Triangular Consistency as a Universal Constraint for Learning Optical Flow

Modern optical flow models are typically trained to estimate displacement between two frames, often relying on photometric loss or ground-truth supervision. However, these methods often ignore the fundamental physical property that displacement fields are coordinate transformations that must agree under composition. This paper investigates whether enforcing this compositional consistency—specifically a triangular relationship between three frames—can serve as a universal, architecture-agnostic supervision signal to improve optical flow accuracy.

The authors formalize "triangular consistency" as a constraint where the flow between two frames (t to t+2) must equal the composition of the flows between intermediate frames (t to t+1 and t+1 to t+2). This principle is applied in three ways:

1. Temporal Compositional Consistency: Enforcing the geometric relationship across sequential video frames.
2. Cycle Consistency: A special case where the composition returns to the starting frame.
3. Augmentation Consistency: Using controlled, analytical affine transformations to generate exact ground-truth flow targets for training.

Because this constraint is derived directly from the geometry of coordinate transformations, it requires no additional human annotations and introduces negligible computational overhead. It can be integrated into existing supervised, unsupervised, or transfer learning pipelines without modifying the underlying network architecture.

Experiments demonstrate that triangular consistency provides consistent performance gains across various settings. The authors report significant improvements in cross-dataset generalization and accuracy, including up to 18.1% improvement in single-epoch adaptation, 6-8% gains in unsupervised training, and up to 23.1% improvement in supervised cross-dataset evaluation. The method proves to be a lightweight, "plug-and-play" component that enhances robustness without requiring architectural changes or complex auxiliary losses.