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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
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


1D

2D


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


Convolution

5-9


Discrete
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
○ Separable filters

e.g.,

Laplacian

filter


  • n × n filter:

  • 2 (n × 1)filters:



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


○ High pass filter

○ Low pass filter

e.g., Averaging

filter

  • e.g., Laplacian of

  • Gausian



  • 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


  • 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:


  • 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



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