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Single-view 3D object reconstruction is a challenging fundamental problem incomputer vision, largely due to the morphological diversity of objects in thenatural world. In particular, high curvature regions are not always capturedeffectively by methods trained using only set-based loss functions, resultingin reconstructions short-circuiting the surface or cutting corners. Inparticular, high curvature regions are not always captured effectively bymethods trained using only set-based loss functions, resulting inreconstructions short-circuiting the surface or cutting corners. To addressthis issue, we propose learning an image-conditioned mapping function from acanonical sampling domain to a high dimensional space where the Euclideandistance is equal to the geodesic distance on the object. The first threedimensions of a mapped sample correspond to its 3D coordinates. The additionallifted components contain information about the underlying geodesic structure.Our results show that taking advantage of these learned lifted coordinatesyields better performance for estimating surface normals and generatingsurfaces than using point cloud reconstructions alone. Further, we find thatthis learned geodesic embedding space provides useful information forapplications such as unsupervised object decomposition.

Geodesic-HOF: 3D Reconstruction Without Cutting Corners