COUNTLESS variant that treats zero as "background" that doesn't count for the purposes of choosing the mode.

countless_stippled.py

def countless_stippled(data):
  """
  Vectorized implementation of downsampling a 2D 
  image by 2 on each side using the COUNTLESS algorithm
  that treats zero as "background" that doesn't count
  for the purposes of choosing the mode.
  
  data is a 2D numpy array with even dimensions.
  """
  sections = []
  
  # This loop splits the 2D array apart into four arrays that are
  # all the result of striding by 2 and offset by (0,0), (0,1), (1,0), 
  # and (1,1) representing the A, B, C, and D positions from Figure 1.
  factor = (2,2)
  for offset in np.ndindex(factor):
    part = data[tuple(np.s_[o::f] for o, f in zip(offset, factor))]
    sections.append(part)

  a, b, c, d = sections

  ab_ac = a * ((a == b) | (a == c)) # PICK(A,B) or PICK(A,C) 
  ab_ac |= b * (b == c) # (PICK(A,B) or PICK(A,C)) or PICK(B,C)

  nonzero = a + (a == 0) * (b + (b == 0) * c)
  return ab_ac + (ab_ac == 0) * (d + (d == 0) * nonzero) # AB or AC or BC or D or A or B or C