发表机构
Université de Montréal（蒙特利尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对最小二乘相位解缠，比较规则网格、四叉树和kd树分块策略，发现自适应分块虽减少块数但整体更慢且精度可能下降，建议以完整时间评估其价值。
AI 中文摘要
相位解缠估计测量相位图像中缺失的$2\pi$倍数。对于大图像，分块限制了局部重建问题的规模，并支持并行处理。自适应分块可通过保留几乎无需细化的较大块，进一步减少局部问题和边界的数量。我们研究了这种减少是否能使重建更快。我们比较了规则网格、四叉树和kd树划分的完整重建时间和精度。我们还评估了九个用于决定四叉树块应如何细化的标准，包括残差计数、条纹密度和相位变化度量，在不同块大小和预算下。在异构图像数据集上的单线程实验中，优化的自适应划分使用更少的块，但仍比优化的网格慢，且某些重建损失了相当大的精度。阶段测量解释了原因：构建划分和求解较大的保留块所花费的时间超过了块边界处的节省。标准比较还表明，更多的细化并不总能提高精度。这些结果促使我们通过达到选定重建精度所需的完整时间来评估自适应划分，包括有限的细化是否能提供更快的近似结果。
英文摘要
Phase unwrapping estimates the missing multiples of $2π$ in measured phase images. For large images, tiling limits the size of local reconstruction problems and enables parallel processing. Adaptive tiling could further reduce the number of local problems and boundaries by retaining large tiles where little refinement is needed. We investigate whether this reduction makes reconstruction faster. We compare complete reconstruction time and accuracy for a regular grid, quadtree, and kd-tree partitions. We also evaluate nine criteria for deciding where quadtree tiles should be subdivided, including residue count, fringe density, and measures of phase variation, at different tile sizes and budgets. In single-threaded experiments on a heterogeneous image dataset, optimized adaptive partitions use fewer tiles but remain slower than the optimized grid, and some reconstructions lose substantial accuracy. Stage measurements explain why: constructing the partition and solving larger retained tiles outweigh the savings at tile boundaries. The criterion comparison also shows that more refinement does not consistently improve accuracy. These results motivate evaluating adaptive partitions by the complete time needed to reach a chosen reconstruction accuracy, including whether limited refinement can provide a faster approximate result.
CommentsTechnical report. 15 pages of main text and references, followed by 8 pages of supplementary material. 6 figures, 8 tables and 2 algorithms in total
