IEG 환경지질연구정보센터

AN ACCURACY ASSESSMENT OF 3D GEOPOSITIONING OF WORLDVIEW-1 IN-TRACK STEREO PAIR

Kwan-young Oh ¹ and Hyung-Sup Jung ²

1

Dept. of Geoinformatics, University of Seoul, [email protected]

2

Dept. of Geoinformatics, University of Seoul, [email protected]

ABSTRACT: The successful operation of the WorldView-1 satellite has enabled the advanced high-accuracy mapping with state-of-the-art geolocation accuracy capabilities and half-meter ground resolution distance (GSD). The in-track stereo capability of the WorldView-1 sensor also provides the good opportunity to generate high-resolution digital elevation model (DEM). The objective of this paper is to evaluate a three-dimensional geopositioning accuracy of the WorldView-1 in-track stereo images to extract precise 3D geolocation. In this paper, we accessed a three- dimensional geopositioning accuracy of the WorldView-1 in-track stereo images using rational polynomial coefficient (RPC) model without ground control points (GCP), and also evaluated using RPC adjustment model with GCP. Three- dimensional positioning accuracy achieved by the adjustment of exterior orientation parameters was improved from 2.84 m, 3.33 m, 1.26 m to 1.33 m, 1.04 m, and 0.84 m in X, Y and Z directions. This result implies that the residual errors of rational function model (RFM) model were effectively removed by the proposed method to yield good three- dimensional geopositioning accuracy.

KEY WORDS: WORLDVIEW-1, RPC, 3D-geopositioning 1. INTRODUCTION

Since the WorldView-1 was launched in September 18, 2007, the WorldView-1 satellite has acquired a large number of high resolution images. These have been used for urban and regional mapping, disaster management, classification, and many other purposes (Poli et al, 2009).

The WorldView-1 is equipped with state-of-the-art geopositioning accuracy capability and exhibits efficient in-track stereo collection. To leverage the WorldView-1 images for applications such as DEM generation, urban monitoring, disaster management, 3D Earth model construction, etc, the sensor model of the ortho- rectification of the images is required, because a well- designed sensor model can ensure 3D reconstruction models and ortho-rectification products generated from images.

Physical sensor models and generalized sensor models are the two broad categories of sensor models (McGlone, 1996). The physical sensor model is most accurate, because it requires various information of the camera, orientation parameters, orbit parameters, etc. There are the bundle adjustment model, line-of-sight vector adjustment model, orbital resection model, etc in this physical sensor model. A generalized sensor model uses the approximate conditional equations. The rational function model (RFM) is one of the generalized sensor models, and is capable of achieving high approximation accuracy. The RFM is generally the ratio of two polynomials calculated from the physical sensor model, which does not reveal the sensor parameters.

Many researchers have previously investigated the RFM. Madani (1999) discussed advantages and disadvantages of the RFM, and compared it with physical sensor models. Fraser et al. (2001) compared the RMF, an extended DLT (Direct Linear Transformation) model, and an affine projection model. Tao and Hu (2002) discussed the 3D reconstruction algorithms based on both

the forward and inverse RFM forms and compared the performance of these two reconstruction methods using several stereo pairs. This RFM model has been the most popular method in orthorectifying high resolution images.

In this paper, we accessed a three-dimensional geopositioning accuracy of the WorldView-1 in-track stereo images using rational polynomial coefficient (RPC) model with and without ground control points (GCP).

2. RATIONAL FUNCTION MODEL WorldView-1 RFM is forward method which can be calculated from ground coordinate (latitude, longitude, height) to image coordinate (column, row). The RPC parameters for the coordinate transformation between ground and image positions are given from Auxiliary file.

In the RFM, image pixel coordinates (c, r) are expressed as the ratios of polynomials of ground coordinates (X, Y, Z). In order to improve the numerical stability of equations, the two image coordinates and three ground coordinates are normalized to fit the range from –1.0 to 1.0 using offset values and scale factors.

