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Shape Descriptors

Shape Descriptors. Desired Properties. Uniqueness Invariance Size Rotations Translations Noise . Moments. Discrete Form. Uniqueness Theorem. The double moment sequence {m pq } is uniquely determined by B(x,y) and conversely B(x,y) is uniquely determined by {m pq } .

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Shape Descriptors

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  1. Shape Descriptors

  2. Desired Properties • Uniqueness • Invariance • Size • Rotations • Translations • Noise

  3. Moments Discrete Form

  4. Uniqueness Theorem • The double moment sequence {mpq} is uniquely determined by B(x,y) and conversely B(x,y) is uniquely determined by {mpq}

  5. Characteristic Function/ Moment Generating Function Characteristic Function: Moment Generating Function:

  6. Characteristic Function/ Moment Generating Function Characteristic Function: Moment Generating Function:

  7. Central Moments Translation Invariant

  8. Central Moments

  9. Hu Moments Translation, Rotation, Scaling Invariant

  10. Hu Moments

  11. Hu Moments

  12. Medial Axis Transform

  13. Medial Axis Transform

  14. Medial Axis Transform

  15. Medial Axis Transform

  16. Medial Axis Transform

  17. Medial Axis Transform

  18. Suggested Reading • M-K. Hu., “Visual pattern recognition by moment invariants,” Computer methods in image analysis. • H. Blum, “A transformation for extracting new descriptors of shape,” Computer methods in image analysis. • Chapter 4, Mubarak Shah, “Fundamentals of Computer Vision”.

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