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Chapter 3. Intensity Transformation and Spatial Filtering

Chapter 3. Intensity Transformation and Spatial Filtering. This Session will cover : What is image enhancement Basic Intensity Transformation Functions (Enhancement overview) Histogram Processing. Center for Artificial Intelligence and RObotics (CAIRO). What is Image Enhancement?.

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Chapter 3. Intensity Transformation and Spatial Filtering

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  1. Chapter 3. Intensity Transformation and Spatial Filtering

  2. This Session will cover: • What is image enhancement • Basic Intensity Transformation Functions (Enhancement overview) • Histogram Processing Center for Artificial Intelligence and RObotics (CAIRO)

  3. What is Image Enhancement? • Image enhancement is the process of manipulating an image so that the resultant image is more suitable than original one for specific applications. • The reasons for doing this include: • Highlighting interesting detail in images • Removing noise from images • Making images more visually appealing Center for Artificial Intelligence and RObotics (CAIRO)

  4. What is Image Enhancement? (cont..) • There are two broad categories of image enhancement techniques: • Spatial domain techniques • Direct manipulation of image pixels • Frequency domain techniques • Manipulation of Fourier of an image • For the moment we will concentrate on techniques that operate in the spatial domain Center for Artificial Intelligence and RObotics (CAIRO)

  5. Basic Intensity Transformation Functions (cont…) • Three of the most common are shown here • Linear • Negative/Identity • Logarithmic • Log/Inverse log • Power law • nth power/nth root Center for Artificial Intelligence and RObotics (CAIRO)

  6. Basic Intensity Transformation Functions (1) Image Negatives (Linear) Negative images are useful for enhancing white or grey detail embedded in dark regions of an image s = (L-1) - r s = 1.0 - r Center for Artificial Intelligence and RObotics (CAIRO)

  7. Basic Intensity Transformation Functions (cont…) (2) log Transformation (Logarithmic) • Log functions are particularly useful when the input grey level values may have an extremely large range of values • In the following example the Fourier transform of an image is put through a log transform to reveal more detail s = log(1 + r) Center for Artificial Intelligence and RObotics (CAIRO)

  8. Basic Intensity Transformation Functions (cont…) (3) Gamma Transformation (Power-law) • Power law transformations have the following form s = c * r γ • Varying γ gives a • whole family of curves Center for Artificial Intelligence and RObotics (CAIRO)

  9. Basic Intensity Transformation Functions (cont…) s = r 0.7 s = r 0.4 s = r 0.1 Center for Artificial Intelligence and RObotics (CAIRO)

  10. Basic Intensity Transformation Functions (cont…) s = r 3.0 s = r 4.0 s = r 5.0 Center for Artificial Intelligence and RObotics (CAIRO)

  11. Basic Intensity Transformation Functions (cont…) (5) Piecewise-Linear transformation function • Rather than using a well defined mathematical function we can use arbitrary user-defined transforms • The images below show a contrast stretching linear transform to add contrast to a poor quality image Center for Artificial Intelligence and RObotics (CAIRO)

  12. Basic Intensity Transformation Functions (cont…) Intensity-level slicing is highlighting a specific range of intensities in an image often is of interest. Center for Artificial Intelligence and RObotics (CAIRO)

  13. Basic Intensity Transformation Functions (cont…) Center for Artificial Intelligence and RObotics (CAIRO)

  14. Basic Intensity Transformation Functions (cont…) Bit-plane slicing • Often by isolating particular bits of the pixel values in an image we can highlight interesting aspects of that image • Higher-order bits usually contain most of the significant visual information • Lower-order bits containsubtle details Center for Artificial Intelligence and RObotics (CAIRO)

  15. Basic Intensity Transformation Functions (cont…) Center for Artificial Intelligence and RObotics (CAIRO)

  16. Histogram processing Histogram of an image represents the relative frequency of occurrence of various gray levels in the image · The shape of a histogram provides useful information for contrast enhancement. Center for Artificial Intelligence and RObotics (CAIRO)

