Remove outer hull of 2D scatterpoints in Python

Question

For my project i use 2D images from a telescope. The outer border of each image is known to be oversatured with points due to telescope malfunction. Therefor i want to extract the points that make up the outer border of the 2D image.

So what i want to do is somehow extract the points that make up the outer shell, with a desired width of the shell according to my preference.

What i have tried so far:

In Python i have tried finding the points that make up the edge by using scipy.ConvexHull to find the outer points and then removing these points. When doing this in a loop it should remove the outer edge with a width dependant on the amount of iterations. However, this method is dependant on the point density, and removes less points for places on the edge where the density is large. What i want is that an about equal width of outer edge is removed of the whole image, see images below :

To show what i mean, i have added the ConvexHull result, in red the points it gives as outer edge points after 15x iterations:

For clarification, this is the desired result i would like my algorithm to give me, an outer edge with equal width over the whole image, which is independant of point density.

Answer 1

Since you showed only ideas and graphics without code, I will do the same.

I see several ways to get the smaller polygon within your convex hull with a near-constant width between them. There are also variations on each. I illustrate with a convex hull that is a simplified version of the one in your graphics. Each of my solutions ignores the majority of points in the problem and uses only the vertices of the convex hull, so the "point density" is ignored.

Before choosing a polygon, you could find the "center point" of your convex hull. There are multiple ways to define this. You could use the centroid of the vertices of the hull, where the x- and y-coordinates are the averages of the coordinates of the vertices, but this biases toward parts of the hull with many small segments. You could use the center of the bounding rectangle, where the x- and y-coordinates are the average of the maximum and the minimum coordinates of the hull's vertices. This is the approach I used in my graphics. There are other possible "center points."

My first inner polygon moves each vertex a proportional distance toward the center point. In my example, I moved each point one-fourth of the distance toward the center point.

My second inner polygon moves the vertices a fixed distance toward the center point. I chose a distance one-fourth of the average distance of the vertices from the center point. Note that for this particular example there is very little difference between this polygon and my previous one. The differences would be more obvious for a hull where come points are much closer to the center point than some other points.

My third polygon abandons the center point. It moves each side of the hull a fixed distance toward the inside of the hull. The intersections of these new segments are used to define the new polygon. In other words, I did "inward polygon offsetting" or "polygon buffering." This is a non-trivial task in computational geometry, but some discussion on this task and similar tasks can be found at this SO question. This does look different from the other polygons, since the smaller sides of the hull tend to shrink or completely disappear from the result.

Choose whichever polygon suits your needs--the first two are easier to compute than the third, but the third comes closest to your ideal of "equal width of outer edge."