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# Chapter 5: Neighborhood Processing PowerPoint PPT Presentation

Chapter 5: Neighborhood Processing. Point processing: applies a function to each pixel Neighborhood processing: applies a function to a neighborhood of each pixel. ○ Neighborhood ( mask ). -- can have different shapes and sizes.

Chapter 5: Neighborhood Processing

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### Chapter 5: Neighborhood Processing

• Point processing: applies a function to each

• pixel

• Neighborhood processing: applies a function

• to a neighborhood of each pixel

### ○ Neighborhood (mask)

• -- can have different shapes and sizes

### ○ Function + Mask = Filter

Input signal

Output signal

Filter

1D

2D

◎ Linear filter: linear combination of the gray

values in the mask

### ○ Processing near image boundaries

• Ignore the boundary

• Pad with zeros

• (c) Copy boundary

○ Values outside the range 0-255

• Clip values

• Scale values

◎ Convolution

5-9

### Discrete:

Compared with

Linear filtering:

◎ Correlation

◎ Smoothing Filters

○Averaging

filters

Input 3X3 5X5 7X7

○ Gaussian filters

(1-D):

(2-D):

Averaging filters

Gaussian filters

### ○ Separable filters

e.g.,

Laplacian

filter

• n × n filter:

• 2 (n × 1)filters:

### Frequency domain filters:

Frequency: a measure by which gray

values change with distance

### High pass filter

High frequency components, e.g., edges, noises

Low frequency components, e.g., regions

Frequency domain

Spatialdomain

Fouriertransform

Low pass filter

### High pass

Low pass

○ High pass filter

○ Low pass filter

e.g., Averaging

filter

• e.g., Laplacian of

• Gausian

### ◎ Edge Sharpening or Enhancement

• ○ Unsharp masking

• 。 Idea of unsharp masking

(a) Edge

(b) Blurred edge

(a) – k × (b)

### 。 Perform using a filter

。 Alternatives

(a)

(b) The averaging filter can be replaced

with any low pass filters

### 。 Example:

(a) Original (b) Unsharp Masking

• ○ 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)

### 。 Example:

(a) (A/(A-1))(original) + (1/(A-1))((low pass)

(b) (A/(2A-1))(original) +

((1-A)/(2A-1))((low pass)

### ◎ Non-linear smoothing filters

。 Maximum filter:

。 Minimum filter:

• 。 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