Heat Kernel Signature on a surface

Compute the Laplace–Beltrami decomposition of a small synthetic surface and render its Heat Kernel Signature at one time scale. Replace the icosphere with sb.load_freesurfer_surface("lh.pial") to run on a real cortical surface.

import numpy as np
import pyvista as pv

import spectralbrain as sb

Build a small synthetic surface (a perturbed sphere) so the example is light.

sphere = pv.Icosphere(nsub=4, radius=1.0)
warp = 0.15 * np.sin(4 * sphere.points[:, 2])
sphere.points[:, 0] += warp
vertices = np.asarray(sphere.points)
faces = sphere.faces.reshape(-1, 4)[:, 1:]  # PyVista (n,4) -> (n,3)

Decompose once, then read the descriptor off the decomposition.

mesh = sb.BrainMesh(vertices, faces)
decomp = mesh.decompose(k=80)
hks = sb.compute_hks(decomp, t_values=np.geomspace(0.01, 1.0, 3))

Render the mid-scale HKS channel on the surface.

surf = pv.PolyData(vertices, sphere.faces)
surf["HKS"] = hks[:, 1]

plotter = pv.Plotter(off_screen=True, window_size=(600, 600))
plotter.add_mesh(surf, scalars="HKS", cmap="magma", smooth_shading=True,
                 scalar_bar_args={"title": "HKS (t mid)"})
plotter.view_isometric()
plotter.show()