Connect disjoint edges in binary image

Question

I performed some operations on an image of a cube and I obtained a binary image of the edges of the cube which are disconnected at some places.The image I obtained is shown

Answer 1

This could be one approach -

%// Read in the input image
img = im2bw(imread('http://i.imgur.com/Bl7zhcn.jpg'));

%// There seems to be white border, which seems to be non-intended and
%// therefore could be removed
img = img(5:end-4,5:end-4);

%// Thin input binary image, find the endpoints in it and connect them
im1 = bwmorph(img,'thin',Inf);
[x,y] = find(bwmorph(im1,'endpoints'));
for iter = 1:numel(x)-1
    two_pts = [y(iter) x(iter) y(iter+1) x(iter+1)];
    shapeInserter = vision.ShapeInserter('Shape', 'Lines', 'BorderColor', 'White');
    rectangle = int32(two_pts);
    im1 = step(shapeInserter, im1, rectangle);
end
figure,imshow(im1),title('Thinned endpoints connected image')

%// Dilate the output image a bit
se = strel('diamond', 1);
im2 = imdilate(im1,se);
figure,imshow(im2),title('Dilated Thinned endpoints connected image')

%// Get a convex shaped blob from the endpoints connected and dilate image
im3 = bwconvhull(im2,'objects',4);
figure,imshow(im3),title('Convex blob corresponding to previous output')

%// Detect the boundary of the convex shaped blob and 
%// "attach" to the input image to get the final output
im4 = bwboundaries(im3);
idx = im4{:};

im5 = false(size(im3));
im5(sub2ind(size(im5),idx(:,1),idx(:,2))) = 1;

img_out = img;
img_out(im5==1 & img==0)=1;
figure,imshow(img_out),title('Final output')

Debug images -