Normalized Spectral Map Synchronization

Estimating maps among large collections of objects (e.g., dense correspondences across images and 3D shapes) is a fundamental problem across a wide range of domains. In this paper, we provide theoretical justifications of spectral techniques for the map synchronization problem, i.e., it takes as input a collection of objects and noisy maps estimated between pairs of objects along a connected object graph, and outputs clean maps between all pairs of objects. We show that a simple normalized spectral method (or NormSpecSync) that projects the blocks of the top eigenvectors of a data matrix to the map space, exhibits surprisingly good behavior -- NormSpecSync is much more efficient than state-of-the-art convex optimization techniques, yet still admitting similar exact recovery conditions. We demonstrate the usefulness of NormSpecSync on both synthetic and real datasets.