feature op• Data kinds: voxel → measurement
• Call: import fullseye as fs; fs.ledger.vol_euler_number(vol_binary, connectivity=26) (to call the implementation directly, import volops; volops.vol_euler_number(vol_binary, connectivity=26); from the registry, ops3d.get("vol_euler_number"))
• Return value through the ledger: fullseye.ledger.vol_euler_number(...) returns **only the declared out type measurement** (the underlying function also returns auxiliary values). When you need what was dropped, use fullseye.ledger.vol_euler_number.raw(...) or call volops.vol_euler_number directly.
• Underlying return: chi(b0-b1+b2)
Euler characteristic of a binary volume, split into its three Betti numbers.
`chi = b0 - b1 + b2 where b0 counts **separate objects**, b1`
counts tunnels (handles that pass right through) and `b2` counts
enclosed cavities. For porous media that split is the whole point:
`b1` is open, connected porosity — the paths a fluid can take — while
`b2 is closed porosity that no fluid reaches. A single chi` cannot
tell a foam with many tunnels from one with many sealed bubbles; the three
numbers can.
*connectivity* is `6, 18 or 26` for the foreground; the background
is counted with the complementary neighbourhood (`26 vs 6`), which is
what makes the pair of counts consistent — using the same neighbourhood for
both is the classical way to produce a set that is simultaneously connected
and disconnected.
Returns ``{"euler": chi, "objects": b0, "tunnels": b1, "cavities": b2,
"connectivity": connectivity}`. b1 is derived as b0 + b2 - chi`, so
it inherits the exactness of the other three.
HALCON's `euler_number` is 2-D (regions) only; there is no voxel
equivalent.
• 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.
• ct_porosity_and_fibre_morphometry — py -3.11 examples_3d/ct_porosity_and_fibre_morphometry.py
measurement as input)vol_gaussian_psf · fuse_to_voxel · fresnel_reflectance · snell_angle
feature)sobel3d · hessian3d · curvature_maps · edt_jfa · vol_frangi · vol_local_std · vol_local_thickness · vol_orientation_coherence
*Provenance: volops.py — 3D 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.