Learn

The methods behind SpectralBrain — the why, not just the call signature. Each page introduces a family of descriptors, the intuition for what it measures, the mathematics in brief, and the functions that implement it. Reference-level detail lives in the API; full derivations are reserved for the forthcoming book.

• Foundations: the Laplace–Beltrami operator
• Spectral descriptors, in general
• Global fingerprints & embeddings
• Heat-diffusion descriptors
• Wave / band-pass descriptors
• Bates–Kornfeld signatures
• Spectral wavelets
• Functional maps & distances
• Normative modeling

The descriptor families at a glance

Family	Descriptors	Captures
Foundations	LBO eigenpairs (SpectralDecomposition)	the spectral basis everything else is built on
Descriptors in general	the spectral-filter framework	how a spectrum becomes a shape measurement
Global & embeddings	ShapeDNA, GPS	whole-shape fingerprint; intrinsic point embedding
Heat diffusion	HKS, SI-HKS, anisotropic HKS	multiscale local geometry via heat flow
Wave / band-pass	WKS, anisotropic WKS	frequency-localized geometry
Bates–Kornfeld	Bates signatures, BKS, IBKS	spectral-kernel signatures and their inverse
Spectral wavelets	SGW, ASMWD	multi-resolution, optionally anisotropic
Functional maps & distances	functional maps, SDO, DWKS, WESD & co.	cross-shape correspondence and shape distance

Every descriptor in the table reads the same SpectralDecomposition, so the Foundations page is the natural place to begin.