CIS303 Advanced Forensic Computing

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CIS303Advanced Forensic Computing

• Dr Giles Oatley

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Point Operations

• Point operations are operations performed on
  individual pixels in an image. These operations
  are often based on the image histogram For this
  course we are interested in point operations for
  improving image quality and basic segmentation by
  thresholding, and image arithmetic.
• Sub topics
• Linear point operations
• Non linear point operations
• The grey level histogram.
• Histogram operations
• Thresholding
• Colour thresholding
• Image arithmetic

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The point operation

• A point operation uses a function f to map each
  pixel in the input image to the corresponding
  pixel in the output image.
• A linear point operation uses a simple linear
  mapping function

Pout(x,y) a.Pin(x,y) b
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Consequences of the choice of a and b
Pout(x,y) a.Pin(x,y) b

• If a 1 and b 0 the image is simply copied
• If agt1 the contrast is increased and if a lt 1 the
  contrast is decreased.
• If a 1 and b is non zero then the output image
  has the grey levels moved up or down. Thus the
  entire image becomes darker or lighter.
• If a lt 0 then light areas become dark and dark
  areas become light. In effect the image is
  complemented.

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Examples
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Non linear point operations

• In terms of improving the visible information
  content in an image a non linear point operation
  is often more effective.
• On of the most useful is the gamma correction.
• If gamma (?) lt 1, the mapping is weighted towards
  higher (brighter) output values and if it is gt 1,
  it is weighted towards lower (darker) values.
• See the imadjust function in the IPT.

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gamma correction example
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Logarithmic transformation

• Logarithmic and contrast-stretching
  transformations are basic tools for dynamic range
  manipulation.
• Logarithmic transformations can be implemented
  using the expression
• g c log(1 double(f))
• Where c is a constant
• One of the principal aims is to compress dynamic
  range e.g. a Fourier spectrum might have values
  in the range 0 106 or higher.
• When displayed on a monitor linearly scaled to 8
  bits, the high values dominate the display,
  resulting in lost visual detail for the lower
  intensity values in the spectrum
• By computing the log, a dynamic range of 106 is
  reduced to approximately 14.
• This is illustrated in the next slide.

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Logarithmic plot of Fourier spectrum (taken from
DIPUM)
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Contrast stretching

• The function compresses the input levels lower
  than m into a narrow range of dark levels in the
  output image.
• Similarly, it compresses the values above m into
  a narrow band of light levels in the output.
• The result is an image of higher contrast. The
  limiting case is shown above right the output
  is a binary image and the function is called
  thresholding (used for image segmentation).
• An example is shown on the next slide.

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Contrast-stretching of bone scan image (taken
from DIPUM)
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The grey level histogram

• An image histogram records the frequency of each
  grey level in an image.
• MatLab provides the imhist function to
  accomplish this
• imhist(J,n)
• where J is the image and n is the number of
  bins. For a greyscale image if n is omitted the
  value 256 (0 to 255) is assumed.
• If you need to work with the actual values of the
  histogram you can use the extended format
• counts,x imhist(J,n)
• where counts is the number of counts in each bin
  whose value is given in the vector x

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Displaying histograms in MatLab

• function ShowHistogram
• To demonstrate image histograms
• P imread(house.jpg')
• figure('color','w')
• subplot(2,2,1), imshow(P)
• subplot(2,2,2), imhist(P,256)
• Q imread(house_gamma.jpg')
• subplot(2,2,3), imshow(Q)
• subplot(2,2,4), imhist(Q,256)

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Example
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Other ways of displaying a histogram (DIPUM)
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Histogram equalisation

• A very effective and simple way of bringing out
  detail in an image is carry out histogram
  equalisation. The objective is to produce an
  equal number of pixels in all grey levels.
  Mathematically the operation can be characterised
  by
• Thus the output image is obtained by mapping each
  pixel with level rj into the corresponding pixel
  with level sk, by calculating the cumulative sum
  of the probability density function (PDF) of the
  input image up to each level.
• Note that the above equation assumes black
  white is in the range 0 1. Multiply by a scale
  factor of 255 to make the range 0 255.
• See Gonzalez and Woods for a more mathematical
  explanation.

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Example of histogram equalisation
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MatLab implementation

• MatLab provides the histeq function to perform
  the histogram equalisation operation. We can
  modify the previous version of ShowHistogram to
  demonstrate this
• Additional code is to show the cumulative
  histograms.

