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

Abstract

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 arbitrary magnitude, so no residual-based criterion can recover the global orientation. The theorem further identifies how the issue of global orientation can be resolved: an orientation anchor estimated from the content of a single fragment, lying outside its scope, suffices. To address the above, we propose JigSync, which attains 63.8% and 31.8% absolute accuracy (AA) on GAP-3 and GAP-5, respectively, the highest reported on both, while additionally recovering a rotation per piece that neither benchmark requires. We release JigSync, a degradation protocol that sweeps shape, erosion, photometry, grid size, and rotation independently.