Adaptive Tiling for Least-Squares Phase Unwrapping: Runtime and Accuracy

2026-09-22

AI Summary

This study investigates whether adaptive tiling can enhance both efficiency and accuracy in large-scale image phase unwrapping. By systematically comparing grid, quadtree, and KD-tree partitioning strategies, it quantitatively evaluates the trade-offs between runtime and reconstruction accuracy across nine subdivision criteria. The analysis reveals a counterintuitive mechanism: reducing the number of tiles does not necessarily accelerate computation. Specifically, the overhead of constructing adaptive structures and the increased solving time for larger tiles offset the benefits of reduced boundary length, resulting in single-threaded performance inferior to optimized grid methods alongside partial accuracy degradation. Based on these findings, this work proposes adopting the total time required to achieve a specified accuracy as a more appropriate evaluation metric for this task.

Abstract

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.

Problem

• Phase Unwrapping
• Adaptive Tiling
• Least-Squares
• Reconstruction Accuracy
• Runtime Performance

Innovation

• Phase Unwrapping
• Adaptive Tiling
• Least-Squares
• Quadtree Partition
• Reconstruction Accuracy