# Continuous Dynamic-NeRF: Spline-NeRF

arXiv: https://arxiv.org/abs/2203.13800 · HTML: https://mlsanity.com/paper/2203.13800/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 22 references that are in the map.
- First posted on arXiv 25 Mar 2022.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [NeRD: Neural Reflectance Decomposition from Image Collections](https://mlsanity.com/paper/2012.03918/) (2020)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Neural Scene Graphs for Dynamic Scenes](https://mlsanity.com/paper/2011.10379/) (2020)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [Neural Reflectance Fields for Appearance Acquisition](https://mlsanity.com/paper/2008.03824/) (2020)
- [Learning Compositional Radiance Fields of Dynamic Human Heads](https://mlsanity.com/paper/2012.09955/) (2020)

## Abstract (arXiv)

The problem of reconstructing continuous functions over time is important for problems such as reconstructing moving scenes, and interpolating between time steps. Previous approaches that use deep-learning rely on regularization to ensure that reconstructions are approximately continuous, which works well on short sequences. As sequence length grows, though, it becomes more difficult to regularize, and it becomes less feasible to learn only through regularization. We propose a new architecture for function reconstruction based on classical Bezier splines, which ensures C0 and C1-continuity, where C0 continuity is that forall c:limlimitsx→ c f(x) = f(c), or more intuitively that there are no breaks at any point in the function. In order to demonstrate our architecture, we reconstruct dynamic scenes using Neural Radiance Fields, but hope it is clear that our approach is general and can be applied to a variety of problems. We recover a Bezier spline B(β, t∈[0,1]), parametrized by the control points β. Using Bezier splines ensures reconstructions have C0 and C1 continuity, allowing for guaranteed interpolation over time. We reconstruct β with a multi-layer perceptron (MLP), blending machine learning with classical animation techniques. All code is available at https://github.com/JulianKnodt/nerfatlas, and datasets are from prior work.