Additionally, Cartesian coordinates are highly correlated, that is, the Hessian matrix has many non-diagonal terms that are not close to zero.
32.
The determinant of the Hessian matrix is used as a measure of local change around the point and points are chosen where this determinant is maximal.
33.
The maxima of the determinant of the Hessian matrix are then interpolated in scale and image space with the method proposed by Brown, et al.
34.
Given a function f ( x ), its gradient ( \ nabla f ), and positive definite Hessian matrix B, the Taylor series is:
35.
Like the Harris affine algorithm, these interest points based on the Hessian matrix are also spatially localized using an iterative search based on the Laplacian of Gaussians.
36.
Where is the gradient of w . r . t ., is the Hessian matrix of w . r . t ., and is the trace operator.
37.
In most " real-life " circumstances the Hessian matrix is Schwarz'theorem gives a sufficient condition on " f " for this to occur.
38.
*PM : relations between Hessian matrix and local extrema, id = 3375-- WP guess : relations between Hessian matrix and local extrema-- Status:
39.
*PM : relations between Hessian matrix and local extrema, id = 3375-- WP guess : relations between Hessian matrix and local extrema-- Status:
40.
The Hessian matrix is a matrix of all the second order partial derivatives, which are used to investigate the stationary points of the function, important for mathematical optimization.
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