Explain in detail the matrix normalization function normalize() of OpenCV [norm or value range of the scoped matrix (normalization)], and attach norm_ Example code in the case of minmax

function normalize() There are two prototypes ：
Prototype one ：

void cv::normalize(	InputArray 	src,
					InputOutputArray dst,
					double 	alpha = 1,
					double 	beta = 0,
					int 	norm_type = NORM_L2,
					int 	dtype = -1,
					InputArray 	mask = noArray() 
					)	

Prototype two ：

void cv::normalize(	const SparseMat & 	src,
					SparseMat & 	dst,
					double 	alpha,
					int 	normType 
				  )	

The applicable object of prototype 1 is dense matrix , Usually our matrices are dense matrices .
The applicable object of prototype 2 is sparse matrix , Sparse matrices are not very common , So prototype 2 will not be introduced in this blog post .

Before introducing the meaning of each parameter , Let's talk about the function first normalize() The role of .

function normalize() It does two things ：
The first function is to normalize the norm of the matrix ;
The second function is to normalize the value range of the matrix , The value range of normalized matrix is usually what we call normalization .

The second function is that we often use , So this blog post focuses on its second function , The first function will not be introduced in detail .

When it is used to normalize the norm of a matrix , namely norm_type = NORM_MINMAX when , It achieves the following goals through linear zoom and pan operations ：
$\Vert \text{dst}{\Vert }_{L_p}=\text{alpha}$
On the type of dst Represents the objective matrix .$\Vert \text{dst}{\Vert }_{L_p}$ Represents the norm value of the objective matrix .
In the above formula p The value of can be Inf、1、2, Corresponding to three different norms .
When p=Inf when , The corresponding parameter normType The value is NORM_INF;
When p=1 when , The corresponding parameter normType The value is NORM_L1;
When p=2 when , The corresponding parameter normType The value is NORM_L2.

When it is used to normalize the value range of the matrix , It achieves the following goals through linear zoom and pan operations ：

That is, the function normalize() Will range the values in the original matrix from [min(src), max(src)] Scale linearly to [alpha, beta] The scope of the .

According to the above goal , It can be seen that the specific mathematical expression of the implementation is as follows ：

$\frac{dst(i,j)-alpha}{beta-alpha}=\frac{src(i,j)-min(src)}{max(src)-min(src)}$

According to the above formula , You can get dst(i,j) The expression of , as follows ：

$dst(i,j)=(beta-alpha)\ast \frac{src(i,j)-min(src)}{max(src)-min(src)}+alpha$

Next , Start to introduce the significance of its prototype I parameters , Here, copy the prototype again .

void cv::normalize(	InputArray 	src,
					InputOutputArray dst,
					double 	alpha = 1,
					double 	beta = 0,
					int 	norm_type = NORM_L2,
					int 	dtype = -1,
					InputArray 	mask = noArray() 
					)	

• src— Input matrix
• dst— The output matrix .
• alpha— In the case of the first action of this function , It said norm value; In the case of the second function , function normalize() Will range the values in the original matrix from [min(src), max(src)] Scale linearly to [alpha, beta] The scope of the .
• beta— In the case of the first action of this function , It doesn't work , Is an invalid parameter . In the case of the second function , function normalize() Will range the values in the original matrix from [min(src), max(src)] Scale linearly to [alpha, beta] The scope of the .
• norm_type— This parameter determines the function normalize() What is the specific operation . Its values are shown in the following table ：
  
  The most commonly used is the last enumerated value , namely NORM_MINMAX, At this time, the goal and specific principle of this function have been made clear before introducing the parameter meaning of this function .

Last , Attach a pawn norm_type = NORM_MINMAX At the time of the Python Sample code .

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# !/usr/bin/env python
# -*- coding: utf-8 -*-
# OpenCV The version is 4.4.0


import cv2 as cv
import numpy as np

A = np.array([[1, 2, 3, 4, 5],
              [6, 7, 8, 9, 10],
              [11, 12, 13, 14, 15],
              [16, 17, 18, 19, 20],
              [21, 22, 23, 24, 25]], dtype='uint8')

B = A.copy()

cv.normalize(A, B, alpha=100, beta=200, norm_type=cv.NORM_MINMAX)

The operation results are as follows ：

so , By function normalize() The operation of , The matrix A The values of the elements in range from [1,25] The linearity is scaled to [100,200] The scope of the .