I have three pixels x y z.Pixel x and y are neighbourhood and pixel y and z are also neighbourhood. On what basis/hypothesis I can say pixel x and z are neighbourhood. Please someone help me in clearification of this point.

This depends on what you mean by neighborhood. Something based on distance? Something based on connectedness via other pixels in a set of pixels? Something based on general topological concepts?

based on unit distance. I am confuse about the distance between two points .x , y and y ,z are possible . But how x and z is possible?

If you define neighborhood based on a fixed maximum distance, it will obviously not be transitive. Say if pixels x and y and y and z both have a distance of 1, the distance between x and z could be 2. All you can do is that you say x and z are neighbors based on a more relaxed distance relation. Something like:

```
Neighbor d1 x y -> Neighbor d2 y z -> Neighbor (d1+d2) x z
```

Thank you .

Last updated: Feb 01 2023 at 11:04 UTC