Fix the Match, Not the Solver: STITCH -- a Self-Supervised Compatibility Measure for Eroded Visual Puzzles

Unlike the clean and pixel-aligned complete pieces of standard jigsaw benchmarks, real-world puzzle fragments lose their boundary regions to erosion, destroying the signal that classical compatibility measures (CMs) rely on. We first re-establish, via oracle experiments, that the CM, not the solver, is the performance bottleneck: with a perfect CM, even a simple greedy solver achieves perfect reconstruction. This motivates STITCH, a self-supervised CM that sidesteps missing boundaries by comparing frozen ViT patch tokens from piece interiors via a lightweight cross-attention head (~249K trainable parameters), trained without manual annotation. Plugged into unchanged compatibility-based solvers, STITCH reaches .992/.954 Abs/Perf on JPwLEG-5 (+.629 Perf over the best prior method), nearly saturating the benchmark. On a new ImageNet 7x7 benchmark, it outperforms all alternatives, including inpaint-then-match pipelines built on modern generative models. Importantly, performance remains robust across erosion levels and generalizes to puzzles with over 40% missing pieces without retraining. Trained on the recent GAP datasets of irregular, heavily eroded fragments, the same CM recipe enables compatibility-based solvers to surpass recent learning-based solvers on GAP-3 and GAP-5. Since this leap in performance is achieved by a pluggable CM module, the takeaway is clear: fix the match, not the solver.