Neat enclosed area for a group of points on a plane

Hello!

I will be happy and grateful for help. I need to find the entire enclosed area in a dataset. For example, as you see in the picture (data attached)

I need to find some way to search for the closed area. I tried using the polygen command but it results in wrong areas.

pgonAll = polyshape(P(:,1),P(:,2),'Simplify',false);
pgonAll = simplify(pgonAll);
pgonEach = regions(pgonAll);
figure
plot(P(:,1),P(:,2))
hold on
plot(pgonEach(2))
legend({'P','pgonEach(2)'},'FontSize',12)

Do you have any Idea how can i handle it?

Answer 1

[Matt J]

Your attached Data.mat looks like it contains different Data from your posted figure illustrations.

load Data

shp=alphaShape(Data,0.2);

Warning: Duplicate data points have been detected and removed.

[bf,V] = boundaryFacets(shp);

pgon=polyshape(V);

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

plot(Data(:,1),Data(:,2),'o');hold on
plot(pgon,'FaceColor','none'); hold off
axis([0.4,0.6,0.4,0.6])

[Andrew Sol]

And how will this method work if there is an area NaN inside? Will the outline be drawn from the inside as well? For example for:

[Matt J]

You will have to remove the NaNs, but that is unrelated to the issue of how holes are treated. To include or remove holes, you need to set alphaShape()'s HoleThreshold parameter appropriately to what you want.

https://www.mathworks.com/help/matlab/ref/alphashape.html#d124e21247

[Andrew Sol]

Are there any methods that do not require configuration?

[Matt J]

What is meant by "require configuration"?

[Matt J]

Do you mean, a method that doesn't require tuning parameters? No, that will almost certainly be impossible because the outer boundary that you are trying to find is very subjective.

[Andrew Sol]

@Matt J Yes. Therefore, I propose to add two conditions:

1. mesh is rectangular and uniform

2. display and connect only outer grid points

[Matt J]

I think this should do it,

shp=alphaShape(Data,meshspacing/sqrt(2)*1.01,'HoleThreshold',max(pdist(Data))^2*pi);

[Andrew Sol]

Thanks for the recommendation! This command seems to work. It's not perfect, but it's a significant improvement nonetheless. I also found the "bwboundaries" command. What do you think of her?

[Matt J]

You're welcome, but please Accept-click the answer if you decide that it is the one you will go with.

bwboundaries is for image data, which you do not have. There are ways, I'm sure, that you could construct an image from the points you've shown, but you would still face the same problem as with the methods discussed so far. Namely, you would need some way to seal the gaps between points before bwboundaries could give you what you want, and that would require judgements (as any method would) about which gaps need to be sealed and which ones are legitimate boundaries of the shape.

Answer 2

[Image Analyst]

Did you try boundary?

[Andrew Sol]

Yes, I did some work with this command. This is a good command, but it has one drawback - it requires setting the shrink factor and practically does not build internal barriers.

[Image Analyst]

What "internal barriers" did you want? I didn't see any indicated in your drawings.

[Andrew Sol]

This is not in the original post, I gave this example in one of the comments.

https://www.mathworks.com/matlabcentral/answers/1897610-neat-enclosed-area-for-a-group-of-points-on-a-plane#comment_2575605

[Matt J]

@Andrew Sol The example doesn't explain what "internal barriers" means (to me, at least). Does it mean that boundary() doesn't preserve holes? But In your comments to me, you said you didn't want any holes in the result, so why would that be a problem?

[Andrew Sol]

@Matt J By internal barriers, I meant the boundaries separating the NaNs that are inside the "data cloud" from the rest of the data. The boundary command does not work well enough in this case. The question of "voids" in the data set arose after the question was formed. I have not yet decided whether to edit the question or, as is done now, to mention this case in a comment.

[Matt J]

But again, you said you don't want voids. The solution I gave you gets rid of the voids (as does the boundary() command), and you said you were reasonably happy with it.

[Andrew Sol]

@Matt J Yes, so let's confine ourselves to the case that was discussed and the proposed solution. Other cases will not be discussed for now.