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.