Measuring Positions of Objects using Two or More Cameras

An improved method of computing positions of objects from digitized images acquired by two or more cameras (see figure) has been developed for use in tracking debris shed by a spacecraft during and shortly after launch. The method is also readily adaptable to such applications as (1) tracking moving and possibly interacting objects in other settings in order to determine causes of accidents and (2) measuring positions of stationary objects, as in surveying. Images acquired by cameras fixed to the ground and/or cameras mounted on tracking telescopes can be used in this method. In this method, processing of image data starts with creation of detailed computer- aided design (CAD) models of the objects to be tracked. By rotating, translating, resizing, and overlaying the models with digitized camera images, parameters that characterize the position and orientation of the camera can be determined. The final position error depends on how well the centroids of the objects in the images are measured; how accurately the centroids are interpolated for synchronization of cameras; and how effectively matches are made to determine rotation, scaling, and translation parameters. The method involves use of the perspective camera model (also denoted the point camera model), which is one of several mathematical models developed over the years to represent the relationships between external coordinates of objects and the coordinates of the objects as they appear on the image plane in a camera. The method also involves extensive use of the affine camera model, in which the distance from the camera to an object (or to a small feature on an object) is assumed to be much greater than the size of the object (or feature), resulting in a truly two-dimensional image. The affine camera model does not require advance knowledge of the positions and orientations of the cameras. This is because ultimately, positions and orientations of the cameras and of all objects are computed in a coordinate system attached to one object as defined in its CAD model.