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Math 3360: Mathematical Imaging

Math 3360: Mathematical Imaging. Lecture 2: Image Transformation for Image Processing. Prof. Ronald Lok Ming Lui Department of Mathematics, The Chinese University of Hong Kong. Mathematical definition:

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Math 3360: Mathematical Imaging

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  1. Math 3360: Mathematical Imaging Lecture 2: Image Transformation for Image Processing Prof. Ronald Lok Ming LuiDepartment of Mathematics, The Chinese University of Hong Kong

  2. Mathematical definition: • A 2D (grayscale) digital image is a 2D function defined on a 2D domain (usually rectangular domain): • is called the brightness/intensity/grey level; • (x,y) is the spatial coordinates of the image. • Thus, a 2D digital image looks like this: • Each element in the matrix is called pixel (picture element); • Usually, and Recap: What is a digital image? IMAGE PROCESSING IS RELATED TO LINEAR ALGEBRA!!

  3. Recap: What is a digital image? • Mathematical definition of color image: • A 2D (color) digital image is a 2D function defined on a 2D domain (usually rectangular domain): • are the intensity/brightness/grey level corresponding to R, G and B respectively ; • Combination of R, G, B forms the full spectrum of color! WE WILL FOCUS ON: Grayscale image!

  4. Image resolution: • Recall: A digital image looks like: where: • (N,G) is called the image resolution. • Sometimes, (n,m) is referred to as image resolution as well. Recap: “Image resolution”?

  5. Keep in mind: imread & imwrite! • Please attend TA session when you will learn MATLAB command to do mathematical imaging! Recap: Read & Write image in Matlab?

  6. Major tasks in imaging includes: • To improve the quality of an image in a subjective way, usually by increasing its contrast. This is called image enhancement. • To use as few bits as possible to represent the image, with minimum deterioration in its quality. This is called image compression. • To improve an image in an objective way, for example by reducing its blurring. This is called image restoration. • To extract explicit characteristics of the image which can be used to identify the contents of the image. This is called feature extraction. Main tasks in image processing

  7. Mathematical technique for imaging (in 1 sentence): • TRANSFORM an input image to a better image • Mathematically, • can be LINEAR: • can be NON-LINEAR Main tasks in image processing

  8. Please refer to Supplementary note 1 & 2 • You will learn from Supplementary note 1 & 2: • How linear operator to transform an image (to a better image) is defined? • Shift invariant v.s. convolution • Separable operator Now: some mathematics! Main idea:

  9. You will see that if the operator on an image is linear and separable: • Find suitable and for image enhancement, image deblurring and feature selection etc. Now: some mathematics!

  10. Image enhancement Original Enhanced

  11. Image enhancement Original Deblurred

  12. Feature selection Original image Edge detection

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