Several Basic concepts used in image normalization

Recently I have read about image normalizationArticleAt the beginning, I first read the e-paper. I don't know much about the several concepts used. Please advise me.
1. probility density function (probability density function)
If p (x, y) is used as the gray scale of the image, its probability density function f (x, y) = p (x, y)/[P (x, y) dual points of dxdy in the specified region]
How big is the configuration in the specified region?
2, mean vector (mean vector)
Cx = [x · f (x, y) dual points of dxdy in the specified region]
Cy = [Y · f (x, y) dual points of dxdy in the specified region]
What is the physical significance of this mean vector?
3, central moments (center moment)
The K + R sub-center moment is defined as follows:
UKR = [(X-cx) ^ K · (Y-cy) ^ r · f (x, y) dual points of dxdy in the specified region]
Also ask for the physical meaning
4, covariance matrix (covariance matrix, total variation matrix)
The definition here is a 2*2 matrix.
[U20 u11]
[U11 u02]
Uxx is defined by the above three types
The role of covariance matrix is expressed as follows in the original article:
The goal of the algorithm is to adjust an image through a sequence of two linear transformations so that the covariance matrix of the compacted image becomes a scaled identical matrix.
In pattern recognition, we use the covariance matrix to decoupled correlated features and to scale the features to make the clusters compact.

 

basically, normalization aims to find a set of parameters using the immutable moment of the image so that it can eliminate the influence of other transformation functions on the image transformation. That is to say, it is converted into a unique standard form to resist the affine transformation.
Soo-chang Pei and Chao-nan Lin 'image normalization for pattern recognition ', image and vision computing Volume 13 Number 10 December 1995, pp711 ~ 723