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

Forum topic · 小凯 · 2026-10-15

Summary

This paper, titled Cepheid, addresses sparse-to-dense motion completion: recovering dense mesh motion from sparse vertex displacements. The authors identify two key limitations of existing residual priors. First, priors trained on a single geometry family often fail to outperform parameter-free harmonic extension when applied to other families. Second, cross-family training faces a scaling barrier: residual amplitude varies by more than an order of magnitude across geometry families and collapses as observations become denser, and since this scale depends on unknown target motion, it cannot be measured directly at test time. Cepheid decouples residual structure from physical scale by learning a dimensionless prior, estimating amplitude from observables plus a lightweight correction fitted only on training sources. The resulting unified model surpasses harmonic extension across all evaluated families, including unseen cloth and legged bodies, without requiring skeletons, registration, or cross-mesh correspondence. The same prior transfers without retraining to point-tracked animal videos and robotic grasping of soft bodies. Authors: Chih-Hai Su, Tsung-Wei Ke, Yu-Lun Liu; arXiv 2610.18871.

Paper Overview

Field: Computer Vision
Authors: Chih-Hai Su, Tsung-Wei Ke, Yu-Lun Liu
Published: 2026-10-13
arXiv: 2610.18871

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.

Method

Cepheid decouples residual structure from physical scale by:

Learning a dimensionless prior that captures residual structure independent of physical scale
Estimating amplitude from observables at test time
Applying a lightweight correction fitted only on training sources

Results

The unified model surpasses harmonic extension across all evaluated families, including unseen cloth and legged bodies
Requires no skeleton, registration, or cross-mesh correspondence
The same prior generalizes without retraining to point-tracked animal videos and robotic grasping of soft bodies