Line-of-Sight Vector Adjustment Model for Geopositioning of SPOT-5 Stereo Images

We formulate and present a new geopositioning method for SPOT-5 High-Resolution Geometric (HRG) stereo images, named the line-of-sight (LOS) vector adjustment model. It is applicable to satellites that move along a well-defined close-to-circular elliptical orbit with a predicted orbit close to true. SPOT-5 satisfies these requirements because it has the improved capability of providing accurate satellite attitude and a look angle for each detector. The method’s core idea is that only the LOS vector was adjusted when correcting the geometric distortion of SPOT-5 imagery. One advantage of this method is that it achieves high geopositioning accuracy with a limited number of ground control points (GCPs). Although a minimum of three GCPs is needed for processing, a test result satisfied the accuracy requirement within one pixel of a SPOT-5 panchromatic image even with only three GCPs. The performance in terms of root mean square error (RMSE) improved as the number of GCPs increased. Five GCPs were found to be the optimal number in the practical application of the LOS vector adjustment model. Using five GCPs, the RMSEs were 0.48 m and 0.64 m in planimetry and height, respectively. The test results indicate that the proposed method is superior to the bundle adjustment method for the geopositioning of SPOT-5 HRG stereo images. Introduction Since SPOT-1 was launched in 1986, the SPOT satellites have acquired a large number of stereo pairs. These have been used for urban and regional mapping, disaster management, classification, and many other purposes (Gugan and Dowman, 1988; Yesou and Rolet, 1990; Baraldi and Parmiggiani, 1990). The SPOT systems have, however, the constraints of mis-registration caused by errors in the initial parameters and a low spatial resolution. SPOT-5 is mounted with two High-Resolution Geometric (HRG) viewing instruments that have resolutions of 5 m in the panchromatic and 10 m in the multispectral modes; it also has an improved capability of location accuracy by using a geometrically optimized system (Bouillon et al., 2003; Nonin and Piccard, 2003). Many researchers have previously investigated the geometry of SPOT imagery. The geometric characteristics Line-of-Sight Vector Adjustment Model for Geopositioning of SPOT-5 Stereo Images Hyung-Sup Jung, Sang-Wan Kim, Joong-Sun Won, and Dong-Cheon Lee have been well-studied, and various mathematical models have been proposed. These models can be divided into three main categories based on their different functions and parameters: the bundle adjustment method is based on extended collinearity equations; a further model involves direct linear transformation (DLT); and an orbital resection model utilizes orbital elements rather than the position and velocity of a satellite. Bundle adjustment (Orun and Natarajan, 1994; Mahapatra et al., 2004) is a traditional method based on the collinearity condition, which states that the exposure station, and any ground and image points, all lie along a straight line. The position and attitude of the satellite are used for the model parameters, and are represented by second-order polynomials of time. The optimal local orbit and attitude are calculated by using ground control points (GCPs) with extended collinearity equations; the accuracy of geometric correction obtained is relatively good. For these reasons, this is the most popular method used for the registration of SPOT imagery (Chen and Rau, 1993; Buyuksalih et al., 2005), but it has a disadvantage in that more than six GCPs are generally required. The DLT method (Gupta and Hartley, 1997) is derived from two simplifying assumptions that the sensor array is traveling in a straight line, and its orientation is constant over the image acquisition duration. Under these assumptions, the camera model is represented by a nonlinear Cremona transformation of object space into image space. This method has advantages in the geometric correction of satellite images without orbit information and in computational efficiency. However, more than six GCPs are required for this method also, and the accuracy of geometric correction using DLT is relatively poor. The orbital resection model (Salamonowicz, 1986; Gugan and Dowman, 1988; Radhadevi et al., 1994; Zoej and Petrie, 1998) is based on the general assumption that the satellite has an approximate Keplerian trajectory (Kratky, 1989) in which the position and attitude of a sensor vary continually in a systematic way to keep the satellite pointing towards the center of the Earth. This model is represented by an orthogonal rotation matrix to transform from the geocentric to the sensor coordinate system using the orbit attitude and four orbit parameters. Generally, two orbit parameters of the four are used for the model parameters. This method requires fewer GCPs than the others, and the resulting precision largely depends on the accuracy of the initial orbit parameters used. However, it is difficult to utilize all the PHOTOGRAMMETRIC ENGINEER ING & REMOTE SENS ING Novembe r 2007 1267 Hyung-Sup Jung and Joong-Sun Won are with the Department of Earth System Sciences, Yonsei University, 134 Sinchon-Dong, Seodaemun-Gu, Seoul 120–749, Korea ([email protected]; [email protected]). Sang-Wan Kim and Dong-Cheon Lee are with the Department of Geoinformation Engineering, Sejong University, 98 Gunja-Dong, Gwangjin-Gu, Seoul 143–747, Korea ([email protected]; [email protected]). Photogrammetric Engineering & Remote Sensing Vol. 73, No. 11, November 2007, pp. 1267–1276. 0099-1112/07/7311–1267/$3.00/0 © 2007 American Society for Photogrammetry and Remote Sensing 05-142.qxd 10/3/07 22:47 Page 1267