How to unite the missing parts of a curve - binary images

I have a binary image of a curve with many missing parts and I need an idea to unite the discontinuities in order to obtain a continous curve.

I've attached below 3 examples and I need to code it so that the same code works on all of them

[Paul Simon]

I've managed to get the centroids coordinates of all the blobs but I need to sort them somehow in order to obtain what I need (I've tried using poly2mask without sorthing them and the attached image is the result). Any ideas?

Answer 1

[Image Analyst]

Maybe try boundary()

[Paul Simon]

Could you explain a bit further?

[Paul Simon]

This is the result associated with "example1" after using poly2mask on the boundaries and after applying a morphological gradient, but it's not as good as I need it to be.

[y, x] = find(binaryImage);
K = boundary(x, y);
boundary_x = x(K);
boundary_y = y(K);
mask = poly2mask( boundary_x, boundary_y, size(binaryImage,1), size(binaryImage,2) );

[Image Analyst]

Change the options for boundary() to make it fit tighter if you want.

[Paul Simon]

I think it would be more efficient if I had the coordinates of the starting and ending point of each blob but I don't really know how to obtain them