hessian3d — 3D feature op

Data kinds: voxelhessian

Call: import fullseye as fs; fs.ledger.hessian3d(vol, device='cpu') (to call the implementation directly, import match3d; match3d.hessian3d(vol, device='cpu'); from the registry, ops3d.get("hessian3d"))

GPU: this op has a GPU path (device="cuda")

Usage

The six independent components of the 3-D Hessian (fzz, fyy, fxx, fzy, fzx, fyx). Separable conv3d (second/first order × smoothing).

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

カーネル: 2 階 [1,−2,1] (利得 1)、1 階 [−0.5,0,0.5] (利得 1)、残りの軸は [1,2,1]/4 の平滑

(利得 1)。対角成分は「その軸の 2 階 × 他 2 軸の平滑」、交差成分は「2 軸の 1 階 × 残り軸の

平滑」。単位は 1/voxel² の真の値(`sobel3d` の 32 倍利得とは違う)。端は replicate。

返り値は list の torch tensor 6 本、各 `(D,H,W) float32、device` 上、順は

(zz, yy, xx, zy, zx, yx)(軸 0=z, 1=y, 2=x)。numpy が要れば `.cpu().numpy()`。入力は

numpy 相当(float32 に変換)。

用途: `curvature_maps の主曲率(sobel3d` と組で使う)、blob/管状構造の検出。

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.

Runnable examples (verified samples that actually call this op)

diff_featurespy -3.11 examples_3d/diff_features.py

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

fuse_to_voxel

Same category (feature)

sobel3d · curvature_maps · edt_jfa · vol_frangi · vol_local_std · vol_local_thickness · vol_orientation_coherence · vol_euler_number


*Provenance: match3d.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.