A good key point is the angle. This comes from Harris' corner work and good tracking features (KLT), and then is highlighted by the publication of Mikolajczyk and Schmid .
Intuitively, the angle is a good function because it is the intersection of two lines, while one line segment can move along its direction, which leads to less accurate localization. A line segment is an edge, i.e. First order derivative (gradient). An angle is an edge that changes direction dramatically. This is measured by a second-order derivative, therefore, the Hessian matrix is used, containing the values of the second derivatives of the direction.