im2col and col2im

Function im2col formats image blocks to columns and col2im does the inverse operation.

When you independently apply some operation on each image patches and then merge the patches, these functions are useful. The code is like
  img = im2double(imread(‘lena.png’));
  p  = im2col(img , [y, x], ‘sliding’);
For formatting Y-by-X size image into y-by-x size patches, im2col outputs (Y-y+1)-by-(X-x+1) matrix. To recover the same image, some website says like
  img2 = col2im(mean(p), [y, x], [Y, X], ‘sliding’);
What we obtain is (Y-y+1)-by-(X-x+1) blurry image.

If you want to same size and non-blurry image, you should carefully format the patches as following,
function [img] = mergePatch(p, y, x, Y, X)
  img = zeros(Y, X);
  coeff = zeros(Y, X);
  p_idx = 1;
  for xx=1:x
      for yy=1:y
          pp = col2im(p(p_idx,:), [y x], [Y X], ‘sliding’);
          img(yy:yy+Y-y,xx:xx+X-x) = img(yy:yy+Y-y,xx:xx+X-x)+pp;
          coeff(yy:yy+Y-y,xx:xx+X-x) = coeff(yy:yy+Y-y,xx:xx+X-x)+1;
          p_idx = p_idx+1;
      end
  end
  img = img ./ coeff;
  return;

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