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 X X X7

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:

19. can be written in complex form
where
The relationships between their coefficients
3-19

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

23. Low pass filter High frequency components, e.g., edges, noises
Low frequency components, e.g., regions
Frequency domain
Spatial domain
Fourier transform
Low pass filter
High pass filter

24. Fourier transform
Input image
Low pass
High pass

25. Output ○ In spatial domain Low pass filter High pass filter e.g., LoG
e.g., Averaging filter
High pass filter
e.g., LoG

26. ◎ Edge Sharpening or Enhancement
○ Unsharp masking

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

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

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

30. ○ 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)

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

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

33. 。 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

34. ◎ Region of Interest Processing