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This paper investigates the challenge of learning image manifolds,specifically pose manifolds, of 3D objects using limited training data. Itproposes a DNN approach to manifold learning and for predicting images ofobjects for novel, continuous 3D rotations. The approach uses two distinctconcepts: (1) Geometric Style-GAN (Geom-SGAN), which maps images tolow-dimensional latent representations and maintains the (first-order) manifoldgeometry. That is, it seeks to preserve the pairwise distances between basepoints and their tangent spaces, and (2) uses Euler's elastica to smoothlyinterpolate between directed points (points + tangent directions) in thelow-dimensional latent space. When mapped back to the larger image space, theresulting interpolations resemble videos of rotating objects. Extensiveexperiments establish the superiority of this framework in learning paths onrotation manifolds, both visually and quantitatively, relative tostate-of-the-art GANs and VAEs.

Learning Pose Image Manifolds Using Geometry-Preserving GANs and Elasticae