# FourierHandFlow: Neural 4D Hand Representation Using Fourier Query Flow

arXiv: https://arxiv.org/abs/2307.08100 · HTML: https://mlsanity.com/paper/2307.08100/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 57 references that are in the map.
- First posted on arXiv 16 Jul 2023.

## Builds on (most cited first, 30 of 45)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Expressive Body Capture: 3D Hands, Face, and Body from a Single Image](https://mlsanity.com/paper/1904.05866/) (2019)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [End-to-End Human Pose and Mesh Reconstruction with Transformers](https://mlsanity.com/paper/2012.09760/) (2020)
- [Learning joint reconstruction of hands and manipulated objects](https://mlsanity.com/paper/1904.05767/) (2019)
- [InterHand2.6M: A Dataset and Baseline for 3D Interacting Hand Pose Estimation from a Single RGB Image](https://mlsanity.com/paper/2008.09309/) (2020)
- [3D Hand Shape and Pose from Images in the Wild](https://mlsanity.com/paper/1902.03451/) (2019)
- [SCANimate: Weakly Supervised Learning of Skinned Clothed Avatar Networks](https://mlsanity.com/paper/2104.03313/) (2021)
- [GANerated Hands for Real-time 3D Hand Tracking from Monocular RGB](https://mlsanity.com/paper/1712.01057/) (2017)
- [Weakly-Supervised Mesh-Convolutional Hand Reconstruction in the Wild](https://mlsanity.com/paper/2004.01946/) (2020)
- [Leveraging Photometric Consistency over Time for Sparsely Supervised Hand-Object Reconstruction](https://mlsanity.com/paper/2004.13449/) (2020)
- [Neural Wavelet-domain Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2209.08725/) (2022)
- [End-to-end Hand Mesh Recovery from a Monocular RGB Image](https://mlsanity.com/paper/1902.09305/) (2019)
- [Pushing the Envelope for RGB-based Dense 3D Hand Pose Estimation via Neural Rendering](https://mlsanity.com/paper/1904.04196/) (2019)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [LEAP: Learning Articulated Occupancy of People](https://mlsanity.com/paper/2104.06849/) (2021)
- [What's in your hands? 3D Reconstruction of Generic Objects in Hands](https://mlsanity.com/paper/2204.07153/) (2022)
- [Interacting Attention Graph for Single Image Two-Hand Reconstruction](https://mlsanity.com/paper/2203.09364/) (2022)

## Built on by (most cited first, 10 of 10)

- [Dyn-HaMR: Recovering 4D Interacting Hand Motion from a Dynamic Camera](https://mlsanity.com/paper/2412.12861/) (2024)
- [InterHandGen: Two-Hand Interaction Generation via Cascaded Reverse Diffusion](https://mlsanity.com/paper/2403.17422/) (2024)
- [BiTT: Bi-directional Texture Reconstruction of Interacting Two Hands from a Single Image](https://mlsanity.com/paper/2403.08262/) (2024)
- [MPMAvatar: Learning 3D Gaussian Avatars with Accurate and Robust Physics-Based Dynamics](https://mlsanity.com/paper/2510.01619/) (2025)
- [CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences](https://mlsanity.com/paper/2406.18582/) (2024)
- [Multi-hypotheses Conditioned Point Cloud Diffusion for 3D Human Reconstruction from Occluded Images](https://mlsanity.com/paper/2409.18364/) (2024)
- [Diffusion-based 3D Hand Motion Recovery with Intuitive Physics](https://mlsanity.com/paper/2508.01835/) (2025)
- [SRHand: Super-Resolving Hand Images and 3D Shapes via View/Pose-aware Neural Image Representations and Explicit 3D Meshes](https://mlsanity.com/paper/2509.21859/) (2025)
- [LieHMR: Autoregressive Human Mesh Recovery with SO(3) Diffusion](https://mlsanity.com/paper/2509.25739/) (2025)
- [Cascaded Diffusion Framework for Probabilistic Coarse-to-Fine Hand Pose Estimation](https://mlsanity.com/paper/2510.00527/) (2025)

## Abstract (arXiv)

Recent 4D shape representations model continuous temporal evolution of implicit shapes by (1) learning query flows without leveraging shape and articulation priors or (2) decoding shape occupancies separately for each time value. Thus, they do not effectively capture implicit correspondences between articulated shapes or regularize jittery temporal deformations. In this work, we present FourierHandFlow, which is a spatio-temporally continuous representation for human hands that combines a 3D occupancy field with articulation-aware query flows represented as Fourier series. Given an input RGB sequence, we aim to learn a fixed number of Fourier coefficients for each query flow to guarantee smooth and continuous temporal shape dynamics. To effectively model spatio-temporal deformations of articulated hands, we compose our 4D representation based on two types of Fourier query flow: (1) pose flow that models query dynamics influenced by hand articulation changes via implicit linear blend skinning and (2) shape flow that models query-wise displacement flow. In the experiments, our method achieves state-of-the-art results on video-based 4D reconstruction while being computationally more efficient than the existing 3D/4D implicit shape representations. We additionally show our results on motion inter- and extrapolation and texture transfer using the learned correspondences of implicit shapes. To the best of our knowledge, FourierHandFlow is the first neural 4D continuous hand representation learned from RGB videos. The code will be publicly accessible.