Shape Descriptors

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
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Medial Axis Transform
15
Medial Axis Transform
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Medial Axis Transform
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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.