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.

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Chapter 5: Neighborhood Processing

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Chapter 5 neighborhood processing

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

○ Neighborhood (mask)

  • -- can have different shapes and sizes


Function mask filter

○ Function + Mask = Filter

Input signal

Output signal

Filter


Chapter 5 neighborhood processing

1D

2D


Chapter 5 neighborhood processing

◎ Linear filter: linear combination of the gray

values in the mask


Example

。Example


Processing near image boundaries

○ Processing near image boundaries

  • Ignore the boundary

  • Pad with zeros

  • (c) Copy boundary

○ Values outside the range 0-255

  • Clip values

  • Scale values


Chapter 5 neighborhood processing

◎ Convolution

5-9


Discrete

Discrete:

Compared with

Linear filtering:


Chapter 5 neighborhood processing

◎ Correlation


Chapter 5 neighborhood processing

◎ Smoothing Filters

○Averaging

filters

Input 3X3 5X5 7X7


Chapter 5 neighborhood processing

○ Gaussian filters

(1-D):

(2-D):


Chapter 5 neighborhood processing

Averaging filters

Gaussian filters


Separable filters

○ Separable filters

e.g.,

Laplacian

filter


Chapter 5 neighborhood processing

  • n × n filter:

  • 2 (n × 1)filters:


Frequency domain filters

Frequency domain filters:


Chapter 5 neighborhood processing

Frequency: a measure by which gray

values change with distance


High pass filter

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

High pass

Low pass


Chapter 5 neighborhood processing

○ High pass filter

○ Low pass filter

e.g., Averaging

filter

  • e.g., Laplacian of

  • Gausian


Edge sharpening or enhancement

◎ Edge Sharpening or Enhancement

  • ○ Unsharp masking


Chapter 5 neighborhood processing

  • 。 Idea of unsharp masking

(a) Edge

(b) Blurred edge

(a) – k × (b)


Perform using a filter

。 Perform using a filter

。 Alternatives

(a)

(b) The averaging filter can be replaced

with any low pass filters


Example1

。 Example:

(a) Original (b) Unsharp Masking


Chapter 5 neighborhood processing

  • ○ 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)


Example2

。 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

◎ Non-linear smoothing filters

: mask elements

。 Maximum filter:

。 Minimum filter:


Chapter 5 neighborhood processing

  • 。 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


Region of interest processing

◎ Region of Interest Processing


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