region op• Data kinds: region → region
• Call: fullseye.apply(img, "em_skeleton", 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):
▸ em_skeleton: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ em_skeleton: other inputs (docs site)
Eckhardt–Maderlechner-style invariant thinning (the same family as HALCON skeleton).
Source: U. Eckhardt, G. Maderlechner, "Invariant Thinning", Int. J. Pattern Recognition and AI 7:1115-1144 (1993). The implementation rules follow M. Couprie "Note on fifteen 2D parallel thinning algorithms": a clean-room implementation of the EM93 definition. Checked against the EM93 reference outputs published in that note: for shape 1 the skeleton's pixel set matches bit for bit (724/724), for shapes 2/3 the pixel counts match the published values (2434 / 3895). tests/test_regions2.py::test_em_skeleton_matches_published_em93_reference. (No direct comparison with an actual HALCON installation has been made, but it matches the reference output of the same published algorithm that HALCON relies on):
interior = pixel whose 4-neighbours are all foreground
simple = (8,4) simple point (1 foreground 8-connected component ∧ 1 adjacent background 4-connected component)
perfect = the neighbour in some 4-direction is interior, and the opposite direction is background
repeat "delete all pixels that are both simple and perfect simultaneously" until a fixed point
Note: if the note's transcription is implemented literally, "count simple using strong (4) connected components only", the parallel deletion removes diagonal bridges simultaneously and breaks the topology (measured on a counterexample). This implementation, with simple taken as the standard (8,4) simple point, matched the reference output bit for bit, which confirms that this is the correct reading of EM93.
Fully parallel, symmetric (commutes with 90-degree rotation/mirroring), topology-preserving and idempotent. Keeps more branches than the Zhang–Suen-family sk_skeleton (measured 1.4-1.5 times the pixel count = consistent with the character of EM in Couprie's comparison table: symmetric, many branches). Post-processing spurs with pruning is also the same practice as HALCON. Knobs a, b are unused.
Border handling: treat everything outside the image as background (0) (measured; tools/impl2/border_probe.py).
• gallery2d_region family guide
• 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 canonical algorithm (author, year) and its uses are named in the family usage guide above.
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.
threshold 0.50 0.50 em_skeleton 0.50 0.50
▸ Load this pipeline · Load & run
• gallery2d_region — py -3.11 examples/gallery2d_region.py
region as input)identity · reg_erode · reg_dilate · reg_open · reg_close · fill_holes · select_largest · remove_small
region)reg_erode · reg_dilate · reg_open · reg_close · fill_holes · select_largest · remove_small · invert_region
*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.