3D shape reconstruction from a single image has been a long-standing problem in computer vision. The problem is ill-posed and highly challenging due to the information loss and occlusion that occurred during the imagery capture. In contrast to previo
us methods that learn holistic shape priors, we propose a method to learn spatial pattern priors for inferring the invisible regions of the underlying shape, wherein each 3D sample in the implicit shape representation is associated with a set of points generated by hand-crafted 3D mappings, along with their local image features. The proposed spatial pattern is significantly more informative and has distinctive descriptions on both visible and occluded locations. Most importantly, the key to our work is the ubiquitousness of the spatial patterns across shapes, which enables reasoning invisible parts of the underlying objects and thus greatly mitigates the occlusion issue. We devise a neural network that integrates spatial pattern representations and demonstrate the superiority of the proposed method on widely used metrics.
In this work, we study the topological phases of the dimerized square lattice in the presence of an external magnetic field. The dimerization pattern in the lattices hopping amplitudes can induce a series of bulk energy gap openings in the Hofstadter
spectrum at certain fractional fillings, giving rise to various topological phases. In particular, we show that at $frac{1}{2}$-filling the topological quadrupole insulator phase with a quadrupole moment quantized to $frac{e}{2}$ and associated corner-localized mid-gap states exists in certain parameter regime for all magnetic fluxes. At $frac{1}{4}$ filling, the system can host obstructed atomic limit phases or Chern insulator phases. For those configurations gapped at fillings below $frac{1}{4}$, the system is in Chern insulator phases of various non-vanishing Chern numbers. Across the phase diagram, both bulk-obstructed and boundary-obstructed topological phase transitions exist in this model.
