Representation and Description

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Chapter 11

• Representation and Description

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Preview

• Representing a region involves two choices
• In terms of its external characteristics (its
  boundary)
• In terms of its internal characteristics (the
  pixels comprising the region)
• Describe the boundary by features such as length,
  orientation, number of concavities.
• Descriptors should be as insensitive as possible
  to variations in size, translation and rotation.

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Representation Chain Code

• Represent a boundary by a connected sequence of
  straight-line segment of specified length and
  direction.
• Based on 4- or 8-connectivity

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Chain Code
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Polygonal Approximations

• Minimum perimeter polygons
• Merging techniques
• Splitting techniques

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Signatures

• 1-D functional representation of a boundary.

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Boundary Segments

• Convex hulls, convex deficiency

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Skeletons

• Medial axis transform (MAT)
• Thinning process

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Boundary Descriptors

• Simple descriptors length, diameter, major/minor
  axis, ratio of major to minor axis
  (eccentricity), curvature.
• Shape numbers

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Fourier Descriptors

• (x0,y0),(x1,y1,),,(xK-1,yK-1)
• Viewed a series of complex numbers
  s(k)x(k)jy(k)
• Take Fourier transform of s(k) and keep only P
  terms. (P lt K)

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Illustration
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Statistical Moments

• The nth moment of v about its mean is defined as

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Regional Descriptors

• Simple descriptors area, perimeter, compactness,
  mean, median, max, min.
• Topological descriptor Euler number EC-H.
• Texture
• Moments of 2-D functions

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More descriptors

• PCA
• Relational descriptors