ParaScale: Scale-Calibrated Camera-Motion Transfer via a Gauge-Invariant Parallax Number

The Challenge of Scale in Motion Transfer

Reference-driven video generation allows creators to apply camera movements from one video to another. However, a fundamental geometric problem arises when the reference and target scenes differ in scale—such as a camera sweeping over a galaxy versus moving across a desk. Naively applying the raw translation trajectory leads to motion that is either imperceptible or violently exaggerated, as the perceived camera movement depends on the ratio of translation to scene depth.

The Parallax Number

This paper identifies that monocular camera trajectories are only meaningful up to a depth-scale gauge. The author introduces the Parallax Number (Pi), a dimensionless, gauge-invariant descriptor defined as the ratio of inter-frame baseline translation to median scene depth. The research proves that Pi is the unique quantity that must be preserved to ensure scale-faithful motion transfer. By matching Pi rather than the raw trajectory, the system ensures that the perceived camera movement remains consistent across different environments.

ParaScale: A Plug-and-Play Solution

ParaScale is a lightweight, training-free module that integrates into existing pose-conditioned video generators. It calculates the Parallax Number from a reference video and re-realizes it in the target scene by adjusting the translation per frame based on the target's own depth, while leaving rotation untouched. This approach avoids the need for retraining and is agnostic to the underlying generative backbone. To validate this, the author introduces the Parallax Consistency Error (PCE), a scale-symmetric metric that effectively exposes scene-scale mismatches that traditional similarity-aligned metrics ignore.

Empirical Performance

Experiments across four orders of magnitude—ranging from tabletop objects to cosmic scales—demonstrate that ParaScale keeps realized parallax on the identity line. The module consistently cuts PCE by more than 3x compared to uncalibrated transfer methods, all while maintaining visual fidelity and requiring no additional training. The results confirm that per-frame adaptivity is both necessary and sufficient to preserve the intended temporal parallax profile.