Triangular Consistency as a Universal Constraint for Learning Optical Flow

2026-06-18

AI Summary

This work addresses the lack of a universal, model-agnostic geometric constraint in existing optical flow learning methods, which often leads to inconsistent performance across varying supervision schemes and data configurations. The authors propose trilinear consistency as a fundamental geometric prior: given any two optical flow fields, the third can be derived through composition, and consistency among all three is explicitly enforced. This constraint is applicable across diverse scenarios—including image pairs, multi-frame videos, and synthetically transformed sequences—and is introduced for the first time in a plug-and-play manner that is independent of network architecture, supervision type, or additional annotations. It seamlessly integrates with existing methods for joint optimization. Extensive experiments demonstrate consistent performance gains under supervised, unsupervised, and transfer learning settings, with negligible computational overhead.

Abstract

We propose triangular consistency as a first-principled constraint for optical flow, which is agnostic to network architecture, supervision type, and dataset, and applies to both image-pair and multi-frame settings. This simple but powerful constraint is to compose two flows to induce a third flow and enforce consistency among the three. The composed flows may arise from (i) image pairs, yielding cycle consistency; (ii) multiple video frames, producing longer-range motion through temporal chaining; or (iii) image pairs combined with controlled synthetic transformations, which becomes data augmentation. This triangular consistency introduces negligible computational overhead and requires no additional annotations. Since it is derived directly from the geometry of optical flow, it does not rely on model-specific assumptions and serves as a ``universal'' plug-and-play component for optical flow training. Experiments show consistent improvement across supervised, unsupervised, and transfer learning settings.

Problem

• optical flow
• triangular consistency
• geometric constraint
• universal constraint
• flow consistency

Innovation

• triangular consistency
• optical flow
• cycle consistency
• temporal chaining
• data augmentation