# How to select, or filter, the external border/boundary in a set of (x,y)-points? [Part 2]

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Hi, in a previous question, I asked about a method to obtain the external border from a set of points.

% Obtain coordinates corresponding to outside border by performing

% exclusive OR on the data, between "border b1" and "border b2":

z = setxor(b1,b2,'rows','stable');

to a larger dataset, that composes numerous "borders". The larger dataset is the following (here attached as well):

% load borders and plot them

load('borders2.mat','a')

figure; hold on

for i = 1 : length(a)

line(a{i}(:,1),a{i}(:,2),'color','k');

end

hold off

When I tried to use iteratively the method proposed by @Dyuman Joshi, I got a wrong output (and stuck) and I do not know how to solve the issue.. any idea or suggestion?

% remove iteratively "common edges", and plot the external common border

figure; hold on

b=a{1};

for i = 2 : length(a)

c=a{i};

b=setxor(b,c,'rows','stable');

plot(b(:,1),b(:,2),'r')

end

hold off

Note: as alternative method, I also tried to use the boundary function, with the maximum shrinking factor, but, still, it does not follow the exact shape of the external common border (as I would like).

##### 2 Comments

Dyuman Joshi
on 12 Jul 2023

The points that still appear on the inside (of outer boundary) are the points of intersection of 3 or more borders, which makes sense.

One approach would be to eliminate the intersection points (as mentioned below) before processing the data via for loop, but that seems difficult to implement.

I'll keep you updated if I find a solution.

load('borders2.mat','a')

figure

hold on

for i = 1 : length(a)

line(a{i}(:,1),a{i}(:,2),'color','k');

end

%a = cellfun(@(x) unique(x,'rows', 'stable'), a, 'uni', 0);

b=a{1};

for i = 2:numel(a)

c=a{i};

b=setxor(b,c,'rows','stable');

end

plot(b(:,1),b(:,2),'ro ','MarkerSize',5)

### Accepted Answer

Bruno Luong
on 12 Jul 2023

Edited: Bruno Luong
on 12 Jul 2023

load('borders2.mat')

n = length(a);

warning('off','MATLAB:polyshape:repairedBySimplify')

Q = polyshape(zeros(0,2));

for k=1:n

Q = union(polyshape(a{k}),Q);

end

plot(Q)

##### 9 Comments

Bruno Luong
on 12 Jul 2023

### More Answers (1)

Kanishk Singhal
on 11 Jul 2023

If you plot after the loop,

figure; hold on

b=a{1};

for i = 2 : length(a)

c=a{i};

b=setxor(b,c,'rows','stable');

end

plot(b(:,1),b(:,2), '.')

hold off

you will get a plot like this.

Most boundary is removed but this the data is not perfect, some points which are inside are must be shared at unique to a cell.

Here you have two possibilities,

- Either clean the data remove these points or add these points in another cell.
- You get all the points from b, plot the points but make some kind of distance function which can identify these points.

In my opinion cleaning the data is a better option.

##### 2 Comments

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