Module curvature 

Surface Curvature Calculation for QSMART

This module computes Gaussian and mean curvatures at the surface of a 3D binary mask, based on the discrete differential geometry approach.

The curvatures are used in QSMART to weight the spatially-dependent filtering near brain boundaries to reduce artifacts.

Uses 2D Delaunay triangulation (via delaunator crate) matching MATLAB’s approach: tri = delaunay(x, y) - triangulates on x,y coordinates with z as height.

Reference: Meyer, M., Desbrun, M., Schröder, P., Barr, A.H. (2003). “Discrete Differential-Geometry Operators for Triangulated 2-Manifolds.” Visualization and Mathematics III, 35-57. https://doi.org/10.1007/978-3-662-05105-4_2

Reference implementation: https://www.mathworks.com/matlabcentral/fileexchange/61136-curvatures

Structs

CurvatureResult

Result of curvature calculation

Point3D 🔒

Simple 3D point structure

Triangle 🔒

Triangle structure

Functions

calculate_curvature_proximity

Calculate proximity maps using curvature at the brain surface

calculate_gaussian_curvature

Simple Gaussian curvature calculation for mask boundary Returns full volume with curvature values at surface voxels

compute_curvatures_from_mesh 🔒

Compute Gaussian and mean curvatures using discrete differential geometry

convolve_1d_direction_masked 🔒

1D convolution with Gaussian kernel along specified axis Uses replicate padding to match MATLAB’s imgaussfilt3 behavior

create_surface_mask 🔒

Create a surface mask (boundary voxels)

dilate_mask 🔒

Dilate a binary mask using spherical structuring element

erode_mask 🔒

Erode a binary mask using spherical structuring element

extract_surface_voxels 🔒

Extract surface voxels from a binary mask

gaussian_smooth_3d_masked 🔒

3D Gaussian smoothing with anisotropic sigma

morphological_close

Morphological closing (dilation followed by erosion)

triangulate_surface 🔒

2D Delaunay triangulation of surface points