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This study benchmarks adaptive spatial partitioning schemes (quadtree and kd-tree using nine subdivision criteria) against standard uniform grid tiling for least-squares phase unwrapping across heterogeneous image datasets. Evaluating the true end-to-end runtime of adaptive tiling is critical because theoretical reductions in subproblem counts often fail to account for partitioning overhead and non-linear solver scaling. The authors show that optimized adaptive tiling is consistently slower than an optimized uniform grid—and occasionally degrades accuracy—because the costs of constructing partitions and solving disproportionately large tiles outweigh the boundary stitching savings.
Fewer tiles do not mean faster solves: adaptive quadtree and kd-tree partitioning actually underperform naive uniform grids in least-squares phase unwrapping due to partition construction overhead and the superlinear cost of solving large retained tiles.
Phase unwrapping estimates the missing multiples of $2\pi$ 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.