lens_area — SEGMENTATION world op

• Data kinds: none → scalar (an op determined by its arguments alone — it takes no image or data input)

• Call: import fullseye as fs; fs.ledger.lens_area(r: 'float', d: 'float') -> 'float' (to call the implementation directly, import segworld; segworld.lens_area(r: 'float', d: 'float') -> 'float'; from the registry, opssegmentation.get("lens_area"))

Usage

Closed-form overlap (lens) area of two equal-radius-r circles at centre distance d; 0 when d >= 2r (lens_area).

Detailed usage guide

• halcon_segmentation family guide

Background guides (the physics and conventions behind this op)

• segmentation_scoring_and_worlds — Scoring segmentations and synthetic worlds with ground truth — which metric is blind to which failure

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.

Runnable examples (verified samples that actually call this op)

• (none yet)

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

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Same category (world)

world_blobs_touching · world_grains_voronoi · world_parts_with_shadow · world_texture_regions · world_gradient_illumination · world_thin_structures · voronoi_cells

*Provenance: segworld.py — SEGMENTATION 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.