CSC 381/481 Quarter: Fall

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CSC 381/481 Quarter Fall 03/04

• Daniela Stan Raicu
• Email draicu_at_cs.depaul.edu
• Homepage http//facweb.cs.depaul.edu/dstan
• School of CTI, DePaul University

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Outline

• Chapter 3 Image Enhancement in the Spatial
  Domain
• Introduction (Section 3.1)
• Enhancement by point processing (Section 3.2)
• Image negatives
• Log transformations
• Power-law transformations
• Piecewise-linear transformations
• Histogram Processing (Section 3.3)
• Final Projects discussion

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Introduction

• Image Enhancement procedures are techniques used
  to achieve a subjective improvement in image
  quality for a specific application
  (problem-oriented).
• Typical applications
• noise removal
• geometric correction
• smoothing
• sharpening
• edge enhancement or extraction.
• Usually ad hoc procedures.
• Image Enhancement
• in the Spatial Domain (pixel operators)
• the Frequency Domain (frequency filtering).

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Spatial Domain Methods

• Procedures that operate directly on the
  aggregate/neighborhood of pixels composing an
  image
• A neighborhood about (x,y) is defined by using a
  square (or rectangular) subimage area centered at
  (x,y).

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Spatial Domain Methods

• When the neighborhood is 1 x 1 then g depends
  only on the value of f at (x,y) and T becomes a
  gray-level transformation (also called an
  intensity or mapping) function
• sT(r)
• r,s gray levels of f(x,y) and g(x,y) at any
  point (x,y)
• r denotes the pixel intensity before processing
• s denotes the pixel intensity after processing.
• These intensity transformations are also called
  point processing techniques.

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Enhancement by Point Processing

• The following methods are based only on the
  intensity of single pixels.
• Image negatives
• Log transformations
• Power-law transformations
• Piecewise-Linear Transformation Functions
• Contrast stretching
• Gray-level slicing
• Bit-plane slicing

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Image Enhancement in the Spatial Domain
Linear Negative, Identity Logarithmic Log,
Inverse Log Power-Law nth power, nth root
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Image Negatives

• Are obtained by using the transformation function
  sT(r).
• Function T reverses the order from black to white
  so that the intensity of the output image
  decreases as the intensity of the input increases.

0,L-1 the range of gray levels S L-1-r
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Image Enhancement in the Spatial Domain
Medical applications much easier to analyze the
breast tissue in the negative image
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Log Transformations

• s c log(1r)
• c constant, r gt0
• Compresses the dynamic range of images with large
  variations in pixel values

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Piecewise-Linear Transformation Functions
Contrast Stretching

• To increase the dynamic range of the gray levels
  in the image being processed.

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Contrast Stretching

• The locations of (r1,s1) and (r2,s2) control the
  shape of the transformation function.
• If r1 s1 and r2 s2 the transformation is a
  linear function and produces no changes.
• If r1r2, s10 and s2L-1, the transformation
  becomes a thresholding function that creates a
  binary image.

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Image Enhancement in the Spatial Domain
Contrast Stretching
Thresholding
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Contrast Stretching

• More on function shapes
• Intermediate values of (r1,s1) and (r2,s2)
  produce various degrees of spread in the gray
  levels of the output image, thus affecting its
  contrast.
• Generally, r1r2 and s1s2 is assumed.

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Image Enhancement in the Spatial Domain
Low contrast image
High contrast image
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Spatial Domain Methods

• Mask processing or filtering when the values of
  f in a predefined neighborhood of (x,y) determine
  the value of g at (x,y).
• Through the use of masks (or kernels, templates,
  or windows, or filters).
• More in the next lecture when we discuss about
  Basics of Spatial filtering (Section 3.5)

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Example of the use of a mask
Step 1 Move the window to the first location
where we want to compute the average
value and then select only pixels
inside the window.
Step 2 Compute the average value
Sub image p
Step 3 Place the result at the pixel in the
output image
Original image
4.3
Step 4 Move the window to the next
location and go to Step 2
Output image
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Histogram Processing

• The histogram of a digital image with gray levels
  from 0 to L-1 is a discrete function h(rk)nk,
  where
• rk is the kth gray level
• nk is the pixels in the image with that gray
  level
• n is the total number of pixels in the image
• k 0, 1, 2, , L-1
• Normalized histogram p(rk)nk/n
• sum of all components 1

To visualize the histogram of a digital image, we
plot pr(rk) versus rk
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Image Enhancement in the Spatial Domain
The shape of the histogram of an image does
provide useful info about the possibility for
contrast enhancement.
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Types of Histogram Processing

• Histogram equalization
• Histogram matching (specification)
• Local enhancement

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Histogram Equalization

• As mentioned above, for gray levels that take on
  discrete values, we deal with probabilities
• pr(rk)nk/n, k0,1,.., L-1
• The plot of pr(rk) versus rk is called a
  histogram and the technique used for obtaining a
  uniform histogram is known as histogram
  equalization (or histogram linearization).

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Histogram Equalization (HE)

• The technique used for obtaining a uniform
  histogram
• is known as histogram equalization (or histogram
  linearization).

where pr(rk)nk/n, k0,1,.., L-1

• Histogram equalization(HE) results are similar to
  contrast stretching but offer the advantage of
  full automation, since HE automatically
  determines a transformation function to produce a
  new image with a uniform histogram.

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Local Enhancement

• When it is necessary to enhance details over
  smaller areas, then we need to devise
  transformation functions based on the gray-level
  distribution in the neighborhood of every pixel

The procedure is 1. Define a square (or
rectangular) neighborhood and move the center of
this area from pixel to pixel. 2. At each
location, the histogram of the points in the
neighborhood is computed and either a histogram
equalization or histogram specification
transformation function is obtained. 3. This
function is finally used to map the gray level of
the pixel centered in the neighborhood. The
center is then moved to an adjacent pixel
location and the procedure is repeated.