For the ground-to-image transformation, the defined ratios of polynomials have the forward form as defined as (Greve et al., 1992; OGC, 1999):

1 , ,

2 , , , 3 , ,

4 , , 1 Let

to be the un-normalized coordinate values of points in object space. The normalization of the ground coordinates can be computed using the following equations.

,

(2)

, , Z

Where , , , , c = offset values , , , , c = scale values.

Polynomials 1, 2, 3,4 have the general form as follows.

, ,

2 2

2 2

2 2 2

2 2

3 Where the are polynomial coefficients, which are called rational function coefficients (RFCS), and the order of the polynomials is limited by 0 3, 0

3, 0 3 and 3.

For image-to-ground transformation, an inverse form can be defined as (Yang, 2000):

X p5 r, c, Z

P6 r, c, Z , Y p7 r, c, Z

P8 r, c, Z 4 The (4) expresses the planar object point coordinates as RFM of the image coordinates and the vertical object coordinate.

3. TEST RESULTS

The WorldView-1 in-track stereo images were used for an accuracy assessment of 3D geopositioning. The product level of the stereo images is the basic 1B. And the tested images were also acquired on 27 June 2008 in Daejeon City, Korea, which consists of steep mountains, plains, lakes, and man-made structures such as buildings, roads, and bridges. More details of the test images are listed in Table 1.

Table 1. Parameters of the test stereo pair used.

Parameters Forward

Image Backward Image

Size 18473*35180(Row*Columns) GSD 0.5m Level 1B Date 2008.06.27

View angle 31.1 -5.8

Six GCPs and 14 check points (CPs) for accuracy evaluation were selected in the images. They are randomly scattered, as shown in Figure 1. The GCPs and CPs were measured in the field using differential GPS, and their accuracy was approximately 0.1 m in both horizontal and vertical dimensions.

Figure 1. Location of six GCPs and fourteen CPs. Open and solid diamonds denote GCPs and CPs.

The WorldView-1 RPC is provided with the image and the auxiliary data, which includes the attitude and orbit information. The relation between the image and the ground coordinates can be expressed from the RPC. It has been well-known that the geopositioning accuracy achieved by the direct sensor orientation of WorldView-1 is about 3 m (Buyuksalih et al, 2009).

The direct sensor orientation using RPC was applied to the stereo images, and its projection accuracy was evaluated. The residual errors in the row and column direction were calculated at all GCPs and CPs. In the forward image, the mean values of row and column directions were 2.01 m and 1.55 m, with standard deviations of 0.76 m and 0.58 m, respectively. And, means of row and column directions were 1.20 m and 3.22 m, with standard deviations of 0.91 m and 0.71 m respectively, for the backward image. While the means of scaled residuals were very large, their standard deviations were relatively small. Figure 2 shows the residual error vector of the image coordinate system. The length of each vector is proportional to the magnitude of residual errors.

The residual error vectors had a single dominant direction and magnitude in each image as indicated by the mean and standard deviation values. This suggests that the errors can be adjusted by GCPs.

Three-dimensional positioning accuracy was calculated for the direct sensor orientation of the in-track stereo pair with B/H ratios of about 0.75. RMSEs of residual errors at the twenty ground points were estimated from the stereo pair. For the stereo pair, RMSEs in (X, Y, Z) space for the ground points were (2.84 m, 3.33 m, 1.26 m).

Figure 3 shows error histograms of the ground points for

the in-track stereo pair. The error histograms in Figure 3

generally follow a Gaussian distribution with bias, and

the number of residual errors decreases with distance

from the mean. The means of X, Y and Z directions were

2.61 m, -3.25 m and -1.08 m, respectively. This indicates

that the 3D geopositioning calculated by the direct sensor

orientation of the in-track stereo pair are shifted by 2.61 m, -3.25 m and -1.08 m in X, Y and Z directions, respectively.

Figure 2. Residual error vectors of ground points for (a) forward and (b) backward images.

Figure 3. Error histograms of (a) X- , (b) Y-, and (c) Z- dimensions for the in-track stereo pair.

