TutteNet: Injective 3D Deformations by Composition of 2D Mesh Deformations

This work proposes a novel representation of injective deformations of 3D space, which overcomes existing limi-tations of injective methods, namely inaccuracy, lack of ro-bustness, and incompatibility with general learning and op-timization frameworks. Our core idea is to reduce the prob-lem to a “deep” composition of multiple 2D mesh-based piecewise-linear maps. Namely, we build differentiable lay-ers that produce mesh deformations through Tutte's embed-ding (guaranteed to be injective in 2D), and compose these layers over different planes to create complex 3D injective deformations of the 3D volume. We show our method pro-vides the ability to efficiently and accurately optimize and learn complex deformations, outperforming other injective approaches. As a main application, we produce complex and artifact-free NeRF and SDF deformations.