PE&RS January 2003

Peer-Reviewed Articles

33 Rational Functions and Potential for Rigorous Sensor Model Recovery
Kaichang Di, Ruijin Ma, and Ron Li

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Rational functions (RFs) have been applied in photogrammetry and remote sensing to represent the transformation between the image space and object space whenever the rigorous model is made unavailable intentionally or unintentionally. It attracts more attention now because Ikonos high-resolution images are being released to users with only RF coefficients. This paper briefly introduces the RF for photogrammetric processing. Equations of space intersection with upward RF are derived. The computational experimental result with one-meter resolution Ikonos Geo stereo images and other airborne data verified the accuracy of the upward RF-based space intersection. We demonstrated different ways to improve the geopositioning accuracy of Ikonos Geo stereo imagery with ground control points by either refining the vendor-provided Ikonos RF coefficients or refining the RF-derived ground coordinates. The accuracy of 3D ground point determination was improved to 1 to 2 meters after the refinement. Finally, we showed the potential for recovering sensor models of a frame image and a linear array image from the RF.

43 Error Tracking in Ikonos Geometric Processing Using a 3D Parametric Model
Thierry Toutin

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Thirteen panchromatic (Pan) and multiband (XS) Ikonos Geo-product images over seven study sites with various environments and terrain were tested using different cartographic data and accuracies with a 3D parametric model developed at the Canada Centre for Remote Sensing, Natural Resources Canada. The objectives of this study were to define the relationship between the final accuracy and the number and accuracy of input data, to track error propagation during the full geometric correction process (bundle adjustment and ortho-rectification), and to advise on the applicability of the model in operational environments. When ground control points (GCPs) have an accuracy poorer than 3 m, 20 GCPs over the entire image are a good compromise to obtain a 3- to 4-m accuracy in the bundle adjustment. When GCP accuracy is better than 1 m, ten GCPs are enough to decrease the bundle adjustment error of either panchromatic or multiband images to 2 to 3 m. Because GCP residuals reflect the input data errors (map and/or plotting), these errors did not propagate through the 3D parametric model, and the internal accuracy of the geometric model is thus better (around a pixel or less). Quantitative and qualitative evaluations of ortho-images were thus performed with either independent check points or overlaid digital vector files. Generally, the measured errors confirmed the predicted errors or were even slightly better, and a 2- to 4-m positioning accuracy was achieved for the ortho-images depending upon the elevation accuracy (DEM and grid spacing). To achieve a better final positioning accuracy, such as 1 m, a DEM with an accuracy of 1 to 2 m and with a fine grid spacing is required, in addition to well-defined GCPs with an accuracy of 1 m.

53 Bias Compensation in Rational Functions for Ikonos Satellite Imagery
Clive S. Fraser and Harry B. Hanley

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A method for the removal of exterior orientation biases in rational function coefficients (RPCs) for Ikonos imagery is developed. These biases, which are inherent in RPCs derived without the aid of ground control, give rise to geopositioning errors. The 3D positioning error can subsequently be compensated during spatial intersection by two additional parameters in image space that effect a translation of image coordinates. The resulting bias parameters can then be used to correct the RPCs supplied with Ikonos Geo imagery such that a practical means is provided for bias-free ground point determination, nominally to meter-level absolute accuracy, using entirely standard procedures on any photogrammetric workstation that supports Ikonos RPCs. The method requires provision of one or more ground control points. Aside from developing the bias compensation method, the paper also summarizes practical testing with bias-corrected RPCs that has demonstrated sub-meter geopositioning accuracy from Ikonos Geo imagery.

