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with intensity values in the range (Min,Max), into a new image
<math>I_N:\{\mathbb{X}\subseteq\mathbb{R}^n\}\rightarrow\{\text{newMin},..,\text{newMax}\}</math>
with intensity values in the range (newMin,newMax).
The [[linear]] normalization of a [[grayscale]] [[digital image]] is performed according to the formula
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:<math>I_N=(I-\text{Min})\frac{\text{newMax}-\text{newMin}}{\text{Max}-\text{Min}}+\text{newMin}</math>
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 [[linear]] relationship between <math>I</math> and <math>I_N</math>. An example of non-linear normalization is when the normalization follows a [[sigmoid function]], in that case, the normalized image is computed according to the formula
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:<math>I_N=(\text{newMax}-\text{newMin})\frac{1}{1+e^{-\frac{I-\beta}{\alpha}}}+\text{newMin}</math>
Where <math>\alpha</math> defines the width of the input intensity range, and <math>\beta</math> defines the intensity around which the range is centered.<ref>[http://www.itk.org/ItkSoftwareGuide.pdf ITK Software Guide]</ref>
Auto-normalization in image processing software typically normalizes to the full dynamic range of the number system specified in the image file format.
== See also ==
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