Unsupervised and Accurate Extraction of Primitive Unit Cells from Crystal Images

We present a novel method for the unsupervised estimation of a primitive unit cell, i.e. a unit cell that can’t be further simplified, from a crystal image. Significant peaks of the projective standard deviations of the image serve as candidate lattice vector angles. Corresponding fundamental periods are determined by clustering local minima of a periodicity energy. Robust unsupervised selection of the number of clusters is obtained from the likelihoods of multi-variance cluster models induced by the Akaike information criterion. Initial estimates for lattice angles and periods obtained in this manner are refined jointly using non-linear optimization. Results on both synthetic and experimental images show that the method is able to estimate complex primitive unit cells with sub-pixel accuracy, despite high levels of noise.