ShengFang Huang

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Digital Image Processing

• Sheng-Fang Huang
• Chapter 11 part I

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Chapter 11Representation and Description

• After the image is segmented into regions, how to
  represent and describe these regions?
• In terms of its external characteristics
  (boundary)
• In terms of its internal characteristics (pixels
  in the region)

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11.1 Representation Chain code

• Chain codes are used to represent a boundary as a
  connected sequence of straight line segments of
  specified length and direction.
• Based on 4- or 8- connectivity.
• Chain code is generated by following a boundary
  in clockwise direction and assigning a direction
  to the segments connecting every pair of pixels.
• Disadvantages
• The chain code is quite long.
• Any small disturbance along the boundary due to
  noise cause change in the code.
• ?resample the boundary with a larger grid
  spacing.

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11.1 Representation Chain codes

• The chain code of a boundary depends on the
  starting point and is not rotation invariant.
• We can normalize chain codes by using the first
  difference of the chain code.
• Example
• The 4-direction chain code 10103322
• The first difference of the code 33133030
• 3 (1-2) mod 4 3
• 3 (0-1) mod 4 3
• 1 (1-0) mod 4 1

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11.1 Representation Signature

• 1-D functional representation of a boundary.
• Plot the distance from the centroid to the
  boundary as a function of angles, r(?).
• Invariant to translation, but depend on the
  rotation and scaling.
• Normalize with respect to rotation
• Select the starting point as the point farthest
  to the centroid.
• Normalize with respect to size
• Scale all r(?) so that they always span the same
  range, say, 0, 1.
• Divided by the maximum.
• Divided by the variance of r(?).

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11.1 Representation Skeletons

• An important approach to representing the
  structural shape is to reduce it to a graph.
• This reduction may be achieved by obtaining its
  skeleton via a thinning algorithm
  (skeletonization).
• Medial axis transformation (MAT)
• proposed by Blum 1967
• For each point p in region R, we find its closest
  neighbor in the border B.
• If p has more than one such neighbor, it is said
  to belong to the medial axis (skeleton) of R.

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11.1 Representation Skeletons

• Thinning algorithm iteratively delete the edge
  points of a region subject to the following
  constraints
• Does not remove the end points,
• Does not break connectivity, and
• Does not cause excessive erosion of the region.

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11.2 Boundary Descriptor

• What is the difference between representation and
  description?
• Simple descriptors
• Length
• Diameter Diam(B)maxD(pi, pj) where pi and pj
  are two furthest points on the boundary.
• The line between these two extremes are called
  the major axis.
• The minor axis is the one perpendicular to the
  major axis where the major and minor axes form
  the basic rectangle.
• Eccentricity major axis/minor axis
• Curvature changes of slope.
• Difficult in digit boundaries, because they are
  usually ragged.
• Can be improved by using the curvature between
  adjacent boundary segments.

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11.2.4 Statistical Moments

• The shape of boundary segments can be described
  by simple statistical moments, such as mean,
  variance, and higher-order moments.
• The nth moment of v about its mean m is

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11.2.4 Statistical Moments

• Figure 11.5 represented as 1-D function g(r).
• Treat the amplitude of g as a discrete random
  variable v and form an amplitude histogram p(vi),
  i0,1,A-1, where A is the number of discrete
  amplitude increments in which we divide the
  amplitude scale.

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• The two endpoints are linked by a line segment.
• The coordinates of points are rotated until the
  line is horizontal.
• The distance of each point to the horizontal
  axis is normalized and treated as a discrete
  random variable to form an histogram p(vi) where
  i0,1,A-1,

• g(ri) is treated as the probability of which the
  value ri occurs.

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• The moments are
• where
• The second moment measures the spread of the
  curve about the mean value of r
• The third moment measures its symmetry with
  reference to the mean.

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11.3 Regional Descriptors -Simple Descriptor

• The area of a region is the number of pixels in
  the region.
• Perimeter is the length of the boundary.
• Compactness perimeter2 / area.

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11.3 Regional Descriptors - Topological Descriptor

• Topology is the study of properties of a figure
  that are unaffected by any deformation
  (rubber-sheet distortion).
• The number of holes H
• The number of connected components C
• Euler number E E C - H.
• Regions represented by straight-line segments
  (polygonal networks), such as fig. 11.20, has the
  following relationship in topology as
• E V - Q F C- H
• where V is the number of vertices and Q is
  the number of edges.

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