tb_lf_epi_slope — 2D typed op

Data kinds: lightfieldimage

Call: fullseye.apply(img, "tb_lf_epi_slope", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

Usage

Per-pixel slope from the EPI line orientation (structure tensor, one pass).

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*.

Typed bridge of the lightfield op `lf_epi_slope into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. This op has no tunable parameter; a and b` are unused.

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

• (none yet)

Ops the type connects to (they accept image as input)

identity · gaussian · mean_box · bilateral · unsharp · median · min_filter · max_filter

Same category (typed)

tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_angle_3points · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal


*Provenance: ops.py — 2D 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.