CIS303 Advanced Forensic Computing

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CIS303Advanced Forensic Computing

• Dr Giles Oatley

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Morphological Image Processing

• The word morphology denotes a branch of biology
  that deals with the form and structure of animals
  and plants. In image processing, the word is used
  in the context of tools for extracting image
  components that are useful e.g. by removing
  imperfections such as those caused by noise,
  texture or inaccurate specification of a
  threshold. Morphological techniques can also be
  applied to greyscale images, where they can be
  used for non-linear smoothing and feature
  enhancement.
• Sub topics
• Erosion.
• Dilation.
• Opening and closing.
• Hit-and-Miss Transform.
• Thinning and thickening.

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Erosion

• Erosion shrinks or thins objects in a binary
  image.
• The manner and extent of shrinking is controlled
  by a structuring element.

• Structuring element

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Erosion

• Erosion is the set of all points in the image,
  where the structuring element fits into.
• Consider each foreground pixel in the input
  image. If the structuring element fits in, write
  a 1 at the origin of the structuring element.
• Simple application of pattern matching.
• Erosion shrinks foreground and enlarges the
  background

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Matlab function strel

• The IPT function strel constructs structuring
  elements with a variety of shapes and sizes. Its
  syntax is
• se strel(shape, parameters)
• See Matlab help for the various syntax forms.
  However, they include diamond, linear, disk,
  octagon, rectangle, square, arbitrary etc.
• Examples of an image eroded with a disk of radius
  10, 5 and 20 are shown below

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Structuring element (kernel)

• Structuring Elements can have varying sizes.
• Usually, element values are 0,1 and none.
• Structural Elements have an origin.
• For thinning, other values are possible.
• Empty spots in the Structuring Elements are dont
  cares.

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1-D Erosion example (1)
Input image
Structuring Element
Output Image
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1-D Erosion example (2)
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1-D Erosion example (3)
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1-D Erosion example (4)
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1-D Erosion example (5)
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1-D Erosion example (6)
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1-D Erosion example (7)
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1-D Erosion example (8)
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Counting coins example

• Counting objects can be difficult when they touch
  each other.
• Solution Binarization and Erosion separates
  them.
• Note that the coins become smaller can be a
  problem if structuring element causes object to
  disappear!

In Matlab, use the strel function to construct
the structuring element, in conjunction with
imerode to perform the erosion process.
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Dilation

• Dilation has the opposite effect of erosion.
• It grows or thickens objects in a binary
  image.
• As in erosion, this is controlled by the
  structuring element.

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Exercise
In the 1-D example below, deduce the final image
following dilation.
Input image
Structuring Element
Output Image
Solution
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Dilation examples
Edge Detection (a) Dilate input image (b)
Subtract input image from dilated image (c)
Edges remain.
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Opening and Closing

• Derived from the fundamental operations of
  Dilatation and Erosion.
• Usually applied to binary images, but gray value
  images are also possible.
• Opening and closing are dual operations.
• Opening and Closing are idempotent repeated
  application has no further effects.
• Opening
• Similar to Erosion.
• Used mainly for spot and noise removal.
• However, it is less destructive than erosion.
• Opening is defined as an Erosion, followed by a
  Dilatation using the same structuring element for
  both operations.

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Opening

• Take the structuring element (SE) and slide it
  around inside each foreground region.
• All pixels which can be covered by the SE with
  the SE being entirely within the foreground
  region will be preserved.
• All foreground pixels which can not be reached by
  the structuring element without lapping over the
  edge of the foreground object will be eroded
  away!
• Example Structuring element 3x3 square

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Opening examples
Opening with a 11 pixel diameter disc
3x9 and 9x3 Structuring Element
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Closing

• Closing
• Similar to Dilation used for removal of holes.
• Tends to enlarge regions and shrink backgrounds.
• Closing is defined as a Dilatation, followed by
  an Erosion using the same structuring element for
  both operations.
• Take the structuring element (SE) and slide it
  around outside each foreground region.
• All background pixels which can be covered by the
  SE with the SE being entirely within the
  background region will be preserved.
• All background pixels which can not be reached by
  the structuring element without lapping over the
  edge of the foreground object will be turned into
  a foreground.

