, 51–62 (2019).
[Crossref]

Y. Jiang, K. Xu, R. Zhao, G. Zhang, K. Cheng, and P. Zhou, “Stitching images of dual-cameras onboard satellite,” ISPRS J. Photogramm. Remote Sens. 128, 274–286 (2017).
[Crossref]

B. Yang, Y. Pi, X. Li, and Y. Yang, “Integrated geometric self-calibration of stereo cameras onboard the ZiYuan-3 satellite,” ISPRS J. Photogramm. Remote Sens. 162, 173–183 (2020).
[Crossref]

Opt. Express (3)

Photogramm. Eng. Remote Sens. (1)

C. S. Fraser and H. B. Hanley, “Bias-compensated RPCs for sensor orientation of high-resolution satellite imagery,” Photogramm. Eng. Remote Sens. 71(8), 909–915 (2005).
[Crossref]

Photogramm. Rec. (4)

J. Cao, X. Yuan, and J. Gong, “In-orbit geometric calibration and validation of ZY-3 three-line cameras based on CCD-detector look angles,” Photogramm. Rec. 30(150), 211–226 (2015).
[Crossref]

S. Liu, C. S. Fraser, C. Zhang, M. Ravanbakhsh, and X. Tong, “Georeferencing performance of THEOS satellite imagery,” Photogramm. Rec. 26(134), 250–262 (2011).
[Crossref]

S. Kocaman and A. Gruen, “Orientation and self-calibration of ALOS PRISM imagery,” Photogramm. Rec. 23(123), 323–340 (2008).
[Crossref]

P. V. Radhadevi and S. S. Solanki, “In-flight geometric calibration of different cameras of IRS-P6 using a physical sensor model,” Photogramm. Rec. 23(121), 69–89 (2008).
[Crossref]

Remote Sens. (2)

M. Wang, B. Yang, F. Hu, and X. Zang, “On-orbit geometric calibration model and its applications for high-resolution optical satellite imagery,” Remote Sens. 6(5), 4391–4408 (2014).
[Crossref]

S. Lee and D. Shin, “On-orbit camera misalignment estimation framework and its application to earth observation satellite,” Remote Sens. 7(3), 3320–3346 (2015).
[Crossref]

Remote Sens. Lett. (1)

Y. Cheng, S. Jin, M. Wang, Y. Zhu, and Z. Dong, “A new image mosaicking approach for the multiple camera system of the optical remote sensing satellite GaoFen1,” Remote Sens. Lett. 8(11), 1042–1051 (2017).
[Crossref]

Other (2)

CGIAR. SRTM 90 m DEM Digital Elevation Database. https://srtm.csi.cgiar.org/ [accessed on 14th April 2021].

J. Grodecki and G Dial., “IKONOS geometric accuracy validation,” Proceedings of ISPRS Commission I Mid-Term Symposium, Denver, Colorado, USA. 6 pages (on CD-ROM), 2002.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (10)

Fig. 1.
Fig. 1. The imaging sketch map of the HaiYang-1C CZI.
Fig. 2.
Fig. 2. Geometric calibration of the HaiYang-1C CZI with a single field.
Fig. 3.
Fig. 3. Sensor orientation errors of twelve CZI image blocks in different fields.
Fig. 4.
Fig. 4. Sensor orientation accuracies of twelve CZI image blocks in different fields.
Fig. 5.
Fig. 5. Four CZI sub-images covering the master field.
Fig. 6.
Fig. 6. (a) Sub-image 1, (b) sum-image 3, and (c) sub-image 4 covering different fields.
Fig. 7.
Fig. 7. GCP distribution in (a) sub-image 1, (b) sub-image 2, (c) sub-image 3, and (d) sub-image 4 of image 1.
Fig. 8.
Fig. 8. GCP distribution in (a) sub-image 1 of image 1, (b) sub-image 3 of image 3, and (c) sub-image 4 of image 4.
Fig. 9.
Fig. 9. Geometric stitching results in (a) experiment E1, (b) experiment E2, and (c) experiment E3.
Fig. 10.
Fig. 10. GCP distribution in image 5 in (a) scenario S1 and (b) scenario S2.

Tables (5)

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Table 1. General characteristics of the HaiYang-1C CZI images

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Table 2. Geometric calibration accuracies of four CZI CCDs. a

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Table 3. Geometric stitching accuracies of the HaiYang-1C CZI sub-images.

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Table 4. Geometric stitching accuracies of the HaiYang-1C CZI sub-images.

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Table 5. Internal accuracies of the HaiYang-1C CZI images.

Equations (7)

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[ tan ϕ x tan ϕ y 1 ] = λ R ADS Camera ( φ , ω , κ ) R J2000 ADS ( q 0 , q 1 , q 2 , q 3 ) R WGS84 J2000 ( [ X Y Z ] WGS 84 [ X S Y S Z S ] WGS84 )
R ADS Camera ( φ , ω , κ ) = [ cos φ 0 sin φ 0 1 0 sin φ 0 cos φ ] [ 1 0 0 0 cos ω sin ω 0 sin ω cos ω ] [ cos κ sin κ 0 sin κ cos κ 0 0 0 1 ]
R J2000 ADS ( q 0 , q 1 , q 2 , q 3 ) = [ 1 2 ( q 2 q 2 + q 3 q 3 ) 2 ( q 1 q 2 q 0 q 3 ) 2 ( q 1 q 3 + q 0 q 2 ) 2 ( q 1 q 2 + q 0 q 3 ) 1 2 ( q 1 q 1 + q 3 q 3 ) 2 ( q 2 q 3 q 0 q 1 ) 2 ( q 1 q 3 q 0 q 2 ) 2 ( q 2 q 3 + q 0 q 1 ) 1 2 ( q 1 q 1 + q 2 q 2 ) ]
{ tan ϕ x = a 0 + a 1 n + a 2 n 2 + a 3 n 3 tan ϕ y = b 0 + b 1 n + b 2 n 2 + b 3 n 3
{ Δ a 0 = 1 m i = 1 m ( tan ϕ x p  -  tan ϕ x t ) i Δ b 0 = 1 m i = 1 m ( tan ϕ y p  -  tan ϕ y t ) i
{ tan ϕ x = a 0 + a 1 n + a 2 n 2 + a 3 n 3 tan ϕ y = b 0 + b 1 n + b 2 n 2 + b 3 n 3
{ a 0 = a 0 + Δ a 0 b 0 = b 0 + Δ b 0

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