This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.
Point cloud
From Intelligent Perception
It is in fact a triple torus.
But what if we zoom in:
We realize that the "object" is just a bunch of points suspended in space! It is called a point cloud.
Another example:
Where do point clouds come from?
They come from scanning:
They come from data:
Usually a simplicial complex is created to tell what's behind the point cloud.
How? A simplistic approach is to choose a threshold r and then
- add an edge between any two points if they are within r from each other,
- add a face spanning three points if the diameter of the triangle is less then r,
etc.
To capture all r's and to deal with noise, persistence is used.
