Digital Image Processing

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Digital Image Processing

• Chapter 3 Image Enhancement in the Spatial Domain

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Background

• Spatial domain process
• where is the input image, is
  the processed image, and T is an operator on f,
  defined over some neighborhood of

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• Neighborhood about a point

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• Gray-level transformation function
• where r is the gray level of and s is
  the gray level of at any point

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• Contrast enhancement
• For example, a thresholding function

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• Masks (filters, kernels, templates, windows)
• A small 2-D array in which the values of the mask
  coefficients determine the nature of the process

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Some Basic Gray Level Transformations
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• Image negatives
• Enhance white or gray details

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• Log transformations
• Compress the dynamic range of images with large
  variations in pixel values

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• From the range 0- to the range 0 to 6.2

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• Power-law transformations
• or
• maps a narrow range of dark input values
  into a wider range of output values, while
  maps a narrow range of bright input values into
  a wider range of output values
• gamma, gamma correction

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• Monitor,

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• Piecewise-linear transformation functions
• The form of piecewise functions can be
  arbitrarily complex

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• Contrast stretching

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• Gray-level slicing

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• Bit-plane slicing

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Histogram Processing

• Histogram
• where is the kth gray level and is the
  number of pixels in the image having gray level
  
• Normalized histogram

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• Histogram equalization

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• Probability density functions (PDF)

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• Histogram matching (specification)

is the desired PDF
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• Histogram matching
• Obtain the histogram of the given image, T(r)
• Precompute a mapped level for each level
• Obtain the transformation function G from the
  given
• Precompute for each value of
• Map to its corresponding level then
  map level into the final level

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• Local enhancement
• Histogram using a local neighborhood, for example
  77 neighborhood

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• Use of histogram statistics for image enhancement
• denotes a discrete random variable
• denotes the normalized histogram
  component corresponding to the ith value of
• Mean

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• The nth moment
• The second moment

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• Global enhancement The global mean and variance
  are measured over an entire image
• Local enhancement The local mean and variance
  are used as the basis for making changes

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• is the gray level at coordinates (s,t)
  in the neighborhood
• is the neighborhood normalized
  histogram component
• mean
• local variance

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• are specified parameters
• is the global mean
• is the global standard deviation
• Mapping

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Enhancement Using Arithmetic/Logic Operations

• AND
• OR
• NOT
• Subtraction
• Addition
• Multiplication
• Division

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• Image subtraction
• Enhancement of differences between images

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• Mask mode radiography

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• Image Averaging
• Averaging K different noisy images

,
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Basics of Spatial Filtering
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• Image size
• Mask size
• and
• and

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Smoothing Spatial Filters

• Smoothing
• Noise reduction
• Smoothing of false contours
• Reduction of irrelevant detail

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• Order-statistic filters
• median filter Replace the value of a pixel by
  the median of the gray levels in the neighborhood
  of that pixel
• Noise-reduction

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Sharpening Spatial Filters

• Foundation
• The first-order derivative
• The second-order derivative

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• Use of second derivatives for enhancement-The
  Laplacian
• Development of the method

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• Simplifications

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• Unsharp masking and high-boost filtering
• Unsharp masking
• Substract a blurred version of an image from the
  image itself
• The image, The
  blurred image

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• High-boost filtering

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• Use the Laplacian as the sharpening filtering

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• Use of first derivatives for enhancementThe
  gradient

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• The magnitude is rotation invariant (isotropic)

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• Computing using cross differences, Roberts
  cross-gradient operators

and
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• Sobel operators
• A weight value of 2 is to achieve some smoothing
  by giving more importance to the center point

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Combining Spatial Enhancement Methods

• An example
• Laplacian to highlight fine detail
• Gradient to enhance prominent edges
• Smoothed version of the gradient image used to
  mask the Laplacian image
• Increase the dynamic range of the gray levels by
  using a gray-level transformation

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Example 1

• Histogram Equalization
• (a) Write a computer program for computing the
  histogram of an image.
• (b) Implement the histogram equalization
  technique discussed in Section 3.3.1.
• (c) Download Fig. 3.8(a) and perform histogram
  equalization on it.
• Fig3.08(a).bmp
• histo.c

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Example 2

• Arithmetic Operations
• Write a computer program capable of performing
  the four arithmetic operations between two
  images. This project is generic, in the sense
  that it will be used in other projects to follow.
  (See comments on pages 112 and 116 regarding
  scaling). In addition to
• multiplying two images, your multiplication
  function must be able to handle multiplication of
  an image by a constant.