  17. Histogram processing Dark Image Center for Artificial Intelligence and RObotics (CAIRO)

  18. Histogram processing Bright Image Center for Artificial Intelligence and RObotics (CAIRO)

  19. Histogram processing Low-Contrast Image Center for Artificial Intelligence and RObotics (CAIRO)

  20. Histogram processing High-Contrast Image Center for Artificial Intelligence and RObotics (CAIRO)

  21. Histogram processing Histogram Equalization · The histogram equalization is an approach to enhance a given image. The approach is to design a transformation T(.) such that the gray values in the output is uniformly distributed in [0, 1]. · Let us assume for the moment that the input image to be enhanced has continuous gray values, with r = 0 representing black and r = 1 representing white. Center for Artificial Intelligence and RObotics (CAIRO)

  22. · we assume that: • T(r) is a monotonically increasing function for 0 < r < 1 (preserves order from black to white). • (2) T(r) maps [0,1] into [0,1] (preserves the range of allowed Gray values).

  23. Histogram processing · Let p(r) and p(s) denote the probability density (pdf) of the gray values in the input and output images. · If p(r) and T(r) are known, and r = T -1(s) satisfies condition 1, we can write (result from probability theory): 1 Center for Artificial Intelligence and RObotics (CAIRO)

  24. Histogram processing Let us take the particular transformation which is monotonic and invertible, since it is the cumulative distribution function (cdf) of r 2 From eq. (1) and (2) ; the transformed variable has an exactly uniform pdf. · This technique is called histogram equalization. Center for Artificial Intelligence and RObotics (CAIRO)

  25. Histogram processing (cont…) How to implement histogram equalization (Discrete)? Step 1:For images with discrete gray values, compute: nk: Number of pixels with gray value rk MN: Total number of pixels in the image Step 2: Based on CDF, compute the discrete version of the previous transformation : Center for Artificial Intelligence and RObotics (CAIRO)

  26. Histogram processing (cont…) Example: · Consider an 3-bit (8-level ) of size 64 x 64 image with gray values (0, 1, …,7): Solution Center for Artificial Intelligence and RObotics (CAIRO)

  27. Histogram processing (cont…) # of pixels PDF of intensity level Gray values Intensity level Center for Artificial Intelligence and RObotics (CAIRO)

  28. Histogram processing (cont…) Center for Artificial Intelligence and RObotics (CAIRO)

  29. Histogram processing (cont…) Histogram Specification (Histogram Matching) · Histogram equalization yields an image whose pixels are (intheory) uniformly distributed among all gray levels. · Sometimes, this may not be desirable. Instead, we may want a transformation that yields an output image with a pre-specified histogram. This technique is called histogram specification. Center for Artificial Intelligence and RObotics (CAIRO)

  30. Histogram processing (cont…) • · Given Information (1) Input image from which we can compute its histogram . (2) Desired histogram. • · Goal Derive a point operation,t hat maps the input image into an output image that has the user-specified histogram. · Again, we will assume, for the moment, continuous-gray values. Center for Artificial Intelligence and RObotics (CAIRO)

  31. · First apply the transformation Histogram processing (cont…) This gives an image with a uniform probability density. · If the desired output image were available, then the following transformation would generate an image with uniform density: Center for Artificial Intelligence and RObotics (CAIRO)

  32. Histogram processing (cont…) · For discrete gray levels, we have Center for Artificial Intelligence and RObotics (CAIRO)

  33. Histogram processing (cont…) Example: · Consider an 3-bit (8-level ) of size 64 x 64 image with gray values (0, 1, …,7): It is desired to transform this image into a new image, with histogram as specified below: Solution Center for Artificial Intelligence and RObotics (CAIRO)

  34. Histogram processing (cont…) Center for Artificial Intelligence and RObotics (CAIRO)

  35. Histogram processing (cont…) Compare between histogram equalization and histogram matching Center for Artificial Intelligence and RObotics (CAIRO)

  36. Histogram processing (cont…) Center for Artificial Intelligence and RObotics (CAIRO)

  37. Histogram processing (cont…) Center for Artificial Intelligence and RObotics (CAIRO)

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