Digital image processing (Digital Image Processing) is a method and technology for removing noise, enhancing, restoring, segmenting, and extracting features of an image through a computer. This column will summarize the key basic knowledge of digital image processing in the form of study notes. Welcome to learn and communicate together!
Column link: Digital image processing study notes

1. Array and matrix operations

The image can be regarded as a matrix equivalently

In fact, in many cases, operations between images are performed using matrix theory

For example 2 × 2 images $\begin{bmatrix} a_{11} &a_{12} \\ a_{21}&a_{22} \end{bmatrix}$ and $\begin{bmatrix} b_{11} &b_{12} \\ b_{21}&b_{22} \end{bmatrix}$

Array multiplication is $\begin{bmatrix} a_{11} &a_{12} \\ a_{21}&a_{22} \end{bmatrix}\begin{bmatrix} b_{11} &b_{12} \\ b_{21}&b_{22} \end{bmatrix}=\begin{bmatrix} a_{11}b_{11} &a_{12}b_{12} \\ a_{21}b_{21}&a_{22}b_{22} \end{bmatrix}$

Multiplying arrays in digital image processing corresponds to dot product (. *) In MATLAB

☞When we talk about the exponentiation of an image, it means that every pixel is exponentiated;
☞When we talk about an image divided by another image, it means that there is a phase between the corresponding pixels. except.

Second, linear operation and nonlinear operation

One of the most important classifications of image processing methods is whether it is linear or nonlinear.
Consider the general operator H, which produces an output image g (x, y) for a given input image f (x, y)
H [f (x, y)] = g (x, y)

If it is , then call H a linear operator.

Now suppose that H is a summation operator ∑, whose function is to simply sum

$\sum [a_{i}f_{i}(x,y)+a_{j}f_{j}(x,y)]=\sum a_{i}f_{i}(x,y)+\sum a_{j}f_{j}(x,y)$ $=a_{i}\sum f_{i}(x,y)+ a_{j}\sum f_{j}(x,y)$ $=a_{i}g_{i}(x,y)+a_{j}g_{j}(x,y)$
Note: It is an array summation, not all elements of the image, so the summation of a single image is the image itself

This method is used to prove whether the corresponding operation is linear operation or nonlinear operation ( left = right → linear; left ≠ right → nonlinear )

Example: There are two images for maximum value operation. Now suppose let $a{_{1}}$ = 1 and $a{_{2}}$ = -1,

Calculate the left

Calculate the right

We found that the left side is not equal to the right side (-2 ≠ -4), so far it has been proved that the operation of finding the maximum value is usually non-linear.

Three, arithmetic operation

The arithmetic operations between images are array operations (the arithmetic operations are performed between the corresponding arithmetic pairs)

Image arithmetic operations involve images of the same size

Image with added : S (X, Y) = F (X, Y) + F (X, Y)
image with subtraction : G (X, Y) = F (X, Y) - F (X, Y)
image with by : D (X, Y) = F (X, Y) × F (X, Y)
image with addition : V (X, Y) = F (X, Y) ÷ F (X, Y)
where, x = 1,2,3, ..., M-1, y = 1,2,3, ..., N-1
Generally, M and N are the rows and columns of the image, s, g, d and v are the size Image for M × N

Image with added : for noisy image noise ;
image with subtraction : enhanced difference
image with the multiplication / division : Correction / eliminate shadows