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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

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

Chapter Outline

  • Detection of discontinuities

  • Edge linking and boundary detection

  • Thresholding

  • Region-based segmentation

  • Morphological watersheds

  • Motion in segmentation

Detection of discontinuities

Detection of Discontinuities

  • Define the response of the mask:

  • Point detection:

Point detection example

Point Detection Example

Line detection

Line Detection

  • Masks that extract lines of different directions.



Edge detection

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

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 2 nd derivative

Zero-Crossings of 2nd Derivative

Noisy edges illustration

Noisy Edges: Illustration

Edge point

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 Operators

  • Gradient:

  • Magnitude:

  • Direction:

Gradient masks

Gradient Masks

Diagonal edge masks

Diagonal Edge Masks



Illustration cont d

Illustration (cont’d)

Illustration cont d1

Illustration (cont’d)

The laplacian

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

Laplacian of Gaussian

  • Definition:



Edge linking local processing

Edge Linking: Local Processing

  • Link edges points with similar gradient magnitude and direction.

Global processing hough transform

Global Processing: Hough Transform

  • Representation of lines in parametric space: Cartesian coordinate

Hough transform

Hough Transform

  • Representation in parametric space: polar coordinate



Illustration cont d2

Illustration (cont’d)

Graphic theoretic techniques

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

The Role of Illumination

Basic global thresholding

Basic Global Thresholding

Another example

Another Example

Basic adaptive thresholding

Basic Adaptive Thresholding

Basic adaptive thresholding cont d

Basic Adaptive Thresholding (cont’d)

Optimal global and adaptive thresholding

Optimal Global and Adaptive Thresholding

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

Thresholds based on several variables

Thresholds Based on Several Variables

Region based segmentation

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 Growing

Region splitting and merging

Region-Splitting and Merging

Morphological watersheds i

Morphological Watersheds (I)

Morphological watersheds ii

Morphological Watersheds (II)

Motion based segmentation i

Motion-based Segmentation (I)

Motion based segmentation ii

Motion-based Segmentation (II)

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