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We propose a novel Deformed Implicit Field (DIF) representation for modeling3D shapes of a category and generating dense correspondences among shapes. WithDIF, a 3D shape is represented by a template implicit field shared across thecategory, together with a 3D deformation field and a correction field dedicatedfor each shape instance. Shape correspondences can be easily established usingtheir deformation fields. Our neural network, dubbed DIF-Net, jointly learns ashape latent space and these fields for 3D objects belonging to a categorywithout using any correspondence or part label. The learned DIF-Net can alsoprovides reliable correspondence uncertainty measurement reflecting shapestructure discrepancy. Experiments show that DIF-Net not only produceshigh-fidelity 3D shapes but also builds high-quality dense correspondencesacross different shapes. We also demonstrate several applications such astexture transfer and shape editing, where our method achieves compellingresults that cannot be achieved by previous methods.

Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence