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JigSync: Gauge-Resolved Synchronization for Jigsaw Reassembly under Unknown Piece Orientation

arXiv · AI, language, vision and robotics · article · Sep 16, 2026 · UTC

Square jigsaw reassembly requires recovering the spatial arrangement of shuffled fragments from their visual content and pairwise relationships. While recent studies have made substantial progress, existing benchmarks typically assume that all fragments are provided upright, reducing reassembly to a permutation problem. We study the generalized problem in which each fragment may also have gone through an unknown rotation. For this setting we establish a gauge-unobservability theorem: the minimum of the weighted least-squares objective is exactly invariant under a uniform global rotation of arb

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