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Intensity Transformations and Spatial Filtering

Intensity Transformations and Spatial Filtering. Basics of Intensity Transformation and Spatial Filtering. Spatial Domain Process Neighborhood is rectangle, centered on ( x,y ), and much smaller in size than image. Neighborhood size is 1x1, 3x3, 5x5, etc. Intensity Transformation.

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Intensity Transformations and Spatial Filtering

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  1. Intensity Transformations and Spatial Filtering

  2. Basics of Intensity Transformation and Spatial Filtering • Spatial Domain Process • Neighborhood is rectangle, centered on (x,y), and much smaller in size than image. • Neighborhood size is 1x1, 3x3, 5x5, etc.

  3. Intensity Transformation • T[f(x,y)] is Intensity Transformation, if the neighborhood size is 1x1. • Intensity Transformation can be written as follows • s = T[r], where s = g(x,y), and r = f(x,y)

  4. Image Negatives • s = L-1 – r where intensity level is in the range [0, L-1]

  5. Log Transformations • s = c Log(1+r) • Log Transformation is used to expand the value of the dark pixels while compressing the higher-level value. • It is used to compress the intensity of an image which has very large dynamic range.

  6. Log Transformations of Fourier Spectrum • We cannot see the Fourier spectrum, because its dynamic range is very large. Original Image Fourier Spectrum Log Transform of Fourier Spectrum

  7. Power-Law (Gamma) Transformations • If <1, expand dark pixels, compress bright pixels. • If >1, compress dark pixels, expand bright pixels.

  8. Examples of Gamma Transformations

  9. Contrast Stretching • If r<r1 then s = r*s1/r1 • If r1<= r<=r2 then s = (r-r1)*(s2-s1)/(r2-r1)+s1 • If r>r2 then s = (r-r2)*(255-s2)/(255-r2)+s2 • If r1=r2 and s1=0,s2=255, the transform is called “Threshold Function”.

  10. Examples of Contrast Stretching

  11. Contrast Stretching in Medical Image • Window Width/Level(Center) s1=0,s2=255 width (w)=r2-r1, level (c)=(r1+r2)/2

  12. Histogram & PDF • h(r) = nr where nr is the number of pixels whose intensity is r. • The Probability Density Function (PDF)

  13. Cumulative Distribution Function (CDF) PDF CDF Transfer Function s r

  14. Example of Histogram and Cumulative Distribution Function (CDF)

  15. Low Contrast Image • The image is highly concentrated on low intensity values. • The low contrast image is the image which is highly concentrated on a narrow histogram. High Concentrate Low Concentrate

  16. Histogram Equalization • The Histogram Equalization is a method which makes the histogram of the image as smooth as possible

  17. The PDF of the Transformed Variable • s = Transformed Variable. • = The PDF of r • = The PDF of s

  18. Transformation Function of Histogram Equalization • The PDF of s

  19. Histogram Equalization Example

  20. Histogram Equalization Example (cont.)

  21. Histogram Matching • How to transform the variable r whose PDF is to the variable t whose PDF is . T( ) G-1( ) r s t

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