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


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)


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.


Illustration


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


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:


Illustration


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


Illustration (cont’d)


Graphic-Theoretic Techniques

  • Minimal-cost path


Illustration


Example


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


Foundation


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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