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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:

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.

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:

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

Graphic-Theoretic Techniques

- Minimal-cost path

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

Optimal Global and Adaptive Thresholding

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

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

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