depth op• Datenarten: lightfield → image2d
• Aufruf: import lightfield; lightfield.lf_epi_slope(lf, *, window=9, min_energy=1e-10) (oder opslightfield.get("lf_epi_slope"))
Steigung pro Pixel aus der Orientierung der EPI-Linien (Strukturtensor, ein Durchlauf).
> Die ausführliche Beschreibung unten ist der Originaltext — Zusammenfassung und Überschriften sind übersetzt.
A scene point traces a straight line in the epipolar-plane image
(:func:lf_epi), so along that line the intensity is constant:
`E_u + s * E_x = 0`. Accumulating that constraint over the whole angular
grid and a `window x window` spatial neighbourhood gives the closed-form
least-squares slope `s = -(J_ux + J_vy) / (J_xx + J_yy)` with
`J_ab = sum(E_a * E_b)` — one pass over the light field, no sweep, both
the horizontal and vertical EPI directions pooled.
This estimator is biased, and the bias is the reason to also run
:func:lf_depth_from_focus. It is ordinary (not total) least squares on
finite differences, so it needs the EPI line to advance less than roughly
one texture correlation length per view. Measured 2026-09-01 on
5x5x64x64 synthetic fields, median over the interior: with texture
`sigma = 1.5 px, true +1.00 -> +1.0004, +0.50 -> +0.5285`,
`+1.50 -> +1.3018, +2.00 -> +1.4614; with sigma = 5.0` px the same
slopes give `+1.0003, +0.5029, +1.4827, +1.9482`. Integer
slopes on a wrapped field come back within 4e-4 and `s = 0` is exact;
`|s| > 1 is under-estimated, by 27% at s = 2` on the roughest texture.
Use it as a fast dense initialiser, not as the final word.
Returns `(slope_map, energy): the (H, W) slope map and the (H, W)`
gradient energy `J_xx + J_yy` that was the denominator. Pixels whose
energy is below *min_energy* have no measurable parallax (a flat patch
of sky); their slope is set to 0 and their energy reported as-is, so you
threshold on `energy` instead of being handed a plausible-looking number
divided by ~0.
Raises `ValueError`: *lf* not a valid light field, an angular/spatial
shape where *neither* EPI direction carries information (the horizontal EPI
needs `U >= 2 **and** W >= 2, the vertical needs V >= 2` and
`H >= 2`), an even or non-positive *window*, a non-positive *min_energy*.
• Leitfaden zur Familie lightfield_depth
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.
• lightfield_depth — py -3.11 examples/lightfield_depth.py
image2d als Eingabe)lf_from_mla · lf_disparity_to_depth · lf_all_in_focus
depth)lf_depth_from_focus · lf_disparity_to_depth · lf_all_in_focus · lf_plenoptic_design
*Provenance: lightfield.py — LIGHTFIELD Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.