photometric op• Data kinds: images → image2d
• Call: import fullseye as fs; fs.ledger.photometric_residual(images, lights, normals=None, albedo=None, normalize=True) (to call the implementation directly, import specularity; specularity.photometric_residual(images, lights, normals=None, albedo=None, normalize=True); from the registry, opsspecular.get("photometric_residual"))
How badly the Lambertian model fails, per pixel. → (H, W) RMS residual.
sqrt(mean_n (albedo * (n.L_n) - I_n)^2) — the root-mean-square disagreement between the linear model and the measurements, in the units of the input radiance. On a synthetic Lambertian surface with the true float64 normals and albedo supplied it measures 1.4e-16 at worst; with them omitted the floor rises to 4.5e-08, because photometric.photometric_stereo returns float32 and that is its precision, not a modelling error (supplying the *same* truth cast to float32 reproduces 4.5e-08 exactly). It is large where the assumption actually broke: 0.50 at worst on the same scene with 3 of 8 lights blocked by a cast shadow — fifteen orders of magnitude above the clean floor. All four numbers measured in tests/test_specularity.py.
This is the diagnostic that tells you *whether* you need photometric_stereo_robust before you reach for it, and it is the map an inspection routine thresholds to find glossy defects.
With *normals* and *albedo* omitted it solves them first with photometric.photometric_stereo and reports the residual of that fit — the honest self-assessment of the plain estimator. Pass them to score an estimate that came from somewhere else (a robust fit, a CAD model, a previous frame).
Note the residual uses n.L without the max(., 0) clamp, because that is the linear system the solver actually inverted; a pixel in attached shadow therefore shows a residual, which is the intended signal rather than an artefact.
Raises ValueError: *images* / *lights* problems as in photometric_stereo_robust; *normals* is not (H, W, 3) matching the images; *albedo* is not (H, W); exactly one of *normals* / *albedo* is given (the pair is meaningless apart — the model is albedo * n).
• specular_photometric family guide
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• specular_photometric — py -3.11 examples/specular_photometric.py
image2d as input)photometric)*Provenance: specularity.py — SPECULAR operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.