Module frangi 

Frangi Vesselness Filter for 3D tubular structure detection

This filter uses eigenvalues of the Hessian matrix to detect tubular (vessel-like) structures.

Reference: Frangi, A.F., Niessen, W.J., Vincken, K.L., Viergever, M.A. (1998). “Multiscale vessel enhancement filtering.” MICCAI’98, LNCS vol 1496, 130-137. https://doi.org/10.1007/BFb0056195

Reference implementation: https://www.mathworks.com/matlabcentral/fileexchange/24409-hessian-based-frangi-vesselness-filter

Structs

FrangiParams

Parameters for Frangi vesselness filter

FrangiResult

Result of Frangi filter including vesselness and scale information

Functions

compute_vesselness 🔒

Compute vesselness measure from sorted eigenvalues |lambda1| <= |lambda2| <= |lambda3|

convolve_1d_direction 🔒

Apply 1D convolution along specified axis with replicate padding Matches MATLAB’s imgaussian which uses ‘replicate’ boundary handling

eigenvalues_3x3_cardano 🔒

Analytical eigenvalues of 3×3 symmetric matrix using Cardano’s method

eigenvalues_3x3_symmetric 🔒

Compute eigenvalues of a 3x3 symmetric matrix using Householder + QL algorithm

frangi_filter_3d

Apply 3D Frangi vesselness filter

frangi_filter_3d_default

Simple wrapper for Frangi filter with default parameters

frangi_filter_3d_with_progress

Frangi filter with progress callback

gaussian_smooth_3d 🔒

3D Gaussian smoothing using separable 1D convolutions

hypot 🔒

Compute hypotenuse avoiding overflow/underflow

sort_by_abs 🔒

Sort three values by absolute value

tql2 🔒

Symmetric tridiagonal QL algorithm

tred2 🔒

Symmetric Householder reduction to tridiagonal form