spectralbrain.compute_wks#

spectralbrain.compute_wks(decomp, e_values=None, *, n_energies=100, sigma=None, normalize=True)[source]#

Wave Kernel Signature — band-pass per-vertex descriptor.

Derived from the Schrödinger equation. Acts as a bank of band-pass filters in log-eigenvalue space, giving balanced weight to all spectral frequencies (unlike HKS which is low-pass).

\[\text{WKS}(x, e) = C_e \sum_{i=1}^{k} \varphi_i^2(x)\, \exp\!\left( -\frac{(e - \log\lambda_i)^2}{2\sigma^2} \right)\]

where \(C_e\) normalises so the filter weights sum to 1.

Parameters:

  • decomp (SpectralDecomposition)

  • e_values (ndarray, shape (E,), optional) – Log-energy levels. None = auto from eigenvalues.

  • n_energies (int) – Number of auto energy levels.

  • sigma (float, optional) – Gaussian bandwidth. None = auto (Aubry convention).

  • normalize (bool) – Normalise each energy slice to unit L2 norm.

Returns:

ndarray, shape (N, E) – WKS evaluated at each vertex and energy level.

Return type:

ndarray[tuple[Any, …], dtype[floating]]

References

Aubry M, Schlickewei U, Cremers D. The wave kernel signature: a quantum mechanical approach to shape analysis. ICCV 2011.