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Closing example
Example structuring element 3x3 square
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Another closing example
Closing operation with a 22 pixel disc, closes
small holes in the foreground.
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And another
Threshold, closing with disc of size 20.
Note that opening is the dual of closing i.e.
opening the foreground pixels with a particular
structuring element is equivalent to closing the
background pixels with the same element.
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DIPUM illustration of opening and closing
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Opening followed by closing example (DIPUM)

• Opening removes the noisy spots in the
  fingerprint image. However, numerous gaps are
  introduced in the ridges of the fingerprint.
• These are filled in by the closing operation
• See imopen and imclose in Matlab.

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Top-hat transformation (grayscale morphology)

• Openings can be used to compensate for
  non-uniform background illumination.
• Uneven illumination can make thresholding
  difficult.
• Opening a grayscale image can produce a
  reasonable estimate of the background to the
  image, provided the structuring element is large
  enough so that it doesnt fit entirely within the
  objects.
• By subtracting this background image from the
  original, we can produce an image of the objects
  with a reasonable even background.
• This is called a top-hat transformation and can
  be done in Matlab using the following IPT
  function
• f2 imtophat(f, se)
• This is illustrated by the example on the
  following slide.

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Top-hat transformation DIPUM example
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Hit-and-miss transform

• Used to look for particular patterns of
  foreground and background pixels
• Very simple object recognition
• Example for a Hit-and-miss Structuring Element
  Contains 0s, 1s and dont cares. Usually a 1
  at the origin

• Similar to Pattern Matching
• If foreground and background pixels in the
  structuring element exactly match foreground and
  background pixels in the image, then the pixel
  underneath the origin of the structuring element
  is set to the foreground colour.

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Hit-and-miss example corner detection

• Structuring Elements representing four corners.
• Apply each Structuring Element.
• Use OR operation to combine the four results.

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Thinning

• Used to remove selected foreground pixels from
  binary images
• After edge detection, lines are often thicker
  than one pixel. Thinning can be used to thin
  those line to one pixel width.
• Definition let K be a kernel and I be an image
• Thin(I,K) I HitAndMiss(I,K)
• with 0-10
• If foreground and background fit the structuring
  element exactly, then the pixel at the origin of
  the SE is set to 0!
• Note that the value of the SE at the origin is 1
  or dont care!

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Thinning example
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Thickening

• Used to grow selected regions of foreground
  pixels e.g. applications like approximation of
  convex hull.
• Definition let K be a kernel and I be an image
• Thicken(I,K) I HitAndMiss(I,K)
• with 111

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Labelling connected components - definitions
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Labelling connected components - bwlabel

• The IPT function bwlabel computes all the
  connected components in a binary image
• L num bwlabel(f, conn)
• Where f is a binary image and conn specifies the
  desired connectivity (default 8).
• Output L contains the labelled matrix. The pixels
  in each different connected component are
  assigned a unique integer, from 1 to the total
  number of connected components.
• In other words, the pixels labelled 1 belong to
  the first connected component, those labelled 2
  belong to the second etc.
• Regional descriptors for the objects can then be
  computed using the Matlab function regionprops.
  (e.g. Area, perimeter etc.)

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Example (DIPUM)
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Tutorial

• In this weeks laboratory, investigate the
  following
• Create M-files to demonstrate the Matlab code
  given on these slides.
• Investigate the following Matlab commands (use
  the Matlab Help information) strel imerode
  imdilate imopen imclose.
• Investigate bwhitmiss and bwmorph in Matlab.
  Using suitable images, try out various operations
  including thickening and thinning.
• Try out the following web sites
• http//www.s2.chalmers.se/research/image/Java/appl
  ets_list.htm
• http//homepages.inf.ed.ac.uk/rbf/HIPR2/fulldemo.h
  tm