# CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences

arXiv: https://arxiv.org/abs/2406.18582 · HTML: https://mlsanity.com/paper/2406.18582/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 107 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Builds on (most cited first, 30 of 56)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [3D Neural Field Generation using Triplane Diffusion](https://mlsanity.com/paper/2211.16677/) (2022)
- [Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle](https://mlsanity.com/paper/2312.03431/) (2023)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [SCANimate: Weakly Supervised Learning of Skinned Clothed Avatar Networks](https://mlsanity.com/paper/2104.03313/) (2021)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [4DComplete: Non-Rigid Motion Estimation Beyond the Observable Surface](https://mlsanity.com/paper/2105.01905/) (2021)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Detailed, accurate, human shape estimation from clothed 3D scan sequences](https://mlsanity.com/paper/1703.04454/) (2017)
- [Learning Smooth Neural Functions via Lipschitz Regularization](https://mlsanity.com/paper/2202.08345/) (2022)
- [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [DiGS : Divergence guided shape implicit neural representation for unoriented point clouds](https://mlsanity.com/paper/2106.10811/) (2021)
- [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)

## Built on by (most cited first, 7 of 7)

- [Molecular Representations in Implicit Functional Space via Hyper-Networks](https://mlsanity.com/paper/2601.22327/) (2026)
- [BiMotion: B-spline Motion for Text-guided Dynamic 3D Character Generation](https://mlsanity.com/paper/2602.18873/) (2026)
- [DynaTok: Token-Based 4D Reconstruction from Partial Point Clouds](https://mlsanity.com/paper/2606.12189/) (2026)
- [GrowFields: Compositional 4D Neural Fields for Topology-Changing Plant Growth](https://mlsanity.com/paper/2607.03330/) (2026)
- [Low-Rank Velocity Fields as a Structural Prior for Unsupervised 4D Medical Image Interpolation](https://mlsanity.com/paper/2608.24025/) (2026)
- [Phase-Aligned Finite-Fourier Periodic Deformation for 4D Medical Image Interpolation](https://mlsanity.com/paper/2608.24027/) (2026)
- [Cepheid: Decoupling Scale from Structure for Cross-Family Motion Completion](https://mlsanity.com/paper/2610.18871/) (2026)

## Abstract (arXiv)

We introduce Canonical Consolidation Fields (CanFields). This novel method interpolates arbitrary-length sequences of independently sampled 3D point clouds into a unified, continuous, and coherent deforming shape. Unlike prior methods that oversmooth geometry or produce topological and geometric artifacts, CanFields optimizes fine-detailed geometry and deformation jointly in an unsupervised fitting with two novel bespoke modules. First, we introduce a dynamic consolidator module that adjusts the input and assigns confidence scores, balancing the optimization of the canonical shape and its motion. Second, we represent the motion as a diffeomorphic flow parameterized by a smooth velocity field. We have validated our robustness and accuracy on more than 50 diverse sequences, demonstrating its superior performance even with missing regions, noisy raw scans, and sparse data. Our project page is at: https://wangmiaowei.github.io/CanFields.github.io/.