typed op• Data kinds: points → signal
• Call: fullseye.apply(img, "tb_mean_curvature", 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_mean_curvature: knob a sweep (docs site)
*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_mean_curvature: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ tb_mean_curvature: other inputs (docs site)
Mean curvature H=(k1+k2)/2. → (N,). An orientation-dependent quantity.
When normals (oriented reference normals, (N,3)) are not given, a convex-side heuristic is used (the concave/convex sign of an open surface is undetermined). Passing oriented normals aligns with the global orientation and gives the correct sign.
Supplement:
• The computation is the same as principal_curvatures (PCA normal of the k+1 neighbourhood + local quadric fit) and returns (k1 + k2) / 2. Units are 1/length.
• The sign convention takes convex as positive; it corresponds to global concave/convex only when normals is given. Without it, H of an open surface is always on the convex side (equivalent to the absolute value).
• Points with fewer than 5 neighbours get 0. k is truncated to N-1.
• A sphere of radius R gives 1/R, a cylinder 1/(2R), a plane 0. A saddle point (k1 = -k2) also gives 0, but gaussian_curvature is negative there, so they can be told apart.
• normals must be (N,3), finite and with non-zero rows (ValueError). Deterministic.
The 3d op mean_curvature 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 k (default 25). b is 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_points 0.50 0.50 tb_mean_curvature 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op mean_curvature. 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).
• curvature_shape_index — py -3.11 examples_3d/curvature_shape_index.py
• minimal_surfaces — py -3.11 examples_3d/minimal_surfaces.py
signal as input)identity · tb_create_funct_1d_array · tb_smooth_funct_1d_gauss · tb_smooth_funct_1d_mean · tb_derivate_funct_1d · tb_integrate_funct_1d · tb_zero_crossings_funct_1d · tb_abs_funct_1d
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.