Intro & What does it mean to normalize a function/an image?

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Normalization refers to the process of adjusting the values of a function or image to a common scale, often to enhance contrast or ensure consistency. In the context of images, normalization involves modifying pixel intensity levels so that they fit within a specific range, improving visual clarity. For mathematical functions, normalization typically means dividing by the function's norm, resulting in a unit vector that retains the original direction but has a magnitude of one. This concept is essential in both image processing and various applications in physics and astronomy. Understanding normalization can significantly aid in data analysis and interpretation in these fields.
John Dolan
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Hi Guy,

My name is John Dolan and I am an Irish student studying Astronomy in the university of Groningen in the Netherlands. I have been interested in Physics and Astronomy since I was knee high to a grasshopper and I look forward to asking questions, finding out new ideas and new ways of thinking and hopefully getting to answer to questions to.

One thing I've always heard but never fully understood was the term "Normalize". What exactly does it mean in terms of a function or in the case I'm dealing with now, an Image. I would be very grateful if anyone could clarify this for me.

Thanks in advance,
Regards,
John Dolan
 
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To normalize a vector is to divide it by its norm. The result is a unit vector (a vector of norm 1) in the same 1-dimensional subspace.

Real-valued and complex-valued functions are vectors in the sense that they are elements of a vector space.
 
Think of it as "contrast". It's changing the intensity levels for the pixels in an image.
 

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