Virtual Image Generation from the Linear Array ImageAli Azizi Centre of Excellence for Geomatics Engineering and Disaster Management, Department of Surveying Engineering, Faculty of Engineering, University of Tehran Mohammad Saadatseresht Centre of Excellence for Geomatics Engineering and Disaster Management, Department of Surveying Engineering, Faculty of Engineering, University of Tehran Abstract The so called push broom images are generated by the linear array technology by which successive lines on the ground are systematically scanned. Consequently, these images have somehow a dynamic geometry in the sense that each image line has its own exterior orientation parameters leading effectively to a multi-projection image. This dynamism in geometry complicates the space resection intersection operations with rigorous mathematical models and necessitates the incorporation of the observed values for the satellite trajectory. Alternatively, the generic approach may be utilized. However, this approach has also its own shortcomings regarding the requirement of large number of the GCPs and resulted instability of the mathematical solution. In this paper we propose a pre-processing stage through which a virtual single projection image is generated from the linear array image by intersecting each pixel position in the scan lines with an approximate digital elevation model (DEM) by a forward intersection approach. This is then followed by an inverse projection to the virtual image plane and gray shade interpolation. The generated virtual image more or less satisfies the geometry of a real single projection image and hence can be treated with conventional mathematical models used in photogrammetry. The errors in the generated virtual image are partly due to the approximations of the DEM and partly due to the attitude and altitude variations of the scan lines. Assuming that the DEM error is negligible, the orientation and position variations of the scan lines may be regarded as a sort of systematic image displacement which can be handled by a rigorous self calibration or similar mathematical models. The potential of the proposed approach, as far as the impact of the relief displacement is concerned, is investigated using a simulation strategy. Introduction Typically, two different approaches of rigorous and generic mathematical models are utilized for the geometric correction of the linear array images. The former approach to be implemented inevitably takes the form of a multi-projection model whereas with the latter method multi-projection assumption is not necessary. Thus, the main drawback of the rigorous sensor model is its complex mathematical model which requires some approximations for the exterior orientation parameters of each scan line. With the generic sensor model, although much simpler mathematical model is used, the number and distribution of GCPs are crucial. In this paper an alternative approach is proposed by which a virtual image having a single projection centre is first generated using the linear array scan lines. The virtual image is then regarded as a conventional camera generated image. Space intersection is then performed on the stereo-virtual images to generate the object space coordinates. In the section that follows, the adopted procedures for the generation of the virtual image are outlined. Virtual image generation The geometry of the single and multi-projection imaging devices is different (Fig.1.). The difference lies in the fact that with the single projection images the relief and tilt displacements are radial from the nadir point and iso-centre respectively. These points are unique in a single-projection image.  Fig.1. Multi and single-projection images.
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