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Advanced Image Processing

Advanced Image Processing. Lecture 1 - Introduction 01/14/10. Image Enhancement. Image Segmentation. Image Restoration. Representation & Description. Image Compression. Recognition & Interpretation. Image Coding. Morphological Image Processing. Wavelet Analysis.

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Advanced Image Processing

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  1. Advanced Image Processing Lecture 1 - Introduction 01/14/10

  2. Image Enhancement Image Segmentation Image Restoration Representation & Description Image Compression Recognition & Interpretation Image Coding Morphological Image Processing Wavelet Analysis Image processing components High-level Image Processing Machine Vision Image Understanding (or Analysis) Low-level Image Processing

  3. Themes and goals • Optimization and consistency • In-depth understanding • Efficient implementation • Distributed processing • Cultivate research style • Research groups • Classic books • Track publications (journal, conf) • Research note

  4. Course organization • Assignments • Homework (63%) • Mostly with programming • Final project (30%) • Algorithm development and paper submission • Final project presentation (7%) • Programming • C++ or Matlab • The Image Processing Library (IPL) • OpenCV

  5. Image enhancement Point-based vs. Neighbor-based processing Spatial domain vs. Frequency domain Image restoration Distortion model Noise model and removal Blur model and removal Least square Constrained least square Low-level image processing • Image compression • Information theory • Lossless • Lossy • Color image processing • Color fundamentals • Pseudo-color generation • Full-color image processing • Morphological operators • Binary morphology • Application • Edge linking • Noise removal • Wavelet analysis • Theory • Application • Image denoising • Image compression

  6. Image enhancement • Point-based • Log transform • Power-law transform • Contrast stretching • Thresholding • Histogram equalization • Image averaging • Mask-based T[f(x,y)] Point processing T[N{f(x,y)}] Mask processing f(x,y) f(x,y) g(x,y) g(x,y)

  7. Log transformation (Dynamic range compression)

  8. Power-Law transformation s = crg

  9. Gamma correction

  10. Contrast stretching

  11. Gray-level slicing Highlighting an intensity range

  12. Histogram equalization

  13. HE – Example 2

  14. HE – Derivation T(r) is single-valued and monotonically increasing within range of r T(r) has the same range as r [0, 1]

  15. Histogram equalization • Transformation function • pr(w) is the probability density function (pdf) • The transformation function is the cumulative distribution function (CDF) • To make the pdf of the transformed image uniform, i.e. to make the histogram of the transformed image uniform

  16. r hist(r) r s 70 10 0 1 2 3 10 80 95 0 1 3 5 70 15 5 10 80 95 15 10 2 100 HE – Discrete case s hist(s) 100

  17. -1 1 -1 1 -1 1 1/9 x -1 1 8 1 1 -1 1/9 x -1 1 1 -1 -1 1 Image enhancement • Mask-based • Lowpass vs. highpass • Linear vs. nonlinear • Lowpass (smoothing) • Average • Weighted average (Gaussian) • Median • Highpass (sharpening) • Unsharp masking (UM) • 1st derivative • 2nd derivative • Point-based • Log transform • Power-law transform • Contrast stretching • Thresholding • Histogram equalization • Image averaging T[N{f(x,y)}] Mask processing T[f(x,y)] Point processing f(x,y) f(x,y) g(x,y) g(x,y)

  18. Unsharp masking and high-boost filters • Unsharp masking • To generate the mask: Subtract a blurred version of the image from itself • Add the mask to the original • Highboost: • k>1 • Application: input image is very dark gmask(x,y) = f(x,y) - f(x,y) g(x,y) = f(x,y) + k*gmask(x,y)

  19. Derivative filters

  20. Filters - 1st derivative • Roberts filter • Prewitt filter • Sobel filter 1 0 0 1 0 -1 -1 0 -1 -1 -1 -1 0 1 0 0 0 -1 0 1 1 1 1 -1 0 1 -1 -2 -1 -1 0 1 0 0 0 -2 0 2 1 2 1 -1 0 1

  21. The Laplacian - Masks 0 1 0 1 1 1 To recover the image: 1 -4 1 1 -8 1 0 1 0 1 1 1 0 -1 0 -1 -1 -1 -1 4 -1 -1 8 1 0 -1 0 -1 -1 -1

  22. Laplacian|Prewitt|Sobel|Roberts Marr-Hildreth|Canny Perfect image Corrupted image

  23. Laplacian|Prewitt|Sobel|Roberts Same with threshold Marr-Hildreth|Canny|Angiogram

  24. Image enhancement • Spatial-based • Frequency-based • Why? • Computational efficiency • More intrinsic information • Lowpass vs. highpass • Notch filters

  25. 2-D Fourier transform • CFT • DFT

  26. Practical issues – Implement convolution in frequency domain • In spatial domain • In frequency domain • f*g  F(f)G(g) • Phase? Mag? • How to pad?

  27. Difference image from convolution in the spatial domain Convolution in the frequency domain No padding With padding Conv. spatially

  28. Lowpass filtering • Ideal filter • D(u, v): distance from point (u, v) to the origin • cutoff frequency (D0) • nonphysical • radially symmetric about the origin • Butterworth filter • Gaussian lowpass filter

  29. Power ratio 99.9699.6599.0497.84

  30. Highpass filter • Ideal filter • Butterworth filter • Gaussian highpass filter

  31. Example

  32. Optimal notch filters

  33. Optimal notch - Derivation

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