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

TL;DR

TutteNet introduces a novel approach for 3D space deformations by composing multiple 2D mesh-based injective maps, enabling accurate, robust, and learnable 3D deformations for applications like NeRF and SDF.

Contribution

It presents a new method that reduces 3D injective deformations to compositions of 2D mesh maps, overcoming limitations of previous approaches.

Findings

Outperforms existing injective deformation methods in accuracy and robustness.

Enables efficient optimization and learning of complex 3D deformations.

Produces artifact-free deformations for NeRF and SDF applications.

Abstract

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.