tb_alpha_shape_boundary — 2D typed op

• Data kinds: points → signal

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

tb_alpha_shape_boundary: input → output

*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_alpha_shape_boundary: stages (docs site)

On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):

▸ tb_alpha_shape_boundary: other inputs (docs site)

Usage

Returns the boundary point indices via alpha shapes (point cloud → boundary points).

Collects the surface triangles (boundary faces) of the tetrahedra of the Delaunay tetrahedralisation whose circumsphere radius < 1/alpha, and takes their vertex set as the boundary points. Suited to extracting only the points of the surface shell from a solid (surface + interior) point cloud. Increasing alpha makes the allowed radius 1/alpha smaller, giving a tighter boundary (picking up detail).

Parameters

points : array_like (N,3)

alpha : float

A positive real number. The radius threshold is 1/alpha. estimate_alpha gives a guideline.

Returns

boundary_point_indices : numpy.ndarray (K,) int64

Indices of the boundary points into points (ascending, no duplicates). An empty array if there is no boundary.

The 3d op alpha_shape_boundary bridged into the 2-D evolution registry. The implementation is the same; only the calling convention is adapted to op(v, a, b). This op has no tuning points; neither a nor b is used.

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.

Try it in Studio

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_alpha_shape_boundary 0.50 0.50

▸ Load this pipeline  ·  Load & run

Runnable examples (verified samples that actually call this op)

The examples below call the underlying ledger op alpha_shape_boundary. 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).

• sfm_recon — py -3.11 examples_3d/sfm_recon.py

Ops the type connects to (they accept 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

Same category (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.