reducing data that are very close to one another

hi! so, I have this problem. I have to do image analysis to get the boundary of an image. I perform image analysis to get a boundary representation of the object. The problem is, there is an overlap of more than one point on the data. the problem occurs due to the pixel width of the boundary. As you can see in the image, I have analysed an image and have the scatter plot showing the coordinates.As you can see, the boundary has more than one element representing it. I need to reduce my vectors such that a boundary is represented by only one line. I attach the code along with the question for your reference.

clc;close all;
clear all;

folder = 'C:\Users\Aaditya\Desktop'; % image folder
baseFileName = 'part8.jpg';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
rgbImage = imread(fullFileName); % read the image
% Get the dimensions of the image.  numberOfColorBands should be = 3.
[rows, columns, numberOfColorBands] = size(rgbImage);
figure;
greenChannel = rgbImage(:, :, 2);

   binaryImage = greenChannel < 200; % convert image to BW
   imshow(binaryImage);

i=1;
j=1;
data=zeros(rows,columns);  
n=1;% sample every n rows or col of the image
img2=zeros(rows/n,columns/n);
for col=1:n:columns                  %reducing the size of the image
    for row=1:n:rows
        if(binaryImage(row,col)==1)
%         data(row,col)=1;
        x(i)=row;
        y(i)=col;           % locate where the image is present
       img2(x(i),y(i))=1;
       i=i+1;
        end

      end

end
figure;
scatter(x,y);
figure;
imshow(img2);
blankImage=zeros(length(1:rows),length(1:columns));

m=1; % counter variable
for k=2:rows-1
    for l=2:columns-1
        if((binaryImage(k+1,l)==0)&&(binaryImage(k,l+1)==0)&&(binaryImage(k-1,l)==0)&&(binaryImage(k,l-1)==0)&&(binaryImage(k,l)==0))
%             % if all surrounding pixels are black, ignore them
            blankImage(k,l)=0;
            elseif((binaryImage(k+1,l)==1)&&(binaryImage(k,l+1)==1)&&(binaryImage(k-1,l)==1)&&(binaryImage(k,l-1)==1)&&(binaryImage(k,l)==1))
            %if all surrounding pix are white ,ignore them
            blankImage(k,l)=0;
           else
            blankImage(k,l)=1; % get the boundary elements
            x_brep(m)=k;
            y_brep(m)=l;

              m=m+1; 
          end
      end
  end
  figure;
  imshow(blankImage);
    figure;
    scatter(x_brep,y_brep);

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how do i delete the "extra" data points so that my boundary is represented by only one "line". note that in some cases i have 3 data points also representing a point.