typed op• Data kinds: lightfield → image
• 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])
*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*
*Knob a does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
Stages (the ops that come before → this op, left to right):
▸ tb_lf_epi_slope: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ tb_lf_epi_slope: other inputs (docs site)
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.
• 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 program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.
img_to_lightfield 0.50 0.50 tb_lf_epi_slope 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op lf_epi_slope. This bridge op is the same implementation adapted to the fn(v, a, b) convention, so the behaviour carries over unchanged (only the call form differs).
• lightfield_depth — py -3.11 examples/lightfield_depth.py
• poc_lightfield_depth — py -3.11 examples/poc_lightfield_depth.py
image as input)identity · gaussian · mean_box · bilateral · unsharp · median · min_filter · max_filter
typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*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.