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Adding micro exercises
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‎exercises/micro/README.md

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Adapted from an idea by Ashwin Srinath, hosted at
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https://github.com/shwina/micro .
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The file `counting.py` contains a simple implementation of a function `count_objects`.
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`count_objects` is used to count objects in
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microscopic images. An example image is given below:
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![Example microscopic image](img/specimen_example.png)
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The images are assumed to be in **binary** format,
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i.e., they can be represented by arrays of 0s (dark pixels)
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and 1s (bright pixels). For example, the image above may be represented
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by the following 32-by-32 array:
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```
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0
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0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0
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0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0
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0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 0 0
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0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 0
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0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0
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0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0
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0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
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0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0
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0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0
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0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
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0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0
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0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
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0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
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0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
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0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0
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0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0
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0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0
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0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0
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0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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```
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The function `count_objects` accepts a (binary) NumPy array
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as input and returns the number of objects found in this "image".
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For example, if `img` is an array representing the above image,
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`count_objects` can be used as follows:
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```python
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>>> count_objects(img)
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16
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```
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**Assumptions**:
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1. The bright pixels (1) representing each object are completely surrounded by dark pixels (0).
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2. There are no "holes" in each object, i.e., each object is a continuous blob of bright pixels (1),
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with no dark pixels (0) inside this blob.
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The file `test_counting.py` contains tests that will allow you to optimize the
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function without breaking its functionality.

‎exercises/micro/counting.py

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import numpy as np
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def external_match(a):
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masks = [np.array([[0, 0], [0, 1]]),
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np.array([[0, 0], [1, 0]]),
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np.array([[1, 0], [0, 0]]),
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np.array([[0, 1], [0, 0]])]
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for mask in masks:
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if np.all(a == mask):
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return True
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return False
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def internal_match(a):
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masks = [np.array([[1, 1], [1, 0]]),
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np.array([[1, 1], [0, 1]]),
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np.array([[0, 1], [1, 1]]),
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np.array([[1, 0], [1, 1]])]
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for mask in masks:
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if np.all(a == mask):
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return True
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return False
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def count_objects(img):
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ny, nx = img.shape
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img[[0, -1], :] = 0
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img[:, [0, -1]] = 0
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E = 0
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I = 0
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for i in range(ny-1):
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for j in range(nx-1):
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if external_match(img[i:i+2, j:j+2]):
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E = E + 1
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if internal_match(img[i:i+2, j:j+2]):
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I = I + 1
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return (E - I)/4

‎exercises/micro/img/specimen_example.png

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‎exercises/micro/script.py

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from scipy.ndimage import imread
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from counting import count_objects
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if __name__ == '__main__':
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img = imread('img/specimen_example.png', flatten=True) // 255
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count = count_objects(img)
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print('Number of objects:', count)

‎exercises/micro/test_counting.py

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import numpy as np
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from numpy.testing import assert_equal
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from counting import count_objects
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def test_count_no_object():
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a = np.zeros([6, 6], dtype=np.float64)
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assert_equal(count_objects(a), 0)
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def test_count_1_object():
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a = np.zeros([6, 6], dtype=np.float64)
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a[1:-1, 1:-1] = 1
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assert_equal(count_objects(a), 1)
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def test_count_objects_2_objects():
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a = np.array(
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[[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
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[ 0., 1., 1., 1., 0., 0., 0., 0., 0., 0.],
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[ 0., 1., 1., 1., 0., 0., 0., 0., 0., 0.],
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[ 0., 1., 1., 1., 0., 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0., 1., 1., 0., 0., 0.],
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[ 0., 0., 0., 0., 0., 1., 1., 0., 0., 0.],
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[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])
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assert_equal(count_objects(a), 2)
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def test_count_1_object_rectangle():
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a = np.array(
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[[ 0., 0., 0., 0., 0.],
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[ 0., 1., 1., 1., 0.],
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[ 0., 1., 1., 1., 1.],
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[ 0., 1., 1., 1., 0.],
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[ 0., 0., 1., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.]])
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assert_equal(count_objects(a), 1)
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def test_count_1_object_irregular():
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a = np.array(
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[[ 0., 0., 0., 0., 0.],
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[ 0., 1., 1., 1., 0.],
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[ 0., 1., 1., 1., 1.],
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[ 0., 1., 1., 1., 0.],
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[ 0., 0., 1., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.],
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[ 0., 0., 0., 0., 0.]])
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assert_equal(count_objects(a), 1)
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def test_count_all_ones():
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a = np.ones([6, 6], dtype=np.int32)
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assert_equal(count_objects(a), 1)

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