Hessian¶
The Hessian matrix collects an image’s second partial derivatives at each pixel. Its two eigenvalues describe the local curvature of the intensity surface along its two principal directions — and their ratio tells you the local shape: roughly equal eigenvalues indicate a blob-like structure, one much larger than the other indicates a ridge/tube-like structure, and both near zero indicates a flat region. This eigenvalue analysis is the shared foundation behind the more specialized ridge/vesselness filters below (Frangi, Meijering, Sato) — each combines the eigenvalues slightly differently to favor a particular kind of structure.
See also
Frangi, Meijering, Sato — filters built directly on this eigenvalue analysis, tuned for tubular/ridge structures
Laplace — a simpler, isotropic second-order filter
Feature Extraction — every other feature