TutteNet: Injective 3D Deformations by Composition of 2D Mesh Deformations
This addresses the need for artifact-free 3D deformations in computer graphics and vision, offering a novel method that is more efficient and accurate than existing injective techniques.
The paper tackles the problem of creating injective 3D deformations by proposing a representation based on composing 2D mesh deformations, which overcomes limitations in accuracy, robustness, and compatibility with learning frameworks, and shows it outperforms other injective approaches in optimizing and learning complex deformations for applications like NeRF and SDF.
This work proposes a novel representation of injective deformations of 3D space, which overcomes existing limitations of injective methods: inaccuracy, lack of robustness, and incompatibility with general learning and optimization frameworks. The core idea is to reduce the problem to a deep composition of multiple 2D mesh-based piecewise-linear maps. Namely, we build differentiable layers that produce mesh deformations through Tutte's embedding (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 provides 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.