Image Enhancement in the Spatial Domain

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Chapter 3

• Image Enhancement in the Spatial Domain

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Outline

• Background
• Basic Gray-level transformation
• Histogram Processing
• Arithmetic-Logic Operation
• Basics of Spatial Filtering
• Smoothing Spatial Filters
• Sharpening Spatial Filters
• Combining Spatial Enhancement Methods

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Background

• Image enhancement approaches fall into two broad
  categories spatial domain methods and frequency
  domain methods.
• The term spatial domain refers to the image plane
  itself.
• g(x,y) Tf(x,y) , T is an operator on f,
  defined over some neighborhood of f(x,y)

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Size of Neighborhood

• Point processing
• Larger neighborhood mask (kernel, template,
  window) processing

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Gray-level Transformation

Contrast stretching
thresholding
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Basic Gray Level Transformation

• Image negatives s L-1-r
• Log transformation s clog(1r)
• Power-law transformation scrg

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Image Negatives
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Log Transformation
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Gamma Correction (I)

• Cathode ray tube (CRT) devices have an
  intensity-to-voltage response that is a power
  function, with exponents varying from 1.8 to 2.5.

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Gamma Correction (II)
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Piece-wise Linear Transformation

• Contrast stretching
• Gray-level slicing(Figure 3.11)
• Bit-plane slicing(Figures 3.13-14)

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Gray-level Slicing

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Bit-plane Slicing
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Histogram Processing

• The histogram of a digital image with gray-levels
  in the range 0,L-1 is a discrete function
  h(rk)nk where rk is the kth gray level and nk is
  the number of pixels in the image having gray
  level rk
• Normalized histogram p(rk)nk/n.
• Easy to compute, good for real-time image
  processing.

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Four Basic Image Types

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Histogram Equalization

• s T(r)
• What if we take the transformation T to be
• It can be shown that ps(s)1
• Discrete version

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Histogram Matching

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Local Enhancements
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Histogram Statistics

• N-th moment of r about its mean

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Logic Operations

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Arithmetic Operations

• Image Subtraction
• Image Averaging

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Basics of Spatial Filtering

• Mask, convolution kernels
• Odd sizes

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Smoothing Spatial Filters

• Smoothing linear filters averaging filters,
  low-pass filters
• Box filter
• Weighted average
• Order-statistics filters
• Median-filter removing salt-and-pepper noise
• Max filter
• Min filter

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Sharpening Spatial Filters

• Foundation

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The Laplacian

• Development of the method

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Image Enhancement

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The Gradient

Simplification
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Combining Spatial Enhancement Methods

• (a) original (b) Laplacian, (c) ab, (d) Sobel of
  (a)

(a)
(b)
(c)
(d)