{"id":877,"date":"2013-09-05T13:28:02","date_gmt":"2013-09-05T17:28:02","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/?p=877"},"modified":"2019-11-01T09:24:42","modified_gmt":"2019-11-01T13:24:42","slug":"defining-and-filling-holes-on-the-border-of-an-image","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2013\/09\/05\/defining-and-filling-holes-on-the-border-of-an-image\/","title":{"rendered":"Defining and filling holes on the border of an image"},"content":{"rendered":"

Blog reader Alex asked a question<\/a> this week about filling holes in this binary image.<\/p>

url = 'https:\/\/blogs.mathworks.com\/images\/steve\/2013\/eye-heart-matlab.png'<\/span>;\r\nbw = imread(url);\r\nimshow(bw)\r\n<\/pre>\"\" 
Alex tried imfill<\/tt> but it didn't give him exactly what he was looking for.<\/p>
bw2 = imfill(bw,'holes'<\/span>);\r\nimshow(bw2)\r\ntitle('Filling holes (first attempt)'<\/span>)\r\n<\/pre>\"\" 
Alex asked how he could fill the objects that are touching the border. At this point, MathWorker Sean de Wolski<\/a> jumped in and pointed out the problem wasn't well defined; there are multiple interpretations and possible solutions.<\/p>
It might not be obvious from Alex's image that this is the case, so let me illustrate with a different example. This image has one object, and it touches the border in a way that divides the background into two regions. Topologically, this object is the same as each of the five \"unfilled\" objects in Alex's image.<\/p>
bw_eye = imdilate(eye(200),ones(5,5));\r\nimshow(bw_eye)\r\n<\/pre>\"\" 
imfill<\/tt> doesn't do anything to this image:<\/p>
imshow(imfill(bw_eye,'holes'<\/span>))\r\ntitle('Output of imfill'<\/span>)\r\n<\/pre>\"\" 
What does it mean to \"fill\" this object? Would you expect the upper-right portion of the background to be filled, or the lower-right? This is the point Sean was making.<\/p>
Well, I stared at Alex's image for a while, trying to come up with a formulation of the problem that would be better defined and that would do what Alex expects.<\/p>
I think I've hit upon a reasonable formulation. It's not the only one, however, and I'd be interested in what ideas other readers have about this.<\/p>
Here's my idea: Fill objects against two adjacent borders at a time. By \"fill against a border\", I mean pad that border with white pixels, do the fill, and then remove the padding.<\/p>
Let's go back to Alex's image and \"fill against\" the left and the top border. The following call to padarray<\/tt> adds a column of white pixels on the left and a row of white pixels on the top.<\/p>
bw_a = padarray(bw,[1 1],1,'pre'<\/span>);\r\nbw_a_filled = imfill(bw_a,'holes'<\/span>);\r\nbw_a_filled = bw_a_filled(2:end,2:end);\r\nimshow(bw_a_filled)\r\n<\/pre>\"\" 
Now fill against the top and the right border.<\/p>
bw_b = padarray(padarray(bw,[1 0],1,'pre'<\/span>),[0 1],1,'post'<\/span>);\r\nbw_b_filled = imfill(bw_b,'holes'<\/span>);\r\nbw_b_filled = bw_b_filled(2:end,1:end-1);\r\nimshow(bw_b_filled);\r\n<\/pre>\"\" 
Next, fill against the right and bottom borders.<\/p>
bw_c = padarray(bw,[1 1],1,'post'<\/span>);\r\nbw_c_filled = imfill(bw_c,'holes'<\/span>);\r\nbw_c_filled = bw_c_filled(1:end-1,1:end-1);\r\nimshow(bw_c_filled)\r\n<\/pre>\"\" 
Finally, fill against the bottom and left borders. (I wouldn't expect this to have any effect on this particular image.)<\/p>
bw_d = padarray(padarray(bw,[1 0],1,'post'<\/span>),[0 1],1,'pre'<\/span>);\r\nbw_d_filled = imfill(bw_d,'holes'<\/span>);\r\nbw_d_filled = bw_d_filled(1:end-1,2:end);\r\nimshow(bw_d_filled)\r\n<\/pre>\"\" 
The last step is then to \"logical OR\" all these images together.<\/p>
bw_filled = bw_a_filled | bw_b_filled | bw_c_filled | bw_d_filled;\r\nimshow(bw_filled)\r\ntitle('Final filled result'<\/span>)\r\n<\/pre>\"\" 
Readers, please post your thoughts about this problem. It wouldn't surprise me at all to learn of other useful ways to think about it and other implementation methods.<\/p>
Alex, I hope you find this useful.<\/p>