vol_frangi — 3D `feature` op

• Data kinds: voxel → voxel

• Call: import fullseye as fs; fs.ledger.vol_frangi(vol, scales=(1, 2, 3), alpha=0.5, beta=0.5, c=None, black_ridges=False) (to call the implementation directly, import volops; volops.vol_frangi(vol, scales=(1, 2, 3), alpha=0.5, beta=0.5, c=None, black_ridges=False); from the registry, ops3d.get("vol_frangi"))

Usage

3-D Frangi vesselness — multiscale tubular-structure enhancement.

For every `sigma` in *scales* the gamma-normalised Hessian is formed, its

three eigenvalues `|l1| <= |l2| <= |l3|` are taken, and the Frangi response

V = (1 - exp(-Ra2 / 2 alpha2)) * exp(-Rb2 / 2 beta2)

• (1 - exp(-S2 / 2 c2))

is evaluated, where `Ra = |l2|/|l3| (plate vs. line), Rb = |l1|/sqrt|l2 l3|`

(blob deviation) and `S = sqrt(l1**2 + l2**2 + l3**2)` (structure strength).

The response is set to 0 where the contrast polarity is wrong (bright tube:

`l2 > 0 or l3 > 0; black_ridges=True` flips this). The maximum over

scales is taken and the volume is normalised to `[0, 1]`.

Parameters

----------

scales : sequence of float — Gaussian sigmas, in voxels, to bracket the

vessel *radii* of interest (see the module "scale-dependent" limitation).

alpha, beta : sensitivities of the plate- and blob-suppression terms (Frangi's

defaults 0.5).

c : half the maximum Hessian norm `S at each scale when None` (Frangi's

adaptive suggestion); otherwise a fixed structure-strength scale.

black_ridges : `False` (default) enhances *bright* tubes on a dark

background; `True` enhances *dark* tubes on a bright background.

Returns a `(D, H, W) float64 volume in [0, 1]`. Reference: Frangi et al.,

MICCAI 1998.

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)

• vessel_metrology — py -3.11 examples_3d/vessel_metrology.py

• volume_downsampling — py -3.11 examples_3d/volume_downsampling.py

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

voxel_to_mips · voxel_to_mesh · signed_distance_field · to_points · sobel3d · hessian3d · curvature_maps · edt_jfa

Same category (`feature`)

sobel3d · hessian3d · curvature_maps · edt_jfa · vol_local_std · vol_local_thickness · vol_orientation_coherence · vol_euler_number

*Provenance: volops.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

vol_frangi — 3D feature op