Counting objects in an image

To count the objects in a picture, make a mask, then count each separate group of touching object pixels. Each group is a connected region, and the program gives it a number called a label. The same idea counts coins, cells in a slide and cars in a car park.

In this lesson you label regions, measure their size and find a small piece inside a larger picture.

Take a mask of 0 and 1. Two 1-pixels belong to the same connected region if you can walk from one to the other through 1-pixels that touch.

Give each region its own number, 1, 2, 3 and so on. Zero stays the background. That numbering is labelling, and the biggest label is the count.

docker exec jupyter python3 -c "import numpy as np; from PIL import Image; from skimage import measure; a = np.array(Image.open('images/shapes.png').convert('L')); l = measure.label(a < 250); print(l.max(), sorted(int(r.area) for r in measure.regionprops(l)))"

The Run keeps every pixel darker than 250, so the white page is background. It labels what is left and prints the count and the areas.

The answer has the form 6 [1581, 1581, 2909, 2909, 3621, 4941]: six shapes. The area is a count of pixels, so the two matching pairs are the same size: two triangles and two circles.

grid = [
    [1, 1, 0, 0],
    [0, 1, 0, 1],
    [0, 0, 0, 1],
    [1, 0, 0, 1],
]
seen = []
for row in grid:
    seen.append([False] * len(row))

count = 0
for r in range(len(grid)):
    for c in range(len(grid[r])):
        if grid[r][c] == 1 and not seen[r][c]:
            count = count + 1
            todo = [[r, c]]
            seen[r][c] = True
            while len(todo) > 0:
                here = todo.pop()
                for step in [[1, 0], [-1, 0], [0, 1], [0, -1]]:
                    nr = here[0] + step[0]
                    nc = here[1] + step[1]
                    if 0 <= nr < len(grid) and 0 <= nc < len(grid[0]):
                        if grid[nr][nc] == 1 and not seen[nr][nc]:
                            seen[nr][nc] = True
                            todo.append([nr, nc])
print("regions:", count)

Do two pixels that meet only at a corner touch? With 4-connectivity they do not: only left, right, up and down count. With 8-connectivity they do.

The rule changes the count. The loop above uses four directions, so two pixels on a diagonal are two regions.

docker exec jupyter python3 -c "import numpy as np; from skimage import measure; a = np.array([[1, 0], [0, 1]]); print(measure.label(a, connectivity=1).max(), measure.label(a, connectivity=2).max())"

docker exec jupyter python3 -c "import numpy as np; from PIL import Image; from skimage import measure; a = np.array(Image.open('images/coins.png').convert('L')); print(measure.label(a > 30).max(), measure.label(a > 160).max())"

The coin picture holds nine coins. The Run prints 3 11. A level of 30 is inside the background noise, so the noise joins several coins into one lump and the count falls to 3. A level of 160 cuts into the coins and leaves 11 bright pieces.

A level of 100, in the gap between background and coins, gives 9. Always check the count against what you can see.

To find a known object, cut out a small piece of it, called a template. Slide it over the picture and score how closely each place matches. The best score marks the place.

A score of 1.0 is a perfect match. The method works when the object looks the same each time, but it struggles when the object is turned or resized.

docker exec jupyter python3 steps/find.py

In a notebook, label coins.png above 100 and print [(int(r.centroid[0]), int(r.centroid[1])) for r in measure.regionprops(labels)].

Each pair is the row and column of a coin's centre. Check two of them against the picture.