Adaptive nonlocal means filtering for structured light depth maps via plane transformation

Depth maps acquired from structured light systems are corrupted by noise that degrades three-dimensional (3D) reconstruction quality. Conventional nonlocal means (NLM) filtering computes patch similarity in the two-dimensional (2D) image space and ignores the underlying geometry of depth maps. On inclined surfaces, the systematic depth gradient makes geometrically identical patches appear dissimilar, which shrinks the pool of usable candidates and weakens noise suppression. We present PT-NLM, a geometry-aware extension that embeds a plane transformation into the NLM framework. The method fits a local plane by least squares to obtain the surface normal, builds a rotation matrix from the Rodrigues formula to align each patch with a horizontal reference frame, and evaluates similarity in that common frame; a coplanarity screen on the smoothed surface trend keeps the candidate pool consistent on curved surfaces, and the filtered value is mapped back through the inverse transform. Unlike slope-compensated bilateral filtering, which applies a post-hoc local correction, PT-NLM integrates geometric alignment directly into the similarity metric while retaining nonlocal self-similarity. We evaluate PT-NLM on a physically modeled synthetic benchmark comprising inclined planes (0 to 45 deg) and a 25.42 mm sphere. PT-NLM performs comparably to conventional NLM on horizontal surfaces and reduces the residual standard deviation by 15% to 22% on inclined planes (e.g., from 6.4 to 5.0 μm at 15 deg and from 6.2 to 5.3 μm at 30 deg), and lowers spherical form error from 33.8 to 30.4 μm and RMS sphericity from 6.57 to 5.97 μm. The improvements are statistically significant (n=10, p<0.001, Cohen’s d up to 5.4) at negligible additional computational cost over conventional NLM. A real structured-light scan of a calibrated inclined plane and sphere reproduces these trends on hardware: PT-NLM attains the lowest error on both artifacts, where the local edge- and slope-based baselines fail. On a further real machined step gauge (nominal step height 10 mm, included angle 90 deg), PT-NLM attains the smallest deviation from the nominal step height and the smallest equivalent edge radius of all methods, even below the unfiltered data.