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Image Enhancement in the Spatial Domain

Learn about image enhancement techniques in the spatial domain, including gray-level transformations, log transformations, power law transformations, and piecewise-linear transformations. Understand the concept of image histograms and histogram equalization. Practice implementing these techniques in MATLAB.

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Image Enhancement in the Spatial Domain

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  1. CIS 601 – 04 Image ENHANCEMENT in the SPATIAL DOMAIN Longin Jan Latecki Based on Slides by Dr. Rolf Lakaemper

  2. Most of these slides base on the textbook Digital Image Processing by Gonzales/Woods/Eddins Chapter 3

  3. Introduction • Image Enhancement ? • Enhance otherwise hidden information • Filter important image features • Discard unimportant image features • Spatial Domain ? • Refers to the image plane (the ‘natural’ image) • Direct image manipulation

  4. Remember ? A 2D gray value - image is a 2D -> 1D function, v = f(x,y)

  5. Remember ? As we have a function, we can apply operators to this function, e.g. T(f(x,y)) = f(x,y) / 2 Operator Image (= function !)

  6. Remember ? T transforms the given image f(x,y) into another image g(x,y) T f(x,y) g(x,y)

  7. Spatial Domain • The operator T can be defined over • The set of pixels (x,y) of the image • The set of ‘neighborhoods’ N(x,y) of each pixel • A set of images f1,f2,f3,…

  8. Spatial Domain Operation on the set of image-pixels 6 8 2 0 3 4 1 0 12 200 20 10 6 100 10 5 (Operator: Div. by 2)

  9. 6 8 12 200 Spatial Domain Operation on the set of ‘neighbourhoods’ N(x,y) of each pixel (Operator: sum) 6 8 2 0 226 12 200 20 10

  10. Spatial Domain Operation on a set of images f1,f2,… 6 8 2 0 12 200 20 10 11 13 3 0 (Operator: sum) 14 220 23 14 5 5 1 0 2 20 3 4

  11. Spatial Domain • Operation on the set of image-pixels • Remark: these operations can also be seen as operations on the neighborhood of a pixel (x,y), by defining the neighborhood as the pixel itself. • The easiest case of operators • g(x,y) = T(f(x,y)) depends only on the value of f at (x,y) • T is called a • gray-level or intensity transformation function

  12. Transformations • Basic Gray Level Transformations • Image Negatives • Log Transformations • Power Law Transformations • Piecewise-Linear Transformation Functions • For the following slides L denotes the max. possible gray value of the image, i.e. f(x,y)  [0,L]

  13. Transformations Image Negatives: T(f)= L-f T(f)=L-f Output gray level Input gray level

  14. Transformations Log Transformations: T(f) = c * log (1+ f)

  15. Transformations Log Transformations InvLog Log

  16. Transformations Log Transformations

  17. Transformations Power Law Transformations T(f) = c*f 

  18. Transformations • varying gamma () obtains family of possible transformation curves •  > 1 • Compresses dark values • Expands bright values •  < 1 • Expands dark values • Compresses bright values

  19. Transformations • Used for gamma-correction

  20. Transformations • Used for general purpose contrast manipulation

  21. Transformations Piecewise Linear Transformations

  22. Piecewise Linear Transformations Thresholding Function g(x,y) = L if f(x,y) > t, 0 else t = ‘threshold level’ Output gray level Input gray level

  23. Piecewise Linear Transformations • Gray Level Slicing • Purpose: Highlight a specific range of grayvalues • Two approaches: • Display high value for range of interest, low value else (‘discard background’) • Display high value for range of interest, original value else (‘preserve background’)

  24. Piecewise Linear Transformations Gray Level Slicing

  25. Image Histogram (3, 8, 5)

  26. Image histogram is a vector If f:[1, n]x[1, m]  [0, 255] is a gray value image, then H(f): [0, 255]  [0, n*m] is its histogram, where H(f)(k) is the number of pixels (i, j)such that F(i, j)=k Similar images have similar histograms Warning: Different images can have similar histograms

  27. Histograms Histogram Processing 1 4 5 0 3 1 5 1 Number of Pixels gray level

  28. Hg Hr Hb

  29. Histogram Equalization Let h=[n1, n2, …, nG] be an image histogram, i.e., h(rk)=nk for rk is kth intensity level in interval [0,G] Normalized histogram is a probability density function (PDF) : p(rk) = h(rk) / n = nk / n - probability of occurrence of intensity level rk, where n is the total number of pixels. Equalized histogram is a cumulative distribution function (CDP):

  30. Implement in Matlab histogram equalization and Find an example image for which histogram equalization improves its quality Find an example image for which histogram equalization degrades its quality Homework 2

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