Image Segmentation

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Chapter 10

• Image Segmentation

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Preview

• Segmentation subdivides an image into its
  constituent regions or objects.
• Level of division depends on the problem being
  solved.
• Image segmentation algorithms generally are based
  on one of two basic properties of intensity
  values discontinuity (e.g. edges) and similarity
  (e.g., thresholding, region growing, region
  splitting and merging)

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Chapter Outline

• Detection of discontinuities
• Edge linking and boundary detection
• Thresholding
• Region-based segmentation
• Morphological watersheds
• Motion in segmentation

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Detection of Discontinuities

• Define the response of the mask
• Point detection

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Point Detection Example
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Line Detection

• Masks that extract lines of different directions.

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Illustration
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Edge Detection

• An ideal edge has the properties of the model
  shown to the right
• A set of connected pixels, each of which is
  located at an orthogonal step transition ingray
  level.
• Edge local concept
• Region Boundary global idea

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Ramp Digital Edge

• In practice, optics, sampling and other image
  acquisition imperfections yield edges that area
  blurred.
• Slope of the ramp determined by the degree of
  blurring.

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Zero-Crossings of 2nd Derivative
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Noisy Edges Illustration
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Edge Point

• We define a point in an image as being an edge
  point if its 2-D 1st order derivative is greater
  than a specified threshold.
• A set of such points that are connected according
  to a predefined criterion of connectedness is by
  definition an edge.

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Gradient Operators

• Gradient
• Magnitude
• Direction

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Gradient Masks
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Diagonal Edge Masks
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Illustration
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Illustration (contd)
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Illustration (contd)
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The Laplacian

• Definition
• Generally not used in its original form due to
  sensitivity to noise.
• Role of Laplacian in segmentation
• Zero-crossings
• Tell whether a pixel is on the dark or light side
  of an edge.

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Laplacian of Gaussian

• Definition

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Illustration
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Edge Linking Local Processing

• Link edges points with similar gradient magnitude
  and direction.

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Global Processing Hough Transform

• Representation of lines in parametric space
  Cartesian coordinate

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Hough Transform

• Representation in parametric space polar
  coordinate

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Illustration
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Illustration (contd)
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Graphic-Theoretic Techniques

• Minimal-cost path

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Illustration
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Example
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Thresholding

• Foundation background point vs. object point
• The role of illumination f(x,y)i(x,y)r(x,y)
• Basic global thresholding
• Adaptive thresholding
• Optimal global and adaptive thresholding
• Use of boundary characteristics for histogram
  improvement and local thresholding
• Thresholds based on several variables

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Foundation
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The Role of Illumination
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Basic Global Thresholding
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Another Example
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Basic Adaptive Thresholding
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Basic Adaptive Thresholding (contd)
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Optimal Global and Adaptive Thresholding

• Refer to Chapter 2 of the Pattern
  Classification textbook by Duda, Hart and Stork.

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Thresholds Based on Several Variables
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Region-Based Segmentation

• Let R represent the entire image region. We may
  view segmentation as a process that partitions R
  into n sub-regions R1, R2, , Rn such that
• (a)
• (b) Ri is a connected region
• (c)
• (d) P(Ri) TRUE for i1,2,n
• (e) P(Ri U Rj) FALSE for i ! j

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Region Growing
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Region-Splitting and Merging

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Morphological Watersheds (I)
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Morphological Watersheds (II)
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Motion-based Segmentation (I)
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Motion-based Segmentation (II)