Triangular Consistency as a Universal Constraint for Learning Optical Flow

[Submitted on 18 Jun 2026 (v1), last revised 2 Jul 2026 (this version, v3)]

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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.

Submission history

From: Dong Lao [view email]
[v1] Thu, 18 Jun 2026 08:34:32 UTC (1,283 KB)
[v2] Wed, 1 Jul 2026 01:37:02 UTC (1,280 KB)
[v3] Thu, 2 Jul 2026 19:40:00 UTC (1,281 KB)