Normalization (image processing)

In <a href="/facts/Image_processing/zenalNCf">image processing</a>, normalization is a process that changes the range of <a href="/facts/Pixel/UzwBvXBV">pixel</a> intensity values. Applications include photographs with poor <a href="/facts/Contrast_(vision)/zD9F91Je">contrast</a> due to glare, for example. Normalization is sometimes called contrast stretching or <a href="/facts/Histogram/oMmvqGEA">histogram</a> stretching. In more general fields of data processing, such as <a href="/facts/Digital_signal_processing/PEG7azr8">digital signal processing</a>, it is referred to as <a href="/facts/Dynamic_range/zxcuI4Fn">dynamic range</a> expansion.
The purpose of dynamic range expansion in the various applications is usually to bring the image, or other type of signal, into a range that is more familiar or normal to the senses, hence the term normalization. Often, the motivation is to achieve consistency in dynamic range for a set of data, signals, or images to avoid mental distraction or fatigue. For example, a newspaper will strive to make all of the images in an issue share a similar range of <a href="/facts/Grayscale/Tjb9kR8v">grayscale</a>.
Normalization transforms an n-dimensional <a href="/facts/Grayscale/Tjb9kR8v">grayscale</a> image

I
        :
        {
        
          X
        
        ⊆
        
          
            R
          
          
            n
          
        
        }
        →
        {
        
          Min
        
        ,
        .
        .
        ,
        
          Max
        
        }
      
    
    {\displaystyle I:\{\mathbb {X} \subseteq \mathbb {R} ^{n}\}\rightarrow \{{\text{Min}},..,{\text{Max}}\}}

with intensity values in the range 
  
    
      
        (
        
          Min
        
        ,
        
          Max
        
        )
      
    
    {\displaystyle ({\text{Min}},{\text{Max}})}
  
, into a new image

I
 
 N
 
 
 :
 {
 
 X
 
 ⊆
 
 
 R
 
 
 n
 
 
 }
 →
 {
 
 newMin
 
 ,
 .
 .
 ,
 
 newMax
 
 }
 
 
 {\displaystyle I_{N}:\{\mathbb {X} \subseteq \mathbb {R} ^{n}\}\rightarrow \{{\text{newMin}},..,{\text{newMax}}\}}
 
 
with intensity values in the range 
 
 
 
 (
 
 newMin
 
 ,
 
 newMax
 
 )
 
 
 {\displaystyle ({\text{newMin}},{\text{newMax}})}
 
. 
The <a href="/facts/Linear/fChtg3KC">linear</a> normalization of a <a href="/facts/Grayscale/Tjb9kR8v">grayscale</a> <a href="/facts/Digital_image/3TNT47Mv">digital image</a> is performed according to the formula

I
          
            N
          
        
        =
        (
        I
        −
        
          Min
        
        )
        
          
            
              
                newMax
              
              −
              
                newMin
              
            
            
              
                Max
              
              −
              
                Min
              
            
          
        
        +
        
          newMin
        
      
    
    {\displaystyle I_{N}=(I-{\text{Min}}){\frac {{\text{newMax}}-{\text{newMin}}}{{\text{Max}}-{\text{Min}}}}+{\text{newMin}}}

For example, if the intensity range of the image is 50 to 180 and the desired range is 0 to 255 the process entails subtracting 50 from each of pixel intensity, making the range 0 to 130. Then each pixel intensity is multiplied by 255/130, making the range 0 to 255. 
Normalization might also be non linear, this happens when there isn't a <a href="/facts/Linear/fChtg3KC">linear</a> relationship between 
 
 
 
 I
 
 
 {\displaystyle I}
 
 and 
 
 
 
 
 I
 
 N
 
 
 
 
 {\displaystyle I_{N}}
 
. An example of non-linear normalization is when the normalization follows a <a href="/facts/Sigmoid_function/lAXu3AwW">sigmoid function</a>, in that case, the normalized image is computed according to the formula

I
          
            N
          
        
        =
        (
        
          newMax
        
        −
        
          newMin
        
        )
        
          
            1
            
              1
              +
              
                e
                
                  −
                  
                    
                      
                        I
                        −
                        β
                      
                      α
                    
                  
                
              
            
          
        
        +
        
          newMin
        
      
    
    {\displaystyle I_{N}=({\text{newMax}}-{\text{newMin}}){\frac {1}{1+e^{-{\frac {I-\beta }{\alpha }}}}}+{\text{newMin}}}

Where 
 
 
 
 α
 
 
 {\displaystyle \alpha }
 
 defines the width of the input intensity range, and 
 
 
 
 β
 
 
 {\displaystyle \beta }
 
 defines the intensity around which the range is centered. 
Auto-normalization in image processing software typically normalizes to the full dynamic range of the number system specified in the image file format.

Normalization (image processing) open-in-new

Normalization (image processing)