Chapter 10
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Chapter 10. Image Segmentation. Preview. Segmentation subdivides an image into its constituent regions or objects. Level of division depends on the problem being solved.

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Chapter 10

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Chapter 10

Image Segmentation


  • 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)

Chapter Outline

  • Detection of discontinuities

  • Edge linking and boundary detection

  • Thresholding

  • Region-based segmentation

  • Morphological watersheds

  • Motion in segmentation

Detection of Discontinuities

  • Define the response of the mask:

  • Point detection:

Point Detection Example

Line Detection

  • Masks that extract lines of different directions.


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

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.

Zero-Crossings of 2nd Derivative

Noisy Edges: Illustration

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.

Gradient Operators

  • Gradient:

  • Magnitude:

  • Direction:

Gradient Masks

Diagonal Edge Masks


Illustration (cont’d)

Illustration (cont’d)

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.

Laplacian of Gaussian

  • Definition:


Edge Linking: Local Processing

  • Link edges points with similar gradient magnitude and direction.

Global Processing: Hough Transform

  • Representation of lines in parametric space: Cartesian coordinate

Hough Transform

  • Representation in parametric space: polar coordinate


Illustration (cont’d)

Graphic-Theoretic Techniques

  • Minimal-cost path




  • 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


The Role of Illumination

Basic Global Thresholding

Another Example

Basic Adaptive Thresholding

Basic Adaptive Thresholding (cont’d)

Optimal Global and Adaptive Thresholding

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

Thresholds Based on Several Variables

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 i=1,2,…n

    • (e) P(Ri U Rj)= FALSE for i != j

Region Growing

Region-Splitting and Merging

Morphological Watersheds (I)

Morphological Watersheds (II)

Motion-based Segmentation (I)

Motion-based Segmentation (II)

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