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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, B0, B1, and B2. Examples are in the table below.
|
B0 (parts) |
B1 (holes) |
B2 (voids) | |
|
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.
