Mingyang Song

Spline Deformation Field

Revisiting classic splines, blended with modern coordinate neural networks.

Mingyang Song1,2, Yang Zhang1, Marko Mihajlović2, Siyu Tang2, Markus Gross1,2, Tunç Ozan Aydın1 1DisneyResearch|Studios, Switzerland    2ETH Zürich, Switzerland

Playground

Two comparisons, each loaded on demand and decoded entirely in your browser. Within a comparison the panels share one camera and one clock, so any difference on screen is a difference between the models.

Regularizers on a clean sequence

D-NeRF bouncingballs · synthetic · 150 frames · 2.5 MB

The same sequence trained identically apart from the temporal regularizers on the spline deformation field. Both panels share one camera and one clock, so any difference on screen is a difference between the models.

With regularizationvelocity-divergence + acceleration

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Without regularizationboth terms set to zero

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Toggle these to see the trajectory differences clearly — turn on Trajectories and raise Trail to draw each gaussian’s full 150-frame path. Applies to both panels above.

Knot count as a regularizer

HyperNeRF americano · casual hand-held capture · 200 frames · 8.1 MB

The unreliable case, where the input barely constrains the motion. Cutting the number of spline knots removes degrees of freedom from the trajectory, which stabilizes the reconstruction much as the loss terms do, at the cost of some high-frequency detail. The third panel shows what the full knot count does with no regularizers at all.

These three are rendered square and wider than the capture camera, which was a 536×960 portrait frame. You are seeing well outside the filmed frustum, floaters included.

33 knotsregularized · fewest degrees of freedom

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Full knotsregularized

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Full knots, no regvelocity-divergence terms off

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Toggle these to see the trajectory differences clearly — turn on Trajectories and raise Trail to draw each gaussian’s full 200-frame path. Applies to the three panels above.

The two comparisons share a one-time ~31 MB decoder, cached by your browser after the first load. Once a card is loaded: drag inside a panel to orbit · scroll to change fly speed · W/A/S/D and Q/E to move the focused panel.

Citation

📄 Spline Deformation Field
SIGGRAPH Conference Papers ’25, Vancouver, BC, Canada · DOI 10.1145/3721238.3730676

ACM Reference Format
Mingyang Song, Yang Zhang, Marko Mihajlovic, Siyu Tang, Markus Gross, and Tunç Ozan Aydın. 2025. Spline Deformation Field. In Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers (SIGGRAPH Conference Papers ’25), August 10–14, 2025, Vancouver, BC, Canada. ACM, New York, NY, USA, 10 pages. https://doi.org/10.1145/3721238.3730676
BibTeX
@inproceedings{song2025splinedeformationfield,
  author    = {Song, Mingyang and Zhang, Yang and Mihajlovic, Marko and Tang, Siyu and Gross, Markus and Ayd{\i}n, Tun\c{c} Ozan},
  title     = {Spline Deformation Field},
  year      = {2025},
  isbn      = {979-8-4007-1540-2/25/08},
  publisher = {Association for Computing Machinery},
  address   = {New York, NY, USA},
  url       = {https://doi.org/10.1145/3721238.3730676},
  doi       = {10.1145/3721238.3730676},
  booktitle = {Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers (SIGGRAPH Conference Papers '25)},
  numpages  = {10},
  location  = {Vancouver, BC, Canada},
  series    = {SIGGRAPH Conference Papers '25}
}

Datasets

The sequences reconstructed above come from open-source dynamic-scene datasets, used here for research demonstration. Please cite the original authors:

D-NeRF — synthetic dynamic scenes; bouncingballs above.
Albert Pumarola, Enric Corona, Gerard Pons-Moll, and Francesc Moreno-Noguer. 2021. D-NeRF: Neural Radiance Fields for Dynamic Scenes. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

HyperNeRF — casually captured real-world scenes; americano above.
Keunhong Park, Utkarsh Sinha, Peter Hedman, Jonathan T. Barron, Sofien Bouaziz, Dan B Goldman, Ricardo Martin-Brualla, and Steven M. Seitz. 2021. HyperNeRF: A Higher-Dimensional Representation for Topologically Varying Neural Radiance Fields. ACM Transactions on Graphics (Proc. SIGGRAPH Asia) 40, 6 (2021).