59 Block Adjustment of High-Resolution Satellite Images Described by Rational Polynomials
Jacek Grodecki and Gene Dial

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This paper describes how to block adjust high-resolution satellite imagery described by Rational Polynomial Coefficient (RPC) camera models and illustrates the method with an Ikonos example. By incorporating a priori constraints into the adjustment model, multiple independent images can be adjusted with or without ground control. The RPC block adjustment model presented in this paper is directly related to geometric properties of the physical camera model. Multiple physical camera model parameters having the same net effect on the object-image relationship are replaced by a single adjustment parameter. Consequently, the proposed method is numerically more stable than the traditional adjustment of exterior and interior orientation parameters. This method is generally applicable to any photogrammetric camera with a narrow field of view, calibrated, stable interior orientation, and accurate a priori exterior orientation data. As demonstrated in the paper, for Ikonos satellite imagery, the RPC block adjustment achieves the same accuracy as the ground station block adjustment with the full physical camera model.

71 Development and Calibration of the Airborne Three-Line Scanner (TLS) Imaging System
Tianen Chen, Ryosuke Shibasaki, and Murai Shunji

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The Airborne Three-Line-Scanner (TLS) imaging system has provided proof of the concept of stereo and multispectral mapping using the pushbroom mode because frame digital imaging systems with comparable coverage and resolution have not been available and are not likely to be available in the future. A prototype of the TLS system, the STARIMAGER, was developed jointly in 2000 by the STARLABO Corporation of Japan and the University of Tokyo and is introduced in this paper. A laboratory method and algorithm to evaluate the optical characteristics of STARIMAGER are presented. The principle is to measure the object-space angles of a sufficient number of CCD elements in two directions as seen through the optics. These angular measurements reflect the real camera geometry of both the optics and the CCD arrays. A mathematical model based on the central perspective projection has been constructed to estimate the focal length, principle point, and lens distortion of the optics and the alignment errors of the CCD sensors in the focal plane. These calibration parameters have been used in several real test flights, and ground point determination accuracies from 0.03- to 0.08-m (0.5- to 1.5-pixels) in planimetry and from 0.06- to 0.15-m (1.2- to 3-pixels) in elevation from a flying height of 500 m were attained.

79 An Algorithm for the Generation of Voronoi Diagrams on the Sphere Based on QTM
Jun Chen, Xuesheng Zhao, and Zhilin Li

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In order to efficiently store and analyze spatial data on a global scale, the digital expression of Earth data in a data model must be global, continuous, and conjugate, i.e., a spherical dynamic data model is needed. The Voronoi data structure is the only published attempt (Wright and Goodchild, 1997) and the only possible solution currently available (Li et al., 1999) for a dynamic GIS. However, the complexity of the Voronoi algorithm for line sets and area sets in vector mode limits its application in a dynamic GIS. So far, there is no raster-based Voronoi algorithm for objects (including points, arcs, and regions) on a spherical surface. To overcome this serious deficiency, an algorithm for generating a spherical Voronoi diagram is presented, based on the O-QTM (Octahedral Quaternary Triangular Mesh). The principle of the dilation operation in mathematical morphology is extended to the spherical surface. A method is developed for a spherical distance transformation based on the QTM. A detailed algorithm is also presented. This algorithm can handle points, arcs, and area features on a spherical surface. Tests have shown that the computational time consumption of this algorithm with points, arcs, and areas is equal and proportionate to the levels of the spherical surface tessellation; and the difference (distortion) between the great circle distance and the QTM cells distance is slightly related to spherical distance (not as the raster dilation on a planar surface), and is mainly related to the locations of the generating points.

91 Making the Trade-Off Between Decision Quality and Information Cost
S. de Bruin and Gary J. Hunter

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A growing problem confronting users of remotely sensed imagery is whether the use of additional or different imagery to improve decision quality is actually justified by its cost. This paper discusses how to compare these competing factors so that an acceptable trade-off may be made between them. The proposed method is based on probabilistic cost-benefit analysis. The concept of "value of information" is introduced in a practical case study using remote sensing to verify farmers' declarations for a crop subsidy program in the European Union. Application of the method requires that (1) the problem at hand can be represented by a decision tree, (2) the desirability of each decision outcome can be expressed numerically, (3) the imagery reveals information about the occurrence of events not under the decision maker's control, and (4) the probabilities of these events and the extent to which they are detectable in remotely sensed imagery can be assessed.