EE 7730

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EE 7730

• Morphological Image Processing

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Example
Two semiconductor wafer images are given. You are
supposed to determine the defects based on these
images.
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Example
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Example
Absolute value of the difference
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Example
gtgt b zeros(size(a)) gtgt b(agt100) 1 gtgt
figure imshow(b, )
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Example
gtgt c imerode(b,ones(3,3)) gtgt figure
imshow(c,)
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Example
gtgt d imdilate(c,ones(3,3)) gtgt figure
imshow(d,)
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Mathematical Morphology

• We defined an image as a two-dimensional
  function, f(x,y), of discrete (or real)
  coordinate variables, (x,y).
• An alternative definition of an image can be
  based on the notion that an image consists of a
  set of discrete (or continuous) coordinates.

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Morphology
A binary image containing two object sets A and B

• B (0,0), (0,1), (1,0)
• A (5,0), (3,1), (4,1), (5,1), (3,2), (4,2),
  (5,2)

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Morphology

• Sets in morphology represent the shapes of
  objects in an image.
• For example, the set A (a1,a2) represents a
  point in a binary image.
• The set of all black pixels in a binary image is
  a complete description of the image.

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Morphology

• Morphology can be extended to gray-scale images.
• In gray-scale images, sets consist of elements
  whose components are in a 3D space.
• For example, the set A (a1,a2,a3) is a point
  at coordinates (a1,a2) with gray-scale intensity
  (a3).

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Mathematical Morphology

• Morphology is a tool for extracting and
  processing image components based on shapes.
• Morphological techniques include filtering,
  erosion, dilation, thinning, pruning.

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Basic Set Operations
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Some Basic Definitions

• Let A and B be sets with components a(a1,a2) and
  b(b1,b2), respectively.
• The translation of A by x(x1,x2) is
• A x c c a x, for a ? A
• The reflection of A is
• Ar x x -a for a ? A
• The complement of A is
• Ac x x ? A
• The union of A and B is
• A ? B x x ? A or x ? B
• The intersection of A and B is
• A ? B x x ? A and x ? B

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Some Basic Definitions

• The difference of A and B is.
• A B A ? Bc x x ? A and x ? B
• A and B are said to be disjoint or mutually
  exclusive if they have no common elements.
• If every element of a set A is also an element of
  another set B, then A is said to be a subset of
  B.

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Logic Operations
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Some Basic Definitions

• Dilation
• A ? B x (B x) ? A ? ?
• Dilation expands a region.

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Some Basic Definitions
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Some Basic Definitions
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Some Basic Definitions

• Erosion
• A ? B x (B x) ? A
• Erosion shrinks a region.

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Some Basic Definitions
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Some Basic Definitions

• Dilation and erosion are duals of each other
• (A ? B)c Ac ? Br

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Some Basic Definitions

• Opening is erosion followed by dilation
• A ? B (A ? B) ? B
• Opening smoothes regions, removes spurs, breaks
  narrow lines.

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Some Basic Definitions
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Some Basic Definitions

• Closing is dilation followed by erosion
• A ? B (A ? B) ? B
• Closing fills narrow gaps and holes in a region.

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Some Basic Definitions
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Some Basic Definitions
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Some Morphological Algorithms

• Opening followed by closing can eliminate noise
• (A ? B) ? B

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Some Morphological Algorithms
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Some Morphological Algorithms

• Boundary of a set, A, can be found by
• A - (A ? B)

B
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Some Morphological Algorithms

• A region can be filled iteratively by
• Xk1 (Xk ? B) ? Ac ,
• where k 0,1,
• and X0 is a point inside the region.

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Some Morphological Algorithms
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Some Morphological Algorithms

• Connected components can be extracted iteratively
  by
• Xk1 (Xk ? B) ? A ,
• where k 0,1,
• and X0 is the initial point.

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Some Morphological Algorithms
Application example Using connected components
to detect foreign objects in packaged food. There
are four objects with significant size!
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Some Basic Definitions

• Hit-or-miss operation detects shapes
• A ? B (A ? X) ? Ac ? (W-X)
• where A consists of shape X and other shapes,
• B consists of shape X only,
• and W is a window that is larger than X.

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Some Morphological Algorithms

• Thinning Thin regions iteratively retain
  connections and endpoints.
• Skeletons Reduces regions to lines of one pixel
  thick preserves shape.
• Convex hull Follows outline of a region except
  for concavities.
• Pruning Removes small branches.

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Thinning
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Skeleton
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Pruning
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Summary
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Summary
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Summary
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Summary
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Summary
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Extensions to Gray-Scale Images
Dilation
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Extensions to Gray-Scale Images
Erosion
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Extensions to Gray-Scale Images

• Dilation
• Makes image brighter
• Reduces or eliminates dark details
• Erosion
• Makes image lighter
• Reduces or eliminates bright details

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Extensions to Gray-Scale Images
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Extensions to Gray-Scale Images
Opening Narrow bright areas are
reduced. Closing Narrow dark areas are reduced.
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Extensions to Gray-Scale Images
Opening followed by closing ?Morphological
smoothing operation. Removes or attenuates both
bright and dark artifacts/noise.
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Extensions to Gray-Scale Images
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Application Example
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Application Example-Segmentation
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Application Example-Granulometry