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During the last decade, automatic data analysis methods concerning differentaspects of crystal analysis have been developed, e.g., unsupervised primitiveunit cell extraction and automated crystal distortion and defects detection.However, an automatic, unsupervised motif extraction method is still not widelyavailable yet. Here, we propose and demonstrate a novel method for theautomatic motif extraction in real space from crystalline images based on avariational approach involving the unit cell projection operator. Due to thenon-convex nature of the resulting minimization problem, a multi-stagealgorithm is used. First, we determine the primitive unit cell in form of twolattice vectors. Second, a motif image is estimated using the unit cellinformation. Finally, the motif is determined in terms of atom positions insidethe unit cell. The method was tested on various synthetic and experimentalHAADF STEM images. The results are a representation of the motif in form of animage, atomic positions, primitive unit cell vectors, and a denoised and amodeled reconstruction of the input image. The method was applied to extractthe primitive cells of complex $\mu$-phase structuresNb$_\text{6.4}$Co$_\text{6.6}$ and Nb$_\text{7}$Co$_\text{6}$, where subtledifferences between their interplanar spacings were determined.

Direct Motif Extraction from High Resolution Crystalline STEM Images