Chapter 5: Neighborhood Processing

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. ○ Function + Mask = 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. Discrete: Compared with Linear filtering:

11. ◎ Correlation

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

13. ○ Gaussian filters (1-D): (2-D):

14. Averaging filters Gaussian filters

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

16. n × n filter: • 2 (n × 1)filters:

17. Frequency domain filters:

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

22. High pass filter High frequency components, e.g., edges, noises Low frequency components, e.g., regions Frequency domain Spatialdomain Fouriertransform Low pass filter

23. High pass Low pass

24. ○ High pass filter ○ Low pass filter e.g., Averaging filter • e.g., Laplacian of • Gausian

25. ◎ Edge Sharpening or Enhancement • ○ Unsharp masking

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

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

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

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

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

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

32. 。 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

33. ◎ Region of Interest Processing