# Hamiltonian Dynamics for Real-World Shape Interpolation

arXiv: https://arxiv.org/abs/2004.05199 · HTML: https://mlsanity.com/paper/2004.05199/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2020.

## Built on by (most cited first, 13 of 13)

- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Augmenting Implicit Neural Shape Representations with Explicit Deformation Fields](https://mlsanity.com/paper/2108.08931/) (2021)
- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models](https://mlsanity.com/paper/2304.10523/) (2023)
- [Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matching](https://mlsanity.com/paper/2211.14604/) (2022)
- [4Deform: Neural Surface Deformation for Robust Shape Interpolation](https://mlsanity.com/paper/2502.20208/) (2025)
- [Multiview Regenerative Morphing with Dual Flows](https://mlsanity.com/paper/2208.01287/) (2022)
- [ARC-Flow : Articulated, Resolution-Agnostic, Correspondence-Free Matching and Interpolation of 3D Shapes Under Flow Fields](https://mlsanity.com/paper/2503.02606/) (2025)
- [SemMorph3D: Unsupervised Semantic-Aware 3D Morphing via Mesh-Guided Gaussians](https://mlsanity.com/paper/2510.02034/) (2025)
- [Shortest Paths in Graphs with Matrix-Valued Edges: Concepts, Algorithm and Application to 3D Multi-Shape Analysis](https://mlsanity.com/paper/2112.04165/) (2021)
- [3DMorph: Single-Image-Guided Local 3D Shape Editing and Morphing](https://mlsanity.com/paper/2606.07115/) (2026)

## Abstract (arXiv)

We revisit the classical problem of 3D shape interpolation and propose a novel, physically plausible approach based on Hamiltonian dynamics. While most prior work focuses on synthetic input shapes, our formulation is designed to be applicable to real-world scans with imperfect input correspondences and various types of noise. To that end, we use recent progress on dynamic thin shell simulation and divergence-free shape deformation and combine them to address the inverse problem of finding a plausible intermediate sequence for two input shapes. In comparison to prior work that mainly focuses on small distortion of consecutive frames, we explicitly model volume preservation and momentum conservation, as well as an anisotropic local distortion model. We argue that, in order to get a robust interpolation for imperfect inputs, we need to model the input noise explicitly which results in an alignment based formulation. Finally, we show a qualitative and quantitative improvement over prior work on a broad range of synthetic and scanned data. Besides being more robust to noisy inputs, our method yields exactly volume preserving intermediate shapes, avoids self-intersections and is scalable to high resolution scans.