typed op• Data kinds: points → image
• Call: fullseye.apply(img, "tb_normals_to_egi", 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.*
Sweeping knob a (0.1 / 0.5 / 0.9, the other knob at its default):
▸ tb_normals_to_egi: knob a sweep (docs site)
Sweeping knob b (0.1 / 0.5 / 0.9, the other knob at its default):
▸ tb_normals_to_egi: knob b sweep (docs site)
Stages (the ops that come before → this op, left to right):
▸ tb_normals_to_egi: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ tb_normals_to_egi: other inputs (docs site)
Normals (N,3) -> the image2d of the Extended Gaussian Image (n_el, n_az).
A 2-D histogram of directions (Horn, *Extended Gaussian Images*, Proc. IEEE 72(12) 1984). A map of "how much surface faces which way"; for an object dominated by planes, 1 bin gets a peak. Irreversible —— it discards the directional resolution of one bin width. The discarded amount can be measured: the angle between the centre direction of the most frequent bin and the mean input direction is the quantisation error; with the default (36, 18) it is 3.7 degrees measured against a bin width of 10 degrees (reported by selftest).
The elevation bins are equal divisions of sin(el) (equal solid angle). Dividing equally in degrees makes the poles excessively fine and raises a false peak saying "faces are concentrated at the north pole".
★Passing a point cloud of positions raises no exception. backends_typed.TYPE_TO_SORT folds normals into points, so neither the evolver nor the ledger tells them apart. This op only looks at directions (it discards length), so passing (N,3) coordinates returns, plausibly, a histogram of "the direction from the origin to each point". Measured (2026-09-08, a curve of 200 points vs normals all pointing straight up): non-zero bins change 1 → 12 and the maximum bin 200 → 44, and that is all; the sum is 200 in both. "The sum matches the number of points, so it is correct" cannot tell them apart. With fullseye.set_system("extra_checks", "on"), vectors that deviate from unit length are rejected (Raises below).
Args:
normals: (N, 3).
n_az: number of azimuth bins (default 36 = 10-degree steps).
n_el: number of elevation bins (default 18).
Returns:
(n_el, n_az) float64 count map (row = elevation, column = azimuth).
Raises:
ValueError: number of bins below 1 / above the limit / invalid input.
ValueError: with extra_checks='on', when it contains vectors whose length deviates from 1 by more than 1e-6
(catches the accident of passing a point cloud of positions as normals).
The reprconv op normals_to_egi bridged into the 2-D evolution registry. The implementation is the same; only the calling convention is adapted to op(v, a, b). a sweeps n_az (default 36) and b sweeps n_el (default 18). ★The bridged op returns the fraction (the share of normals falling in each bin, summing to 1, range [0,1]) obtained by dividing the counts by the total —— to match the [0,1] contract of the declared sort image (with raw counts, values such as a maximum of 48 came out, 2026-10-07). The raw counts are returned by reprconv.normals_to_egi / fullseye.ledger.normals_to_egi.
• 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_points 0.50 0.50 tb_normals_to_egi 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op normals_to_egi. 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).
• representation_conversion — py -3.11 examples/representation_conversion.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.