hessian_determinant — REPRCONV `derivative` op

• Data kinds: hessian → voxel

• Call: import fullseye as fs; fs.ledger.hessian_determinant(hessian) (to call the implementation directly, import reprconv; reprconv.hessian_determinant(hessian); from the registry, opsreprconv.get("hessian_determinant"))

• GPU: none (CPU reference implementation only)

Usage

3-D Hessian hessian → a volume of the determinant det H voxel (signed). The exit from hessian.

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

det H = λ1 λ2 λ3(固有値の積)。球状の明るい塊の中心では 3 つとも負なので負、暗い塊では正、管や板(固有値の 1 つ以上が 0 に近い)では 0 に近い —— Determinant-of-Hessian の塊検出(Lindeberg 1998)の 3-D 版。単位は hessian3d と同じ 1/voxel² の 3 乗(正規化しない。値の比較は同じ尺度の中だけで)。

固有値を経由せず成分から直接 zz(yy·xx − yx²) − zy(zy·xx − yx·zx) + zx(zy·yx − yy·zx) で計算する(固有値分解の丸めを入れないため)。

Args:

hessian: hessian3d の 6 成分 (zz, yy, xx, zy, zx, yx)。torch でも numpy でもよい。

Returns:

(D, H, W) float64。

Raises:

ValueError: 6 成分でない / 形がそろわない / 非有限 / 空。

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)

• type_connectivity_tour — py -3.11 examples/type_connectivity_tour.py

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

correlation_score

Same category (`derivative`)

gradient_magnitude · gradient_coherence · hessian_vesselness

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

hessian_determinant — REPRCONV derivative op