Hessian

Module to compute curvature measures based on Hessian Matrix

Usefull for filtering vasculature data

hessian(source, sink=None, sigma=None)

Returns the hessian matrix at each location calculatd via finite differences.

Arguments

sourcearray

Input array.

sinkarray

Output, if None, a new array is allocated.

Returns

hessianarray:

5d array with the hessian matrix in the first two dimensions.

eigenvalues(source, sink=None, sigma=None)

Hessiean eigenvalues of source data

Arguments

sourcearray

Input array.

sinkarray

Output, if None, a new array is allocated.

sigmafloat or None

If not None, a Gaussian filter with std sigma is applied initialliy.

Returns

sinkarray

The three eigenvalues along the first axis for each source.

lambda123(source, sink=None, gamma12=1.0, gamma23=1.0, alpha=0.25, sigma=None, threshold=None)

Generalized tubness measure of source data.

Arguments

sourcearray

Input array.

sinkarray

Output, if None, a new array is allocated.

gamma12, gamma23, alphafloat

Parameters for the tubness measure.

sigmafloat or None

If not None, a Gaussian filter with std sigma is applied initialliy.

Returns

sinkarray

The tubness measure.

Note

Reference: Sato et al. Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images, Medical Image Analysis 1998, pp 143–168.

tubeness(source, sink=None, threshold=None, sigma=None)

Tubeness mesure of source data

Arguments

sroucearray

Input array.

sinkarray

Output, if None, a new array is allocated.

thresholdfloat or None

If float, the tubeness is thresholded at this level.

sigmafloat or None

If not None, a Gaussian filter with std sigma is applied initialliy.

Returns

sink3-D array

Tubness output.

Note

The tubness is the geometric mean of the two smallest eigenvalues.