Because guided filter using a local linear model to enhance the image, the edge details remain.
Because the local linear model is more effective in the color space, the edges of gray images cannot be identified but through the color image of the guided filter it can be well-preserved.
Gain vector K is calculated to fulfill the dynamics according to (22) depending on the local linear model defined by the current winning neuron [i.sup.*] or BMU.
The classical approach to get local linear models can be achieved with RLS (Recursive Least Squares) method.
and [[sigma].sub.k] represents the width coefficients of the kth local linear model.
Zhu and Xu  pointed out that the LPV model in (1)-(3) is not easy to identify due to its complex structure and thus proposed a simpler LPV model structure, which is in a form of blended local linear models. The basic principle of the approach is to first identify several local linear models at fixed operating points.
Clustering can be performed independently of the local linear models. Therefore, clustering is first performed identifying a Gaussian mixture model followed by local linear models to eliminate the underlying effects within each class.
The main advantages are that (1) the measurement of the underlying variables is not necessary, (2) the number of Gaussian components can be estimated, (3) the GMM model can be identified independently of the local linear models, and (4) it is a data-based method; no finite element model is needed.
The local linear model
(2) ensures that q has an edge (i.e., discontinuities) only if I has an edge, because [nabla]q = a[nabla]I.
First, the proposed framework solves a quadratic optimization problem in online control without the calculation of piecewise linearisation or online linearisation procedure for local linear models
. Second, the controller parameters are tuned based on the plant data, which is free of subjective factors, and the optimal parameters result in effective optimization framework that could bring about high control accuracy.
From this point of view, (6) is investigated as a local linear model
with M submodels [y.sub.j] = [[phi].sup.T](t)[[OMEGA].sub.j](j = 1, ..., M), and the jth RBF N([p.sub.j], [phi](t)) is regarded as a time-varying interpolation function for associated linear submodel to preserve the local property.
Then, the problem is reduced to identify the parameters of the subsystems defined as local linear models
and the parameters of the activation functions using numerical optimization algorithms.