Wave / band-pass descriptors#

Where the heat signature averages over scales (a low-pass view), the Wave Kernel Signature localizes in frequency — a band-pass view of the same spectral basis. The two are complementary: HKS is better at coarse localization, WKS at separating features that live at similar scales but different “frequencies”.

WKS — the Wave Kernel Signature#

The WKS evaluates the probability of a quantum particle, with a log-energy distribution centered at \(e\), being measured at point \(x\):

\[ \text{WKS}(x, e) = C_e \sum_i \phi_i(x)^2 \, \exp\!\left( -\frac{(e - \log \lambda_i)^2}{2\sigma^2} \right). \]

By scanning the energy \(e\) across the spectrum, each vertex gets a signature that responds to a narrow band of eigenfrequencies at a time. This frequency selectivity makes the WKS sharper than the HKS for fine feature matching.

wks = sb.compute_wks(decomp, n_energies=100)   # (n_vert, n_energies)

Anisotropic WKS#

As with the heat family, an anisotropic WKS replaces the isotropic LBO with a curvature-aligned anisotropic_laplacian(), so the band-pass response becomes direction-sensitive.

from spectralbrain.spectral.anisotropic import compute_anisotropic_wks
a_wks = compute_anisotropic_wks(mesh, ...)

Tip

HKS vs. WKS in one line: HKS = how much heat stays (multiscale, low-pass), WKS = which frequencies live here (band-pass). Many studies stack both.