def test_union_by_rank(self):
uf = UnionFind()
one = uf.MakeSet(1)
two = uf.MakeSet(2)
three = uf.MakeSet(3)
uf.Union(one, two) # 1st added to 2nd
self.assertEqual(uf.Find(one), two)
self.assertEqual(uf.Find(two), two)
self.assertEqual(uf.Find(three), three)
self.assertEqual(one.rank, 0)
self.assertEqual(two.rank, 1)
self.assertEqual(three.rank, 0)
uf.Union(one, three) # arbitrarily, 1st would be added to 2nd
# union by rank -> 3 should be added to (1,2)
self.assertEqual(uf.Find(one), two)
self.assertEqual(uf.Find(two), two)
self.assertEqual(uf.Find(three), two)
self.assertEqual(one.rank, 0)
self.assertEqual(two.rank, 1)
self.assertEqual(three.rank, 0)
self.assertEqual(one.parent, two)
self.assertEqual(two.parent, two)
self.assertEqual(three.parent, two)
def test_find(self):
uf = UnionFind()
five = uf.MakeSet(5)
seven = uf.MakeSet(7)
uf.Union(five, seven)
self.assertEqual(uf.Find(five), seven)
self.assertEqual(uf.Find(seven), seven)
def test_path_compression(self):
uf = UnionFind()
one = uf.MakeSet(1)
two = uf.MakeSet(2)
three = uf.MakeSet(3)
four = uf.MakeSet(4)
uf.Union(one, two)
uf.Union(three, four)
uf.Union(two, three)
# 4
# / \
# 2 3
# /
# 1
self.assertEqual(one.parent, two)
self.assertEqual(two.parent, four)
self.assertEqual(four.parent, four)
self.assertEqual(three.parent, four)
uf.Find(one)
# 4
# / | \
# 1 2 3
self.assertEqual(one.parent, four)
self.assertEqual(two.parent, four)
self.assertEqual(four.parent, four)
self.assertEqual(three.parent, four)
def connected_component_labelling(bool_input_image,
connectivity_type=CONNECTIVITY_8):
"""
2 pass algorithm using disjoint-set data structure with Union-Find algorithms to maintain
record of label equivalences.
Input: binary image as 2D boolean array.
Output: 2D integer array of labelled pixels.
1st pass: label image and record label equivalence classes.
2nd pass: replace labels with their root labels.
(optional 3rd pass: Flatten labels so they are consecutive integers starting from 1.)
"""
if connectivity_type != 4 and connectivity_type != 8:
raise ValueError("Invalid connectivity type (choose 4 or 8)")
image_width = len(bool_input_image[0])
image_height = len(bool_input_image)
# initialize efficient 2D int array with numpy
# N.B. numpy matrix addressing syntax: array[y,x]
labelled_image = np.zeros((image_height, image_width), dtype=np.int16)
uf = UnionFind() # initialise union find data structure
current_label = 1 # initialise label counter
# 1st Pass: label image and record label equivalences
for y, row in enumerate(bool_input_image):
for x, pixel in enumerate(row):
if pixel == False:
# Background pixel - leave output pixel value as 0
pass
else:
# Foreground pixel - work out what its label should be
# Get set of neighbour's labels
labels = neighbouring_labels(labelled_image, connectivity_type,
x, y)
if not labels:
# If no neighbouring foreground pixels, new label -> use current_label
labelled_image[y, x] = current_label
uf.MakeSet(current_label) # record label in disjoint set
current_label = current_label + 1 # increment for next time
else:
# Pixel is definitely part of a connected component: get smallest label of
# neighbours
smallest_label = min(labels)
labelled_image[y, x] = smallest_label
if len(
labels
) > 1: # More than one type of label in component -> add
# equivalence class
for label in labels:
uf.Union(uf.GetNode(smallest_label),
uf.GetNode(label))
# 2nd Pass: replace labels with their root labels
final_labels = {}
new_label_number = 1
for y, row in enumerate(labelled_image):
for x, pixel_value in enumerate(row):
if pixel_value > 0: # Foreground pixel
# Get element's set's representative value and use as the pixel's new label
new_label = uf.Find(uf.GetNode(pixel_value)).value
labelled_image[y, x] = new_label
# Add label to list of labels used, for 3rd pass (flattening label list)
if new_label not in final_labels:
final_labels[new_label] = new_label_number
new_label_number = new_label_number + 1
# 3rd Pass: flatten label list so labels are consecutive integers starting from 1 (in order
# top to bottom, left to right)
# Different implementation of disjoint-set may remove the need for 3rd pass?
for y, row in enumerate(labelled_image):
for x, pixel_value in enumerate(row):
if pixel_value > 0: # Foreground pixel
labelled_image[y, x] = final_labels[pixel_value]
return labelled_image