I have a point cloud and I have a couple of different geometric shapes like rectangle or circle. Are there any mathematical tools to find which one of the geometric shapes we could fit the point cloud into, in a way which would minimize the empty space inside the shape, i.e. space not covered by point cloud?
Asked
Active
Viewed 36 times
0
-
What are the size of the geometric shapes and the point cloud? If the point cloud can be fully contained by the geometric shapes, isn't the empty space just a measurement of the rest of area or numbers of pixels? – Tab1e Apr 21 '22 at 13:50
-
@Tab1e The dimensions of the rectangle and sphere are minimal required to fit the point cloud into. I'm not sure how to define the empty space. – Lenny White Apr 21 '22 at 13:55
-
You have to represent your geometric shapes by point cloud of corresponding geometric shapes. Otherwise, a finite set of points in Rn has measure zero. – Tab1e Apr 21 '22 at 14:02
-
As pointed out, minimizing the "empty area" is meaningless. Do you perhaps mean that you want to find the shape of smallest area that contains your cloud of points? – Tanny Sieben Apr 21 '22 at 15:08
-
In any case, for a circle you can search for Welzl's algorithm and for the smallest area rectangle you can do it in linear time in two dimensions – Tanny Sieben Apr 21 '22 at 15:16