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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

  • 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


。Example


○ 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

: 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


◎ Region of Interest Processing


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