Fill area between x-y data

Hi everyone!

I have a data as shown in the figure. I want to fill/find the polygon area with maximum probability (not necessarily circular, I need to find the shape). Can anyone please help me?

Thank you!

[Matt J]

You'll need to define "maximum probability" for us. Are you sure you don't simply want to take the convex hull?

[Walter Roberson]

Given the coordinates of any particular polygon, how would you calculate the "probability" of it?

Answer 1

[Joe Vinciguerra]

xy = randn(100, 2);
shp = alphaShape(xy, inf);
area = shp.area;
facets = shp.boundaryFacets;

plot(shp, "LineStyle","none", "Marker","none")
hold on;
scatter(xy(:,1), xy(:,2))
grid on;

For more information see: Polygons and polyhedra from points in 2-D and 3-D - MATLAB (mathworks.com)

Answer 2

[Image Analyst]

The polygon with the maximum density would be one that starts at one point and then snakes around until it has "grabbed" every point. The width of the snake would be infinitesimally small.