principal curvature of level surface

Lecture 11: Differential Geometry
Ridges for Image Analysis

my note

图像处理上

The eigenvalues and eigenvectors of the Hessian have geometric meaning:
The first eigenvector (the one whose corresponding eigenvalue has the largest absolute value) is the direction of
greatest curvature (second derivative).
The second eigenvector (the one whose corresponding eigenvalue has the smallest absolute value) is the direction
of least curvature.
The corresponding eigenvalues are the respective amounts of these curvatures.
The eigenvectors of H are called principal directions and are directions of pure curvature (no mixed partial derivative).
They are always orthogonal.
The eigenvalues of H are called principal curvatures and are invariant under rotation. They are denoted 1 and 2
and are always real valued.


为什么图像上 Hess 代替了 T