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We present a novel approach to fully automated delineation of tree structures in noisy 2D images and 3D image stacks. Unlike earlier methods that rely mostly on local evidence, our method builds a set of candidate trees over many different subsets of points likely to belong to the final one and then chooses the best one according to a global objective function. Since we are not systematically trying to span all nodes, our algorithm is able to eliminate noise while retaining the right tree structure. Manually annotated dendrite micrographs and retinal scans are used to evaluate the performance of our method, which is shown to be able to reject noise while retaining the tree structure.