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<p>Algorithms are proposed for reconstructing convex sets given noisy support line measurements. It is observed that a set of measured support lines may not be consistent with any set in the plane. A theory of consistent support lines which serves as a basis for reconstruction algorithms that take the form of constrained optimization algorithms is developed. The formal statement of the problem and constraints reveals a rich geometry that makes it possible to include prior information about object position and boundary smoothness. The algorithms, which use explicit noise models and prior knowledge, are based on maximum-likelihood and maximum a posteriori estimation principles and are implemented using efficient linear and quadratic programming codes. Experimental results are presented. This research sets the stage for a more general approach to the incorporation of prior information concerning the estimation of object shape.</p>
fast Fourier transforms; computerised picture processing; multiframe estimation; trajectories estimation; frequency domain algorithm; multiframe detection; dim targets; moving targets; imaging sensors; directional filtering; detection probabilities; computerised picture processing; fast Fourier transforms; filtering and prediction theory; tracking systems

J. Prince and A. Willsky, "Reconstructing Convex Sets from Support Line Measurements," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 12, no. , pp. 377-389, 1990.
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