Cepheid

Cepheid: Decoupling Scale from Structure
for Cross‑Family Motion Completion

Explore in 3DPaper (arXiv)Code (coming soon)AbstractBibTeX

Chih-Hai Su1Tsung-Wei Ke2Yu-Lun Liu1

1National Yang Ming Chiao Tung University2Department of Computer Science and Information Engineering, National Taiwan University

Sparse-to-Dense Mesh Motion Without Skeletons or Templates

Predict full surface motion from sparse observations without skeletons, templates, registration, or cross-mesh correspondence across distinct geometry families.

Training families
Held out · zero-shot
Held-out clips from each family's evaluation set · showing 2 per family
loading

Abstract

Sparse-to-dense motion completion recovers dense mesh motion from sparse vertex displacements. Residual priors trained on one geometry family frequently fail to beat parameter-free harmonic extension off-family. Moreover, cross-family training meets a scaling barrier: residual amplitude varies by more than an order of magnitude across geometry families and collapses as observations become denser. Since this scale depends on unknown target motion, it cannot be measured directly at test time. We decouple residual structure from physical scale by learning a dimensionless prior, estimating amplitude from observables and a lightweight correction fitted only on training sources. Our unified model surpasses harmonic extension across all evaluated families, including unseen cloth and legged bodies, without skeletons, registration, or cross-mesh correspondence. The same prior applies without retraining to point-tracked animal video and a robot grasping a soft body.

Zero-Shot Applications

Robot

8 points on the robot0 on the payload

In Isaac Lab, Franka lifts a soft bar; from four base and four hand points, the frozen model completes the unobserved object's motion.

Video

Input video | Motion 3-to-4 (reference) | Ours (2% of vertices observed)

Ours observes 2% of the vertices of a video-to-4D reconstruction (Motion 3-to-4) and completes the rest; the middle panel is that reconstruction, shown for reference, not ground truth.

Robot · Fine-tuned

Harmonic: per-vertex error on the arm
Harmonic
Zero-shot: per-vertex error on the arm
Zero-shot
Fine-tuned: per-vertex error on the arm
Fine-tuned
error: lowhigh3 gripper markers

Not zero-shot: the checkpoint fine-tuned to a fixed three-marker placement on the gripper (Appendix G). On a held-out episode, each arm is coloured by its per-vertex error, on one shared scale.

Method

Method overview

Amplitude Recovery Across Diverse Geometry Families

Amplitude recovery

s^=σobs⋅exp⁡(b+w⊤z)\hat{s} = \sigma_{\text{obs}} \cdot \exp(b + w^\top z)

R  →  R/s^R \;\to\; R / \hat{s}

Animal · DT4D
Human · AMASS
Robot Arm · Franka
Cloth · Flag
Legged Robot · GenBot1K
lowhigh
amplitude recovery

Residual (same scale)

The gap between true motion and harmonic extension shows stark amplitude differences across families.

After amplitude recovery (÷ ŝ)

Factoring out estimated amplitude brings residual scales much closer together across seen and held-out families.

Contributions

Closed-Form Harmonic Base

HH
motion: lowhigh

A parameter-free graph solve with fixed observed vertices serves as the base motion and control.

Amplitude Recovery and Rescaling

R=F−HR = F - H
R/s^R / \hat{s}

Dividing the raw residual by estimated amplitude yields a dimensionless target, bringing cross-family scales closer together.

Base Plus Learned Residual

HH
F^=H+s^ Rˉθ\hat{F} = H + \hat{s}\,\bar{R}_\theta
FF
error against the ground truth: lowhigh

Recomposing the harmonic base with scaled flow predictions produces full motion with lower ground-truth error.

Explore in 3D

Explore Mesh Completions

Drag to rotate · ⌘/Ctrl + scroll to zoom

BibTeX

@misc{su2026cepheid,
  title  = {Cepheid: Decoupling Scale from Structure for Cross-Family Motion Completion},
  author = {Su, Chih-Hai and Ke, Tsung-Wei and Liu, Yu-Lun},
  year   = {2026}
}