1. EE 4780 Image Enhancement

2. Bahadir K. Gunturk2 Image Enhancement The objective of image enhancement is to process an image so that the result is more suitable than the original image for a specific application. There are two main approaches:  Image enhancement in spatial domain: Direct manipulation of pixels in an image Point processing: Change pixel intensities Spatial filtering  Image enhancement in frequency domain: Modifying the Fourier transform of an image

3. Bahadir K. Gunturk3 Image Enhancement by Point Processing Intensity Transformation

4. Bahadir K. Gunturk4 Image Enhancement by Point Processing Contrast Stretching

5. Bahadir K. Gunturk5 Image Enhancement by Point Processing Contrast Stretching

6. Bahadir K. Gunturk6 Image Enhancement by Point Processing Intensity Transformation Matlab exercise

7. Bahadir K. Gunturk7 Image Enhancement by Point Processing Intensity Transformation

8. Bahadir K. Gunturk8 Image Enhancement by Point Processing Intensity Transformation

9. Bahadir K. Gunturk9 Image Enhancement by Point Processing Gray-Level Slicing

10. Bahadir K. Gunturk10 Image Enhancement by Point Processing Histogram 0 255

11. Bahadir K. Gunturk11 Histogram Specification Intensity mapping Assume  T(r) is single-valued and monotonically increasing.  The original and transformed intensities can be characterized by their probability density functions (PDFs)

12. Bahadir K. Gunturk12 Histogram Specification The relationship between the PDFs is Consider the mapping Cumulative distribution function of r Histogram equalization!

13. Bahadir K. Gunturk13 Image Enhancement by Point Processing Histogram Equalization

14. Bahadir K. Gunturk14 Image Enhancement by Point Processing Histogram Equalization Example Intensity 0 1 2 3 4 5 6 7 Number of pixels 10 20 12 8 0 0 0 0 Intensity 0 1 2 3 4 5 6 7 Number of pixels 0 10 0 0 20 0 12 8

15. Bahadir K. Gunturk15 Image Enhancement by Point Processing Histogram Equalization

16. Bahadir K. Gunturk16 Histogram Specification

17. Bahadir K. Gunturk17 Histogram Specification

18. Bahadir K. Gunturk18 Histogram Specification

19. Bahadir K. Gunturk19 Histogram Specification

20. Bahadir K. Gunturk20 Local Histogram Processing Histogram processing can be applied locally.

21. Bahadir K. Gunturk21 Image Subtraction The background is subtracted out, the arteries appear bright.

22. Bahadir K. Gunturk22 Image Averaging Original image Noise Corrupted image Assume n(x,y) a white noise with mean=0, and variance If we have a set of noisy images The noise variance in the average image is

23. Bahadir K. Gunturk23 Image Averaging

24. Bahadir K. Gunturk24 Spatial Filtering A low-pass filter A high-pass filter

25. Bahadir K. Gunturk25 Spatial Filtering Median Filter Sort: (10 10 10 20 25 75 85 90 100) 100 100 100 100 10 10 10 10 10 Example Original signal: 100 103 100 100 10 9 10 11 10 Noisy signal: 101 101 70 40 10 10 10 Filter by [ 1 1 1]/3: 100 100 100 10 10 10 10 Filter by 1x3 median filter:

26. Bahadir K. Gunturk26 Spatial Filtering Median filters are nonlinear. Median filtering reduces noise without blurring edges and other sharp details. Median filtering is particularly effective when the noise pattern consists of strong, spike-like components. (Salt-and- pepper noise.)

27. Bahadir K. Gunturk27 Spatial Filtering Original 3x3 averaging filter Salt&Pepper noise added 3x3 median filter

28. Bahadir K. Gunturk28 Spatial Filtering

29. Bahadir K. Gunturk29 Wiener Filter Original image Noise Noisy image Noise variance Signal variance

30. Bahadir K. Gunturk30 Wiener Filter is estimated by Since variance is nonnegative, it is modified as Estimate signal variance locally: N N

31. Bahadir K. Gunturk31 Wiener Filter Noisy,  =10 Denoised (3x3neighborhood) Mean Squared Error is 56 wiener2 in Matlab

32. Bahadir K. Gunturk32 Spatial Filtering Gradient Operators  Averaging of pixels over a region tends to blur detail in an image.  As averaging is analogous to integration, differentiation can be expected to have the opposite effect and thus sharpen an image.  Gradient operators (first-order derivatives) are commonly used in image processing applications.

33. Bahadir K. Gunturk33 Spatial Filtering Gradient Operators These are called the Sobel operators

34. Bahadir K. Gunturk34 Spatial Filtering Laplacian Operators  Laplacian operators are second-order derivatives.

35. Bahadir K. Gunturk35 Spatial Filtering

36. Bahadir K. Gunturk36 Spatial Filtering High-boost or high-frequency-emphasis filter  Sharpens the image but does not remove the low-frequency components unlike high-pass filtering

37. Bahadir K. Gunturk37 Spatial Filtering High-boost or high-frequency-emphasis filter  High pass = Original – Low pass  High boost = (Original) + K*(High pass)

38. Bahadir K. Gunturk38 Spatial Filtering A high-pass filter A high-boost filter

39. Bahadir K. Gunturk39 Spatial Filtering High-boost or high-frequency-emphasis filter

40. Bahadir K. Gunturk40 Spatial Filtering