circularity — 2D features op

• Data kinds: region → feature

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

• HALCON equivalent: circularity (the HALCON reference is a useful guide to its meaning and parameters)

circularity: 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):

▸ circularity: stages (docs site)

Usage

Circularity `min(1, area / (pi * max^2)), where max is the **largest distance from the centre of gravity to a contour pixel**. It is 1 for a circle and smaller for elongated shapes or ones with large bulges or holes. If several connected components are present, only the largest one is evaluated. **The same formula as** HALCON's circularity` (Shape factor for the circularity (similarity to a circle) of a region.).

> The detailed description below is the original text — the summary and the headings are translated.

★2026-09-26 まで等周比 `4π・面積/周囲長²` という別の量を返していた。

名前は HALCON から借りているのに数が違うので、HALCON のレシピを移してきた人が

同じしきい値で違う判定を得ていた(正方形で 0.826 対 0.670 と順序まで変わる)。

`docs/hardening/halcon-named-shape-factors.md`。

`a, b` は未使用。

Detailed usage guide

• gallery2d_features family guide

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.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

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.

threshold 0.50 0.50
circularity 0.50 0.50

▸ Load this pipeline  ·  Load & run

Runnable examples (verified samples that actually call this op)

• gallery2d_features — py -3.11 examples/gallery2d_features.py

• poc_cell_counting — py -3.11 examples/poc_cell_counting.py

• poc_particle_sizing — py -3.11 examples/poc_particle_sizing.py

• poc_rotation_invariance_audit — py -3.11 examples/poc_rotation_invariance_audit.py

• shape_factors_closed_form — py -3.11 examples/shape_factors_closed_form.py

Ops the type connects to (they accept feature as input)

identity · feature_to_img

Same category (features)

effective_bit_depth · blob_count · area_frac · count_contours · total_length · vol_count · sk_euler · sk_entropy_feat


*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.