Chapter 9 Morphological image processing

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Chapter 9 Morphological image processing

• 9.1 Preliminary
• Basic concepts from set theory
• Union
• Intersection
• Complement
• Difference
• Logic operations
• And
• Or
• Exor
• 9.2 dilation and erosion

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• 9.2.1 Dialtion
• Bridging gaps
• resulted directly in a binary image (the approach
  over the low pass filtering)
• 9.2.2 Erosion
• the erosion of A by is defined as
• is the set of all points z such that B,
  translated by z, is contained in A
• dilation and erosion are duals of each other with
  respect to set complement and reflection
• 9.3 Opening and closing
• opening
• smoothes the contour of an object, break narrow
  isthmuses and eliminates thin protrusions
• the closing of set A by structuring B, denoted
  A?B, is defined as A ?B (A?B) ? B

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• the boundary of A?B is established by the points
  in B that reach the farest into the boundary of A
  as B is rolled around the inside if this boundary
• Is obtained by taking the union of all translates
  of B that fit into A
• closing
• fuses narrow breaks and long thin gulfs,
  eliminates small hole, and fill gaps in the
  contour
• geometric interpretatin roll B on the outside of
  the boundary
• opening and closing are duals of each other with
  respect to set complementation and reflection
• the opeing operation satisfies the three
  following properties
• the closing operation satisfies the three
  following properties
• 9.4 The Hit-or Miss transform
• a basic tool for shape detection
• Fig. 9.12 is the local background W-X
• if B denotes the set composed of X and its
  background, the match of B in A, denoted as

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• 9.5 Some basic morphological algorithms
• 9.5.1 Boundary extraction
• the boundary of a set can be obtained by first
  eroding A by B B(A)A-(A(-)B)
• 9.5.2 Region filling
• begin with a point inside the boundary,
• fill the entire region with 1s
• where X0p, and B is the symmetric structuring
  element.
• The set union of Xk and A contains the filled set
  and its boundary
• 9.5.3 Extraction of connected components
• 9.5.4 Convex hull
• 9.5.5 Thinning
• 9.5.6 Thickening

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9.6 Extension to Gray-scale Images

• Develop algorithms for boundary extraction via a
  morphological operation
• 9.6.1 Dilation
• Gray-scale dilation of f by b denoted f b is
  defined as
• If all the values of the SE are positive, the
  output image tends to be brighter
• Dark details either are reduced or eliminated,
  depending on how their values nd shapes related
  to the SE
• For function of on variable Eq. reduces to the
  expression
• 9.6.2Erosion
• Gray-scale erosion of f by b denoted f b is
  defined as
• For function of on variable Eq. reduces to the
  expression
• Gray-scale dilation and erosion are dual with
  respect to function

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• General effect of erosion
• (1) if the elements of the SE are positive
• (2) The effect of bright details in the input
  image are smaller in area thane the SE is reduced
• 9.6.3 Opening and closing
• The gray-scale opening satisfies the following
  properties
• Remove small light details, while leaving the
  overall gray levels and larger right features
• The gray-scale closing satisfies the following
  properties
• Remove dark details from an image while leaving
  bright features relatively undisturbed

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• 9.6.4 Some applications of gray-scale morphology
• Morphological smoothing
• Perform a opening followed by a closing
• Remove or attenuate both bright and dark
  artifacts or noise
• Morphological gradient
• Use a dilation and a erosion to compute the
  morphological gradient
• Highlight sharp transition in the input image
• Use symmetrical structuring elements tends to
  depend less on edge directionality

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Chapter 9 Morphological Image Processing

• Top-hat transformation
• The operation is denoted as
• Use a cylindrical or parallelepiped structuring
  element with a flat-top
• Is useful for enhancing detail in the presence of
  shading
• Texture segmentation
• Close the input image by successively larger
  structuring elements
• When the size of the structuring element
  corresponds to that of the small blobleaving
  only the larger blobs and the light background
  on the left
• A single opening is performed with a structuring
  element that is large in relation to the
  separation between the large blobsremoves the
  light patches between blobs
• Granulometry
• Determine the size of distribution of particles
  in an in an image

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• Morphological operations
• (1) Opening operation with structuring elements
  of increasing size
• (2) The difference between the original and its
  opening is computed after each pass when a
  different structuring element is completed
• (3) Normalize the differences and construct a
  histogram of a particle of similar size
• (4) Measure a the relative number of such
  particles by computing the difference between the
  input and output images
• Useful for describing regions with a predominant
  particle-like character
• Ex 8, 14, 19,