EE 4780

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EE 4780

• Image Enhancement

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Image Enhancement

• The objective of image enhancement is to process
  an image so that the result is more suitable than
  the original image for a specific application.
• There are two main approaches
• Image enhancement in spatial domain Direct
  manipulation of pixels in an image
• Point processing Change pixel intensities
• Spatial filtering
• Image enhancement in frequency domain Modifying
  the Fourier transform of an image

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Image Enhancement by Point Processing

• Intensity Transformation

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Image Enhancement by Point Processing

• Contrast Stretching

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Image Enhancement by Point Processing

• Contrast Stretching

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Image Enhancement by Point Processing

• Intensity Transformation

Matlab exercise
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Image Enhancement by Point Processing

• Intensity Transformation

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Image Enhancement by Point Processing

• Intensity Transformation

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Image Enhancement by Point Processing

• Gray-Level Slicing

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Image Enhancement by Point Processing

• Histogram

255
0
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Histogram Specification

• Intensity mapping
• Assume
• T(r) is single-valued and monotonically
  increasing.
• The original and transformed intensities can be
  characterized by their probability density
  functions (PDFs)

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Histogram Specification

• The relationship between the PDFs is

• Consider the mapping

Cumulative distribution function of r
Histogram equalization!
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Image Enhancement by Point Processing

• Histogram Equalization

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Image Enhancement by Point Processing

• Histogram Equalization Example
• Intensity 0 1 2 3
  4 5 6 7
• Number of pixels 10 20 12 8 0 0
  0 0
• Intensity 0 1 2 3
  4 5 6 7
• Number of pixels 0 10 0 0 20 0
  12 8

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Image Enhancement by Point Processing

• Histogram Equalization

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Histogram Specification
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Histogram Specification
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Histogram Specification
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Histogram Specification
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Local Histogram Processing

• Histogram processing can be applied locally.

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Image Subtraction
The background is subtracted out, the arteries
appear bright.
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Image Averaging
Corrupted image
Original image
Noise
Assume n(x,y) a white noise with mean0, and
variance
If we have a set of noisy images
The noise variance in the average image
is
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Image Averaging
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Spatial Filtering
A low-pass filter
A high-pass filter
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Spatial Filtering

• Median Filter

Sort (10 10 10 20 25 75 85 90 100)

• Example

Original signal
100 100 100 100 10 10 10 10 10
Noisy signal
100 103 100 100 10 9 10 11 10
Filter by 1 1 1/3
101 101 70 40 10 10 10
Filter by 1x3 median filter
100 100 100 10 10 10 10
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Spatial Filtering

• Median filters are nonlinear.
• Median filtering reduces noise without blurring
  edges and other sharp details.
• Median filtering is particularly effective when
  the noise pattern consists of strong, spike-like
  components. (Salt-and-pepper noise.)

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Spatial Filtering
SaltPepper noise added
Original
3x3 averaging filter
3x3 median filter
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Spatial Filtering
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Wiener Filter
Noisy image
Original image
Noise
Wiener Filter
Noise variance
Signal variance
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Wiener Filter
is estimated by
Since variance is nonnegative, it is modified as
Estimate signal variance locally
N
N
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Wiener Filter
Denoised (3x3neighborhood) Mean Squared Error is
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Noisy, ?10
wiener2 in Matlab
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Spatial Filtering

• Gradient Operators
• Averaging of pixels over a region tends to blur
  detail in an image.
• As averaging is analogous to integration,
  differentiation can be expected to have the
  opposite effect and thus sharpen an image.
• Gradient operators (first-order derivatives) are
  commonly used in image processing applications.

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Spatial Filtering

• Gradient Operators

These are called the Sobel operators
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Spatial Filtering

• Laplacian Operators
• Laplacian operators are second-order derivatives.

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Spatial Filtering
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Spatial Filtering

• High-boost or high-frequency-emphasis filter
• Sharpens the image but does not remove the
  low-frequency components unlike high-pass
  filtering

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Spatial Filtering

• High-boost or high-frequency-emphasis filter
• High pass Original Low pass
• High boost (Original) K(High pass)

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Spatial Filtering
A high-pass filter
A high-boost filter
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Spatial Filtering

• High-boost or high-frequency-emphasis filter

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Spatial Filtering