Understanding Image Processing Techniques: Filters and Enhancement Methods

1. Chapter 5: Neighborhood Processing • Point processing: applies a function to each • pixel • Neighborhood processing: applies a function • to a neighborhood of each pixel

2. ○ Neighborhood (mask) • -- can have different shapes and sizes

3. ○ Mask + Function = Filter Input signal Output signal Filter

4. 1D 2D

5. ◎ Linear filter: linear combination of the gray values in the mask

7. 。Example

8. ○ Processing near image boundaries • Ignore the boundary • Pad with zeros • (c) Copy boundary ○ Values outside the range 0-255 • Clip values • Scale values

9. ◎ Convolution 5-9

10. ◎ Correlation

11. 。 Discrete Case: e.g., A = 4, B = 5, A + B – 1 = 8, 7-11

12. ＊ Convolution can be defined in terms of polynomial product Extend f, g to if f, g have different numbers of sample points Let Compute The coefficients of to form the result of convolution 7-27

13. 。Example: Let The coefficients of form the convolution 7-13

14. 7-14

15. Discrete: Compared with Linear filtering: 5-15

16. ◎ Smoothing Filters ○Averaging filters Input 3X3 5X5 7X7

17. ○ Gaussian filters (1-D): (2-D):

18. Averaging filters Gaussian filters

19. ○ Separable filters e.g., Laplacian filter

20. n × n filter: • 2 (n × 1)filters:

21. Frequency domain filters Frequency filters applied to the Fourier transforms of images Spatial filters applied to images Fourier transform (frequency domain) Image (spatial domain)

22. Fourier Transform (FT) Fourier Transform of function f(x) Inverse Fourier Transform of F(u) Discrete FT 5-22

24. 2-D Fourier Transform Fourier Transform of function f(x, y) Inverse Fourier Transform of F(u, v) Discrete FT 5-24

25. Frequency: a measure by which gray values change with distance

26. High pass filter • Frequency filters Spatialdomain Fouriertransform Frequency domain Low pass filter High frequency components, e.g., edges, noises Low frequency components, e.g., regions 5-26

27. High pass Fourier transform Input image Low pass

29. ◎ Edge Sharpening or Enhancement • ○ Unsharp masking

30. 。 Idea of unsharp masking (a) Edge (b) Blurred edge (a) – k × (b)

31. 。 Perform using a filter 。 Alternatives (a) (b) The averaging filter can be replaced with any low pass filters

32. 。 Example: (a) Original (b) Unsharp Masking

33. ○ High-boost filter • high boost = k(original) – (low pass) • = k(original) – ((original) - (high pass) • = (k-1)(original) + (high pass) 。 Alternatives: (a) (k/(k-1))(original) + (1/(k-1))((low pass) (b) (k/(2k-1))(original) + ((1-k)/(2k-1))((low pass)

34. 。 Example: (a) (k/(k-1))(original) + (1/(k-1))((low pass) (b) (k/(2k-1))(original) + ((1-k)/(2k-1))((low pass)

35. ◎ Non-linear smoothing filters Maximum filter: : mask elements Minimum filter:

36. 。 Median filter • 。 K-nearest neighbors (K-NN) • 。 Geometric mean filter • 。 Alpha-trimmed mean filter • i) Order elements • ii) Trim off m end elements • iii) Take mean

37. ◎ Region of Interest Processing

38. Homework: 1. Select an experimental image 2. Apply a 3 by 3 (a) average filter and (b) median filter to the image 3. Unsharp masking 38