Normally there are two ways to improve the accuracy of RFM (Di et al, 2003a; Li et al, 2003). One is to refine the RPCs, and another refines the ground coordinates calculated from the RFM using a polynomial correction.

In this paper, four polynomial models that are listed in Table 2 were testified for the determination of the optimum exterior orientation parameters. Six GCPs were used to adjust the exterior orientation parameters in four models, and fourteen CPs were used to evaluate the accuracy of each model. In the cases of models A and B, there are four unknown parameters, and in the case of models C and D, six and twelve unknown parameters exist, respectively.

Table 2. Four polynomial models used for the determination of the optimum exterior orientation parameters.

Image Space

Adjustment Models

MIN.

No.

Of GCPs Scale

and Trans-

lation A B 2

Affine C c

c 3

Second- order ^D

c

c 6

In the case of model A, RMSEs in (c, r) space for the CPs were (0.90 m, 0.76 m), and RMSEs of model B were (0.91, 0.67). RMSEs of models C and D in (c, r) space were (1.23, 0.63) and (8.22, 0.98), respectively. Table 3 summarizes the RMSEs of four polynomial models. This result indicates that the adjustment model of B is optimal.

Table 3. Accuracy of CPs improved four methods in image space

Method

Forward Image Backward Image

RMSE(m) Total

RMSE(m) RMSE(m) Total RMSE(m)

c r c r

A

B

C

D

Figure 4 displays the residual error vectors of 14 CPs in the row- and column-dimensions of the image coordinate system after the external orientation parameters of model B were adjusted.

Figure 4. Residual error vectors at check points after

external orientation parameters are applied.

The magnitudes of most residual error vectors were less than 1.5 m (or 3 times the GSD) and their directions were random. This result indicates that the systematic residuals have been minimized and that the residual errors after correcting for geometric distortion are dominated by random errors such as positional and image selection error.

Three-dimensional positioning accuracy by the adjstement of exterior orientation parameters was achieved for the in-track stereo pair. RMSEs of residual errors at the GCPs and check points were estimated from the stereo pair and are shown in Table 4. RMSEs in (X, Y, Z) space for the GCPs were (0.55 m, 0.40 m, 0.30 m) and those for the check points were (1.33 m, 1.04 m, 0.84 m).

This result means that the residual errors appear to have been effectively removed to yield good three-dimensional geopositioning accuracy.

Table 4. Three-dimensional positioning accuracy achieved

Stereo Image

RMSE(m) Maximum Difference(m)

X Y Z X Y Z 1.33 1.04 0.84 2.98 2.11 1.26

Figure 5 shows error histograms of the check points.

When the residual errors are dominated by a large distortion error, the center of the error histogram is shifted from zero by bias, as shown in Figure 3.

Figure 5. Error histograms of (a) X- , (b) Y-, and (c) Z- dimensions for the in-track stereo pair after external orientation parameters are applied

Positional error and image selection error are random errors and affect standard deviation rather than mean value. The error histograms in Figure 5 generally follow a

Gaussian distribution with no bias, and the number of residual errors decreases with distance from the center.

Mean residual errors in all dimensions were approximately zero. This result implies that the residual errors preserved in the stereo pair are dominated by positional error and image selection error rather than by distortion error.

4. CONCLUSION

In this paper, we accessed a three-dimensional geopositioning accuracy of the WorldView-1 in-track stereo images using rational polynomial coefficient (RPC) model with and without ground control points (GCP).

Three-dimensional positioning accuracy achieved by the adjustment of exterior orientation parameters was improved from 2.84 m, 3.33 m, 1.26 m to 1.33 m, 1.04 m, and 0.84 m in X, Y and Z directions. This result implies that the residual errors of rational function model (RFM) were effectively removed by the proposed method to yield good three-dimensional geopositioning accuracy.

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ACKNOWLEDGEMENTS

This work was supported by the National Research

Foundation of Korea Grant (2010-0015268) funded by

Ministry of Educational Science and Technology of

Korean government, and researched by the supporting

project to educate GIS experts.