Morphological closing by reconstructions in Matlab

Question

Could you please advice how can I implement morphological closing by reconstruction in Matlab?

As i know imreconstruct command can be used to implement opening by reconstruction (below my code for Opening by reconstruction).

img = rgb2gray(imread("input.jpg"));
img = imcomplement(img);
se=strel("square", 40);
marker= imerode(img,se);
mask=img;
opn_recon=imreconstruct(marker,mask);

Below is the code I wrote for Closing Reconstruction:

%Closing by reconstruction
img = rgb2gray(imread("input.jpg"));
img = imcomplement(img);
se=strel("square", 40);
marker= imdilate(img,se);
tmp=0;

while 1
  marker_loop = marker;
  geodesic=max(marker_loop,img);
  recon=imerode(geodesic,se); 
  if isequal(recon,tmp)==1
    break
  end
  tmp = recon;
  marker = imdilate(marker_loop,se);

end

But code does not work properly. Could you please advice whats my mistake, so i can fix it?

Answer 1

imreconstruct applies an inf-reconstruction, which can be interpreted as the repeated dilation conditioned by a second image (mask). Because it's a dilation, it can be applied after a structural erosion to form an opening (opening by reconstruction).

To form a closing by reconstruction, we need to apply a dilation followed by a sup-reconstruction. The sup-reconstruction is the dual of the inf-reconstruction, and can therefore be interpreted as the repeated erosion conditioned by a second image. Being the dual, we can implement the sup-reconstruction in terms of the ind-reconstruction by inverting the image, applying the operation, and then inverting the result:

out = imcomplement(imreconstruct(imcomplement(marker), imcomplement(mask)));

Thus, the closing by reconstruction is:

img = imread('cameraman.tif');
se = strel('square', 40);
marker = imdilate(img,se);
mask = img;
cls_recon = imcomplement(imreconstruct(imcomplement(marker), imcomplement(mask)));