Mechanism-Constrained Synthetic Data for Detection-Oriented Visual Sensing of Analog Gauges Under Limited Pointer Annotation

Automatic analog-gauge interpretation is constrained by the cost of pointer-level annotation and by limited coverage of rare operating states. This work presents a mechanism-constrained synthetic-data framework (B-data) for detection-oriented gauge sensing under limited pointer supervision. Six real seed templates are decomposed into dial and pointer assets, deterministically re-centered to a common pivot, and synthesized by sampling only within template-specific valid angular intervals. A same-budget unconstrained control uses the same assets, perturbations, and 6000-image budget but samples over the full ${360}^{\circ }$ range. The theoretical valid-arc coverage of unconstrained rotation is 54.91%, and the observed rate is 54.97% (3298/6000), whereas B-data achieves 100% valid-arc compliance. Under the principal setting, in which pointer boxes are available for 25% of the 422 real training images, B-data reaches 62.8 ± 2.2% pointer AP@0.5 across three independent training seeds on a 100-image independent test set from 18 unseen instruments, compared with 54.9 ± 2.5% for unconstrained synthesis and 47.6 ± 2.8% for real-only training. B-data also increases geometry-consistent output to 40.3 ± 1.5%, reduces conditional angular MAE to 5.2 ± 0.7${}^{\circ }$, and raises end-to-end $\le {10}^{\circ }$ success to 35.7 ± 1.5%. These results show that valid-state constraints provide transferable structural supervision beyond synthetic-data quantity alone. The resulting 6000-image mechanism-constrained B-data release, including paired detection annotations and generation metadata, is publicly available on Zenodo.