Photogrammetric Techniques for Panoramic Cameras

Panoramic cameras are used in aerial surveillance for the rapid coverage of large areas of terrain. Different Panoramic camera designs vary substantially, so that there is no such thing as a generic panoramic camera similar in generality to the pinhole model of a frame camera. This is true for instance for methods of forward motion compensation for which different methods are used. Nevertheless, a panoramic camera may be modelled as a camera with a cylindrical focal surface in which the image is acquired by sweeping a slit across the focal cylinder. This model fits most styles of panoramic camera. In this paper, a general model for panoramic cameras is described including options of different methods of forward motion compensation. A Levenberg-Marquardt based parameter estimation program is used to estimate camera parameters from ground control points or image correspondences. The model has 16 parameters including ones for describing the orientation and location of the camera, the velocity of motion of the camera, forward motion control parameters as well as internal parameters such as scale, principal point offsets and digitizing parameters (for use if the panoramic image is digitized from film). It is a peculiarity of the moving camera model that no closed form solution exists to determine the location of the image of a point in space -unless the sweep axis is parallel with the direction of motion. If one permits "crabbing" due to cross winds the world-to-image mapping must be determined by iteration. This complicates the task of parameter solving. An important feature of the parameter solution method is that no initialization of the camera parameters is necessary, except knowledge of the sweep direction, which is usually obvious since the image is far wider in the sweep direction than the cross-sweep direction. The parameter solving program will automatically find an accurate initial parameter estimation and refine it by iteration to the best solution. This program has been used to orthorectify panoramic images for subsequent mosaicing. 1. PARAMETRIZED CAMERA MODELS. A camera model describes a mapping from a three-dimensional world to a two-dimensional image. In denoting coordinates in 2 or 3-dimensional space column vectors will be used. For ease of in-line notation they will be written as transposed row vectors, such as (x, y, z)T. The superscript T denotes transpose. Thus, a camera model describes a mapping from world coordinates (x, y, z)T to image coordinates, (u, v)T. Usually the mapping depends on a number of numerical quantities called parameters. Parameters include such information as the location and orientation of the camera, as well as certain internal characteristics of a camera, such a focal length. Given specific values of the parameters, it is possible to compute the coordinates of the image of any world point (x, y, z)T. Let the parametrized mapping function be denoted by FP, where P = {pj} is the set of parameters. Then for a given choice of parameters, the FP maps a world point (x, y, z)T to an image point (u, v)T = FP(x, y, z)T. Determination of the camera parameters is the inverse problem, given several correspondences of world coordinates (xi, yi, zi)T to image coordinates (ui, vi)T, of finding the best set of parameters to fit this measured data. A standard method of parameter determination is the Levenberg-Marquardt algorithm. We have developed an implementation of the Levenberg-Marquardt algorithm derived from the description in "Numerical Recipes in C"1 and particularly optimized for determining the parameters of camera models. Our implementation allows estimated or measured values to be specified for each of the world coordinates xi, yi or zi, image coordinates ui and vi and parameters pj. In addition, weights (related to estimated standard deviations) may