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# Betti numbers

### From Computer Vision Primer

Betti numbers count the number of topological features in the image:

- objects or connected components – dimension 0,
- holes or tunnels – dimension 1, and
- voids or cavities – dimension 2.

These numbers in each dimension are captured by the Betti numbers, B_{0}, B_{1}, and B_{2}. Examples are in the table below.

B |
B |
B | |

Letter O |
1 |
1 |
0 |

Two letters O |
2 |
2 |
0 |

Letter B |
1 |
2 |
0 |

Donut |
1 |
1 |
0 |

Tire |
1 |
2 |
1 |

Ball |
1 |
0 |
1 |

Betti numbers are combined together to produce the well-known Euler number.

Continue to Topological Features of Images.