JigSync：未知碎片方向下的量规分辨同步拼图重组
JigSync: Gauge-Resolved Synchronization for Jigsaw Reassembly under Unknown Piece Orientation
- Indian Statistical Institute, Kolkata（加尔各答印度统计学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对碎片可能未知旋转的拼图重组，提出量规不可观测性定理并设计JigSync方法，在GAP-3和GAP-5上取得最高绝对准确率，同时恢复每片旋转。
AI中文摘要：
方形拼图重组要求从打乱碎片的视觉内容和成对关系中恢复其空间排列。尽管近期研究已取得实质性进展，但现有基准通常假设所有碎片均以正立方向提供，从而将重组简化为排列问题。我们研究更一般的问题，其中每个碎片还可能经历未知旋转。针对该设定，我们建立了一个量规不可观测性定理：加权最小二乘目标的最小值在任意幅度的均匀全局旋转下严格不变，因此任何基于残差的准则都无法恢复全局方向。该定理进一步指明了如何解决全局方向问题：从单个碎片内容估计的方向锚点（位于其作用域之外）即足以确定全局方向。为解决上述问题，我们提出JigSync，在GAP-3和GAP-5上分别达到63.8%和31.8%的绝对准确率（AA），均为两者上的最高报告值，同时额外恢复每个碎片的旋转，而两个基准均不要求此功能。我们发布了JigSync，一个独立扫描形状、侵蚀、光度、网格大小和旋转的退化协议。
英文摘要：
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.
