curvature_maps — 3D feature op

Data kinds: voxelcurvature

Call: import fullseye as fs; fs.ledger.curvature_maps(vol, device='cpu', mc=0.000625) (to call the implementation directly, import match3d; match3d.curvature_maps(vol, device='cpu', mc=0.000625); from the registry, ops3d.get("curvature_maps"))

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

Usage

Principal curvatures of a level set → the shape index S (Koenderink) and curvedness. Closed form (Kindlmann 2003).

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

2D 輪郭の曲率(スカラー 1 個)の 線→面リフト: 曲面は主曲率 κ1,κ2 の 2 個を持つ。

mean = (κ1+κ2)/2 = (|g|²trH − gᵀHg)/|g|³、Gauss K = κ1κ2 = gᵀadj(H)g/|g|⁴(g=∇, H=Hessian)。

S=(2/π)atan2(κ1+κ2, κ1−κ2) ∈[-1,1] は 強度・回転に不変な局所曲面型(cup−1/rut/saddle0/

ridge+.5/cap+1)。外向き法線規約で明凸 blob=cap(+1)。返り値 (S, curvedness, mask, |g|)、全 torch。

単位系: sobel3d の分離 conv 利得 32(deriv[-1,0,1]×平滑[1,2,1]²)をここで割り戻すので、

κ1,κ2/curvedness は 真の 1/voxel 単位(半径 R の球殻で curvedness=1/R)、|g| と

mask 閾値 mc は voxel あたりの真の勾配単位。旧版(〜2026-08-29)は割り戻しを忘れ

curvedness が 1/32 倍・mc が生 sobel3d 単位だった(shape index S は比なので影響なし)。

旧 mc 値を使っていた場合は 1/32 して渡すこと(既定値 0.02→6.25e-4 も等価変換済み)。

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 curvature as input)

fuse_to_voxel

Same category (feature)

sobel3d · hessian3d · 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.