feature op• データ種: voxel → measurement
• 呼び出し: import fullseye as fs; fs.ledger.vol_euler_number(vol_binary, connectivity=26) (実装を直接呼ぶなら import volops; volops.vol_euler_number(vol_binary, connectivity=26)、台帳から引くなら ops3d.get("vol_euler_number"))
• 台帳経由の戻り値: fullseye.ledger.vol_euler_number(...) は**宣言 out 型 measurement の値だけ**を返す(本体は補助情報も返す)。捨てられた側が要るときは fullseye.ledger.vol_euler_number.raw(...)、または volops.vol_euler_number を直接呼ぶ。
• 本体の返り: 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.
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• ct_porosity_and_fibre_morphometry — py -3.11 examples_3d/ct_porosity_and_fibre_morphometry.py
measurement を入力に取れる)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. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.