title: Calculate perimeter of numpy array
body: <p>I want to calculate the perimeter of a given numpy array structure. With perimeter i mean the exact perimeter of the structure in the numpy array. The structure could include holes.</p>
  
  <p>My current aproach is something like this:</p>
  
  <pre><code>import numpy   
  a = numpy.zeros((6,6), dtype=numpy.int)
  a[1:5, 1:5] = 1;a[3,3] = 0
  # Way 1
  s = ndimage.generate_binary_structure(2,1)
  c = ndimage.binary_dilation(a,s).astype(a.dtype)
  b = c - a  
  numpy.sum(b) # The result, however the hole is calculated as 1, although there are 4 edges
  
  # Way 2
  b = ndimage.distance_transform_cdt(a == 0,metric='taxicab') == 1 
  b = b.astype(int)
  numpy.sum(b) # same as above
  </code></pre>
  
  <p><img src="https://i.stack.imgur.com/asEWI.png" alt="enter image description here"></p>
  
  <p>As you can see it displays all adjacent cells, however the sum of them doesn't equal the perimeter of the patch. The hole in the example array is calculated as 1 although it correctly has 4 edges. There are similar issues with greater holes of different shapes.</p>
  
  <p>I have asked similar questions in the past, but all provided solutions which somehow didn't resolve in the correct output values in the end.
  Someone has an idea how to accomplish this? 
  No other packages than numpy, scipy and the base packages please.</p>