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We present a new robust line matching algorithm for solving the model-to-image registration problem. Given a model consisting of 3D lines and a cluttered perspective image of this model, the algorithm simultaneously estimates the pose of the model and the correspondences of model lines to image lines. The algorithm combines softassign for determining correspondences and POSIT for determining pose. Integrating these algorithms into a deterministic annealing procedure allows the correspondence and pose to evolve from initially uncertain values to a joint local optimum. This research extends to line features the SoftPOSIT algorithm proposed recently for point features. Lines detected in images are typically more stable than points and are less likely to be produced by clutter and noise, especially in man-made environments. Experiments on synthetic and real imagery with high levels of clutter, occlusion, and noise demonstrate the robustness of the algorithm.