Optical EngineeringThree-dimensional location estimation of trajectories of point targets using a projection-based transformation method
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A new computational approach for determining the parameters that characterize the locations of trajectories of point targets in a 3-D space is described. The targets of concern are dim, unresolved point targets moving along straight paths across the same field of view. Since the target's signal-to-noise ratio is low and the spatial extent of the target is less than a pixel, one must rely on integration over a target track that spans many image frames. The proposed method estimates these parameters by transforming the entire set of time-sequential images of a constant field of view into the projection space by using a modified Radon transform. Since the 3-D (spatiotemporal) data can be decomposed into 2-D multiple-view representations along arbitrary orientations, the Radon transform enables us to analyze the 3-D problem in terms of its 2-D projections. When this generalization of the Hough transform-based algorithm using the Radon transform is applied to a set of real infrared images, it produces promising estimation results even under noisy conditions. The noise in the images is assumed to be additive white Gaussian.