文档介绍：Global optimization
Global optimization
Regularization
Robust regularization
Markov random fields
Binary MRFs
Ordinal-valued MRFs
Unordered labels
Conditional random fields
Regularization
It constructs a continuous global energy function that describes the desired characteristics of the solution and then finds a minimum energy solution using sparse linear systems or related iterative techniques.
Regularization
One-dimensional functions:
Two-dimensions functions:
Regularization
Membrane
Thin-plate spline
Thin-plate spline under tension
Controlled-continuity splines
Regularization
Regularization: Smoothness term, data term
The data term measures the distance between the function f(x,y) and a set of data points
di=d(xi,yi),
For a problem like noise removal, a continuous version of this measure can be used,
Regularization
To obtain a global energy that can be minimized, the two energy terms are usually added together,
In order to find the minimum of this continuous problem, the function f(x,y) is usually first discretized on a regular grid. And use finite element analysis.(the function with a piecewise continuous spline)
Regularization
For both the first-order and second-order smoothness functionals, the corresponding discrete smoothness energy functions e
Regularization
The two-dimensional discrete data energy is written as
The total energy of the discretized problem can now be written as a quadratic form
Robust regularization
Non-quadratic robust penalty functions replace Quadratic(L2) norms.
Replace