depth op• Data kinds: lightfield → image2d
• Call: import fullseye as fs; fs.ledger.lf_epi_slope(lf, *, window=9, min_energy=1e-10) (to call the implementation directly, import lightfield; lightfield.lf_epi_slope(lf, *, window=9, min_energy=1e-10); from the registry, opslightfield.get("lf_epi_slope"))
• Return value through the ledger: fullseye.ledger.lf_epi_slope(...) returns only the declared out type image2d (the underlying function also returns auxiliary values). When you need what was dropped, use fullseye.ledger.lf_epi_slope.raw(...) or call lightfield.lf_epi_slope directly.
• GPU: yes (mechanical GPU path from the allow-list, CuPy). device="auto" chooses the GPU from the measured size (589,824 pixels) up
Per-pixel slope from the EPI line orientation (structure tensor, refined by shearing).
A scene point traces a straight line in the epipolar-plane image (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) — both the horizontal and vertical EPI directions pooled.
Why it is iterated (fixed 2026-11-03). A finite difference across views measures a displacement of s px per view, while a finite difference across pixels measures one of 1 px; for a texture component of angular frequency w the ratio is sin(w s) / sin(w) (the pre-fix central differences), equal to s only at |s| in {0, 1}. That is the classic statement that the structure tensor is accurate only for disparities in a small range around zero (Wanner & Goldluecke, CVPR 2012 and TPAMI 36(3) 2014, who handle larger ranges by shearing the light field). So the estimator shears the field by an integer slope k (integer shifts: no resampling blur), measures the residual r = s - k, sets k <- round(k + r) per pixel and repeats until no pixel changes (at most EPI_MAX_ROUNDS rounds, at most EPI_MAX_SHEARS distinct shears). The residual is measured with a matched discretisation (adjacent-view difference against the mean of the two views' Gaussian derivatives, inner scale EPI_INNER_SIGMA), whose error is O(r^3 w^2) with |r| <= 1/2.
Measured 2026-11-03, median over the interior of single-layer lf_synthesize fields (64x64, edge="wrap"), s in [-3, 3] in steps of 0.25: error <= 0.006 px for 5x5 and 9x9 views, <= 0.007 px for 4x4 (even count) and <= 0.012 px for 3x3 and for a single row of 6 views, at texture sigma 1.0 / 1.5 / 2.0 / 5.0 px, for windows 5 / 9 / 15 (the pre-fix estimator read -1.388 for -1.5 at sigma 2 and 1.46 for 2.0 at sigma 1.5). Integer slopes are exact to 1e-9 on a wrapped field. Valid range: the shear ladder starts at k = 0, so the first pass must see the right sign and a non-vanishing magnitude: that holds for |s| <= 3 at any texture correlation length >= 1 px, and (measured) up to |s| = 8 at sigma >= 2; at sigma 1 it fails beyond |s| = 5 (s = 6 read as 0.25 — the texture is aliased: it moves more than its correlation length several times per view). Near an occlusion boundary the window mixes two slopes (no estimator of a single orientation per window can avoid that). With edge="nearest" input the outer |k|*(N-1)/2 px of the frame see clamped border pixels.
Returns (slope_map, energy): the (H, W) slope map (centre-view coordinates) and the (H, W) gradient energy J_xx + J_yy of the unsheared field (the first pass's 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*.
• lightfield_depth 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.
• lightfield_depth — py -3.11 examples/lightfield_depth.py
• poc_lightfield_depth — py -3.11 examples/poc_lightfield_depth.py
image2d as input)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. 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.