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Boundary Representation and Description Techniques in Image Processing

Learn about representing and describing regions in image processing, from chain codes to polygonal approximations and boundary descriptors. Explore techniques such as Fourier descriptors, statistical moments, and texture analysis.

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Boundary Representation and Description Techniques in Image Processing

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  1. Chapter 11 Representation and Description

  2. Preview • Representing a region involves two choices: • In terms of its external characteristics (its boundary) • In terms of its internal characteristics (the pixels comprising the region) • Describe the boundary by features such as length, orientation, number of concavities. • Descriptors should be as insensitive as possible to variations in size, translation and rotation.

  3. Representation: Chain Code • Represent a boundary by a connected sequence of straight-line segment of specified length and direction. • Based on 4- or 8-connectivity

  4. Chain Code

  5. Polygonal Approximations • Minimum perimeter polygons • Merging techniques • Splitting techniques

  6. Signatures • 1-D functional representation of a boundary.

  7. Boundary Segments • Convex hulls, convex deficiency

  8. Skeletons • Medial axis transform (MAT) • Thinning process

  9. Boundary Descriptors • Simple descriptors: length, diameter, major/minor axis, ratio of major to minor axis (eccentricity), curvature. • Shape numbers

  10. Fourier Descriptors • (x0,y0),(x1,y1,),…,(xK-1,yK-1) • Viewed a series of complex numbers s(k)=x(k)+jy(k) • Take Fourier transform of s(k) and keep only P terms. (P < K)

  11. Illustration

  12. Statistical Moments • The nth moment of v about its mean is defined as:

  13. Regional Descriptors • Simple descriptors: area, perimeter, compactness, mean, median, max, min. • Topological descriptor: Euler number E=C-H. • Texture • Moments of 2-D functions

  14. More descriptors • PCA • Relational descriptors

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