Several methods of image enhancement and matlab code

1. Gray linear transformation

Gray linear transformation , It is a method of airspace , Directly operate the gray value of each pixel

Suppose the image is $I$

Then the gray value of each pixel is $I(x,y)$

We can get ：

$I(x,y{)}^{\ast }=k\ast I(x,y)+b$

take $k=1,b=16$ You can get

Here are the key codes

original = imread(strcat(strcat('resource\',name),'.bmp'));
transformed = LinearFunction(original, 1, 16);
subplot(1,3,3);
imshow(transformed)
title(' Image after linear transformation ')
imwrite(transformed,strcat(strcat('result\',name),'(linear).jpg'))

2. Histogram equalization transform

This method is usually used to increase the global contrast of many images , Especially when the contrast of the useful data of the image is quite close . In this way , Brightness can be better distributed on histogram . This can be used to enhance the local contrast without affecting the overall contrast , Histogram equalization can achieve this function by effectively expanding the commonly used brightness .

This method is very useful for both background and foreground images that are too bright or too dark , This method, in particular, can bring about X Better display of bone structure in light images and better details in overexposed or underexposed photos . One of the main advantages of this method is that it is a fairly intuitive technology and reversible operation , If the equalization function is known , Then we can restore the original histogram , And the amount of calculation is not big . One disadvantage of this method is that it does not select the data to be processed , It may increase the contrast of background noise and decrease the contrast of useful signals .

Consider a discrete grayscale image $\{x\}$

Give Way $n_i$ Indicates grayscale $i$ Number of occurrences , So the grayscale of the image is $i$ The probability of pixels appearing is ：

$p_x(i)=p(x=i)=\frac{n_i}{n},0\le i<L$

$L$ Is the number of grayscale in the image （ Usually 255）

Corresponding to $p_x$ The cumulative distribution function of , Defined as ：

$cd{f}_x(i)={\sum }_{j=0}^i{p}_x(j)$

Is the cumulative normalized histogram of the image

We create a form of $y=T(x)$ Transformation of , For each value of the original image, it generates a $y$, such $y$ The cumulative probability function of can be linearized in all value ranges , The conversion formula is defined as ：

$cd{f}_y(i)=iK$

For constants K, $CDF$ The nature of allows us to make such transformations , Defined as ：

$cd{f}_y(y^{\prime })=cd{f}_y(T(k))=cd{f}_x(k)$

among $k\in [0,L)$, Be careful $T$ Map different gray levels to $(0,1)$, To map these values to the original domain , You need to apply the following simple transformation to the result ：

$y^{\prime }=y\ast (max\{x\}-min\{x\})+min\{x\}$

Give some results ：

Give the key code :

m = 255;
subplot(1,3,3);
H = histeq(I,m);
imshow(H,[]);
title(‘ Image after histogram equalization ’);

Similarly , We can rgb Image histogram equalization , Here is the result

[M,N,G]=size(I1);
result=zeros(M,N,3);
% Get every point of every layer RGB value , And determine its value 
for g=1:3
    A=zeros(1,256);
    % After each layer , The parameter should be reinitialized to 0
    average=0;
    for k=1:256
        count=0;
        for i=1:M
            for j=1:N
                value=I1(i,j,g);
                if value==k
                    count=count+1;
                end
            end
        end
        count=count/(M*N*1.0);
        average=average+count;
        A(k)=average;
    end
    A=uint8(255.*A+0.5);
    for i=1:M
        for j=1:N
            I1(i,j,g)=A(I1(i,j,g)+0.5);
        end
    end  
end
% Show the treatment effect 
subplot(1,3,3);
imshow(I1);

3. Homomorphic filtering

Homomorphic filtering is used to remove Multiplicative noise (multiplicative noise), It can increase contrast and standardize brightness at the same time , So as to achieve the purpose of image enhancement .

An image can be represented as its Intensity of illumination (illumination) Weight and Reflection (reflectance) The product of components , Although the two are inseparable in the time domain , But through Fourier transform, the two can be linearly separated in the frequency domain . Since the illuminance can be regarded as the lighting in the environment , The relative change is very small , It can be regarded as the low-frequency component of the image ; The reflectivity changes relatively large , It can be regarded as a high-frequency component . The influence of illuminance and reflectivity on pixel gray value is processed respectively , Usually by High pass filter (high-pass filter), Make the lighting of the image more uniform , Achieve the purpose of enhancing the detailed features of the shadow area .

It is ：

For an image , It can be expressed as the product of illumination component and reflection component , That is to say ：

$m(x,y)=i(x,y)\cdot r(x,y)$

among , $m$ It's an image , $i$ Is the illuminance component , $r$ Is the reflection component

In order to use high pass filter in frequency domain , We have to do Fourier transform , But because the above formula is a product , It is not possible to directly operate the illumination component and reflection component , So take the logarithm of the above formula

$ln(m(x,y))=ln(i(x,y))+ln(r(x,y))$

Then Fourier transform the above formula

$\mathcal{F}\{ln(m(x,y))\}=\mathcal{F}\{ln(i(x,y))\}+\mathcal{F}\{ln(r(x,y))\}$

We will $\mathcal{F}\{ln(m(x,y))\}$ Defined as $M(u,v)$

Next, high pass filter the image , In this way, the illumination of the image can be more uniform , The high-frequency component increases and the low-frequency component decreases

$N(u,v)=H(u,v)\cdot M(u,v)$

among $H$ It's a high pass filter

In order to transfer the image from the frequency domain back to the time domain , We are right. $N$ Do inverse Fourier transform

$n(x,y)={\mathcal{F}}^{-1}\{N(x,y)\}$

Finally, use the exponential function to restore the logarithm we took at the beginning

$m^{\prime }(x,y)=exp\{n(x,y)\}$

The results are given

Give some key codes

I=double(I);
[M,N]=size(I);
rL=0.5;
rH=4.7;% The parameters can be adjusted according to the desired effect 
c=2;
d0=10;
I1=log(I+1);% Take the logarithm 
FI=fft2(I1);% The Fourier transform 
n1=floor(M/2);
n2=floor(N/2);
H = ones(M, N);
for i=1:M
    for j=1:N
        D(i,j)=((i-n1).^2+(j-n2).^2);
        H(i,j)=(rH-rL).*(exp(c*(-D(i,j)./(d0^2))))+rL;% Gaussian homomorphic filtering 
    end
end
I2=ifft2(H.*FI);% Inverse Fourier transform 
I3=real(exp(I2));
subplot(1,3,3),imshow(I3,[]);title(' After homomorphic filtering is enhanced ');