hessian_vesselness — REPRCONV `derivative` op

• Data kinds: hessian → voxel

• Call: import fullseye as fs; fs.ledger.hessian_vesselness(hessian, alpha=0.5, beta=0.5, c=None, black_ridges=False) (to call the implementation directly, import reprconv; reprconv.hessian_vesselness(hessian, alpha=0.5, beta=0.5, c=None, black_ridges=False); from the registry, opsreprconv.get("hessian_vesselness"))

• GPU: none (CPU reference implementation only)

Usage

3-D Hessian → Frangi vesselness voxel, range [0, 1].

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

固有値を |λ1| ≤ |λ2| ≤ |λ3| に並べ、Ra = |λ2|/|λ3|(板と管を分ける)、Rb = |λ1|/sqrt(|λ2 λ3|)(塊を除く)、S = sqrt(λ1²+λ2²+λ3²)(背景の雑音を除く)から

V = (1 − exp(−Ra²/2α²)) · exp(−Rb²/2β²) · (1 − exp(−S²/2c²))

を返す(Frangi et al. 1998, MICCAI)。明るい管(black_ridges=False)では λ2 > 0 か λ3 > 0 の voxel を 0 にする(暗い管なら符号を逆に)。c の既定は Frangi の勧めどおり S の最大値の半分。

vol_frangi は体積から Hessian を自分で作る(尺度ごとに)のに対し、こちらは hessian 型を受ける —— Hessian の出どころ(hessian3d / 外部の微分)を選べ、同じ Hessian から hessian_determinant など複数の量を引き出せる。1 尺度だけ(多尺度の最大は呼ぶ側で取る)。

Args:

hessian: hessian3d の 6 成分 (zz, yy, xx, zy, zx, yx)。

alpha, beta: Frangi の感度(既定 0.5 / 0.5)。> 0。

c: 構造の強さの感度。None で max(S)/2。> 0。全面 0 の Hessian では 0 を返す。

black_ridges: True で暗い管(背景より暗い)を拾う。

Returns:

(D, H, W) float64、[0, 1]。

Raises:

ValueError: 6 成分でない / 非有限 / alpha・beta・c が正でない。

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)

• hessian_numpy_chain — py -3.11 examples/hessian_numpy_chain.py

• type_connectivity_tour — py -3.11 examples/type_connectivity_tour.py

Ops the type connects to (they accept `voxel` as input)

correlation_score · voxel_to_hessian

Same category (`derivative`)

gradient_magnitude · gradient_coherence · voxel_to_hessian · hessian_determinant

*Provenance: reprconv.py — REPRCONV operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

hessian_vesselness — REPRCONV derivative op