Cepheid: Decoupling Scale from Structure for Cross-Family Motion Completion
This paper introduces Cepheid, a novel approach to 'motion completion' – predicting how a 3D object moves when only a few points are observed. It addresses a key challenge where models trained on one type of object (e.g., human bodies) fail to generalize to others (e.g., cloth or animals), by separating the underlying motion pattern from its physical scale.
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This paper introduces Cepheid, a novel approach to 'motion completion' – predicting how a 3D object moves when only a few points are observed. It addresses a key challenge where models trained on one type of object (e.g., human bodies) fail to generalize to others (e.g., cloth or animals), by separating the underlying motion pattern from its physical scale.
Imagine trying to predict the exact shape of a wave in a swimming pool versus a tsunami. While the underlying physics of wave propagation might be similar, their scales (heights) are vastly different. Cepheid learns the 'shape' of motion (dimensionless structure) independently of its 'height' (amplitude), allowing it to apply the same learned pattern to objects of very different sizes and movement magnitudes.
How Cepheid Works to Generalize Motion
- 11. **Identify Sparse Observations**: The system receives a few displacement vectors on a 3D mesh, indicating how specific points have moved.
- 22. **Learn Dimensionless Prior**: Instead of learning the absolute motion, Cepheid learns a 'dimensionless prior' – the relative motion patterns that are independent of the object's size or the magnitude of its movement. This is like learning the 'proportions' of movement.
- 33. **Estimate Amplitude from Observables**: At test time, the system estimates the overall 'scale' or 'amplitude' of the motion using the available sparse observations and a lightweight correction derived from training data.
- 44. **Combine Structure and Scale**: The learned dimensionless structure is then combined with the estimated amplitude to reconstruct the full, dense motion of the object, even for previously unseen object types.
M_dₑₙ_sₑ = A · P_dᵢ_mₑₙ_sᵢ_oₙₗₑ_s_s + C
$M_{dense}$ is the reconstructed dense motion. $A$ is the estimated amplitude (scale). $P_{dimensionless}$ is the learned dimensionless prior (structure). $C$ represents a correction term.
Cepheid can take sparse motion data from a human body and, without retraining, accurately predict the full motion of a piece of cloth or a legged animal, or even a robot grasping a soft object, demonstrating its strong generalization capabilities across diverse geometries and motion types.
Decoupling the 'structure' of motion from its 'scale' allows machine learning models to generalize far more effectively across different object geometries and motion amplitudes, overcoming a major limitation in traditional motion completion.