• function ShowHistogram
• To demonstrate image histograms
• P imread(house.jpg')
• figure('color','w')
• subplot(2,2,1), imshow(P)
• Q T histeq(P)
• subplot(2,2,2), plot(0255,T)
• subplot(2,2,3), imshow(Q)
• C X imhist(Q)
• subplot(2,2,4), plot(0255,cumsum(C)/sum(C))

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Illustration of the cumulative sum
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Further example of equalisation (DIPUM)
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The histeq function

• In the demonstration programme I have used the
  function in the form
• Q,T histeq(P)
• where P is the input image, Q the output image
  and T the cumulative histogram of P used in the
  equalisation process that is the term
• Histogram equalisation is not always successful
  in revealing image content and more subtle
  variants can be invoked such as histogram
  matching where the histogram profile of the
  input image is matched to either a standard
  profile (user defined) or to the profile of a
  second image. MatLab allows this through a simple
  extension of the syntax above
• Q,T histeq(P,hgram)

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Histogram matching example (DIPUM)
Specified histogram (top)
Histogram equalisation
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Contrast-Limited Adaptive Histogram Equalization
(CLAHE).

• Histogram equalisation does generally improve the
  information visibility but it applies the same
  equalisation function to the whole image.
• CLAHE breaks the image into tiles and
  determines the best function to use for each
  tile.
• The result will be an image which shows
  artificial boundaries between tiles and so an
  interpolation scheme is used to smooth the pixel
  intensities between tiles.
• The MatLab function that performs CLAHE is
  adapthisteq
• Two of the simpler forma of the function are
• Q adapthisteq(P)
• which defaults all parameters and
• Q adapthisteq(P,numTiles,m n)
• which declares an analysis using m by n tiles.

COMM2J Vision Intelligent Robots 2005
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Result of using CLAHE
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Grey level thresholding

• If the histogram of a grey level image shows
  distinct features which can be associated with an
  object in the scene we can threshold the scene
  by picking out the pixels which represent the
  feature.
• The process is known as segmentation in which a
  logical test is applied to each pixel of the
  input image and the output image is binary with
  1 representing true and 0 a false.
• Typical test conditions on the image pixel p(x,y)
  might be
• p(x,y)gt160
• 50ltp(x,y)lt100

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Example of grey level thresholding
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Colour thresholding

• The concept of thresholding can easily be
  extended to colour images where we can adopt one
  of the strategies
• Select the colour plane with the greatest
  contrast between the object and the rest of the
  scene and then apply grey level thresholding.
• Select a region of the colour space which
  differentiates the object. This is easiest if the
  region has the same volume geometry as the space
  (e.g. a cube in RGB colour space). However any
  volume shape can be used if appropriate.

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Example of best plane selection using RGB
colours
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Example of best plane selection using HSV
colours
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Example of region selection in RGB space
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Image arithmetic - subtraction
-

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Image subtraction code

• function vansubtract
• function vansubtract Takes an RGB image and
• segments out the vehicle content
• 1. Read images
• a imread('whitevan.jpg')
• b imread('street.jpg')
• 2. Make sure 2 images are the same size
• m,n size(a)
• b imresize(b,m,n)
• 3. Subtract images, resize and display
• cimsubtract(a,b)
• imresize(c,0.75)
• imshow(c)

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Tutorial

• Investigate the following Matlab commands (use
  the Matlab Help information) imadjust imhist
  histeq adapthisteq.
• Create M-files to demonstrate the Matlab code
  given on these slides. Try playing altering the
  gamma correction of the house.jpg image and
  adjust the gamma parameter to see what happens.
• Write an M-file to demonstrate region selection
  in RGB space, using the lego.jpg image.
• Write an M-file to theshold the image bean.jpg.
  To do this you should first convert the image to
  greyscale (for example by selecting the best
  colour channel can this be done
  automatically?).
• Then manipulate the histogram data returned using
  the imhist IPT function. Now investigate the
  built-in function graythresh. Find out how it
  works (by looking on the web) and compare its
  performance with your algorithm.

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Links

• Try the following links with some interesting
  Java Applets
• http//www.s2.chalmers.se/research/image/Java/appl
  ets_list.htm
• http//homepages.inf.ed.ac.uk/rbf/HIPR2/

COMM2J Vision Intelligent Robots 2005