feature op• Data kinds: voxel → hessian
• 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")
The six independent components of the 3-D Hessian (fzz, fyy, fxx, fzy, fzx, fyx). Separable conv3d (second/first order × smoothing).
Kernels: 2nd-order [1,−2,1] (gain 1), 1st-order [−0.5,0,0.5] (gain 1), and smoothing [1,2,1]/4 on the remaining axes (gain 1). Diagonal components are "2nd-order on that axis × smoothing on the other 2 axes", cross components are "1st-order on 2 axes × smoothing on the remaining axis". Units are the true value in 1/voxel² (unlike the 32x gain of sobel3d). Edges replicate. Returns a list of 6 torch tensors, each (D,H,W) float32, on device, in the order (zz, yy, xx, zy, zx, yx) (axis 0=z, 1=y, 2=x). If you need numpy, use .cpu().numpy(). The input is numpy-like (converted to float32).
Uses: principal curvatures in curvature_maps (used together with sobel3d), detection of blob/tubular structures.
• 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.
• diff_features — py -3.11 examples_3d/diff_features.py
hessian as input)feature)sobel3d · curvature_maps · edt_jfa · edt_jfa_vector · vol_frangi · vol_local_std · vol_local_thickness · vol_orientation_coherence
*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.