Spectral wavelets#

Kernel signatures (HKS, WKS, BKS) summarize the spectrum with a single weighting per scale. Spectral wavelets instead build a bank of band-pass filters, giving an explicit multi-resolution decomposition of functions on the surface — the spectral-geometry analogue of a classical wavelet transform.

SGW — Spectral Graph Wavelets#

SGW applies a filter kernel \(g(\cdot)\) dilated by a set of scales \(\{t_j\}\) to the spectrum, then maps each filtered response back onto the surface. With \(\hat g\) a band-pass generator (mexican-hat, heat, or Meyer kernels are provided), the wavelet at scale \(t_j\) and vertex \(x\) is

\[ \psi_{t_j}(x) = \sum_i g(t_j \lambda_i)\, \phi_i(x)\, \phi_i(\cdot). \]

For efficiency the transform is computed with a Chebyshev polynomial approximation of the kernel, avoiding a full eigendecomposition when only the wavelet coefficients are needed.

coeffs = sb.sgw_transform(decomp, scales=[...], kernel="mexican_hat")
desc = sb.sgw_descriptor(decomp, ...)   # per-vertex multi-scale descriptor

Available kernels: mexican_hat, heat, and meyer.

ASMWD — Anisotropic Spectral Mesh Wavelet Descriptor#

ASMWD combines the wavelet idea with the anisotropic (curvature-aligned) Laplacian, producing a multi-resolution descriptor that is also direction-sensitive — useful where both scale and orientation of a feature matter.

from spectralbrain.spectral.anisotropic import compute_asmwd
asmwd = compute_asmwd(mesh, ...)