将Python数组划分为由单个单元或更少单元连接的唯一区域？

Question

我有一个numpy数组,我希望将其划分为具有唯一ID的离散区域,如下所示:

通常对于这样的事情,我会使用scipy.ndimage.label为离散blob生成唯一的id,但是在这种情况下我有几个非常大的连续区域,我也希望将它们分割成更小的独特区域,理想情况是当它们只是连接时通过1个小区的连接到他们的邻居.为了说明,这是一个示例数组,我在运行scipy.ndimage.label时获得的结果,以及我想要的结果:

import numpy as np
import scipy.ndimage as ndimage
import matplotlib.pyplot as plt

# Sample study area array
example_array = np.array([[0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0],
                          [0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1],
                          [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1],
                          [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0],
                          [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1],
                          [1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1],
                          [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1],
                          [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0],
                          [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0],
                          [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0],
                          [1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0],
                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

# Identify discrete regions and assign unique IDs
current_output, num_ids = ndimage.label(example_array, structure=np.ones((3,3)))

# Plot outputs
plt.imshow(example_array, cmap="spectral", interpolation='nearest')
plt.imshow(current_output, cmap="spectral", interpolation='nearest')

细胞的具体编号和分裂不是重要的; 任何类似上面最后一个情节的东西都可以.到目前为止,我最好的尝试是使用形态学图像处理来首先侵蚀我的阵列,运行scipy.ndimage.label然后扩张,但这有消除所有单细胞区域或细线性特征(其中有的)的不幸副作用许多).

非常感谢任何想法!

Answer 1

最简单的方法可能是在 SciPy 标签之前应用以下前置内核（以 2,2 作为原点，“？”可以是 0 或 1）：

IF |? 1 ?| OR |? 0 ?| THEN origin(x,y) == 0
   |0 1 0|    |1 1 1|
   |? 1 ?|    |? 0 ?|

执行：

import numpy as np
import scipy.ndimage as ndimage
import matplotlib.pyplot as plt

# Sample study area array
example_array = np.array([[0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0],
                          [0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1],
                          [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1],
                          [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0],
                          [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1],
                          [1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1],
                          [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1],
                          [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0],
                          [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0],
                          [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0],
                          [1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0],
                          [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

# Get array shape
row_count, column_count = example_array.shape

# Iterate through kernel origins
for (x,y), value in np.ndenumerate(example_array):

    # Skip first and last rows and columns because kernel would be out of bounds
    if not (x == 0 
         or x == row_count-1 
         or y == 0 
         or y == column_count-1):

        # Extract kernel
        kernel = example_array[x-1:x+2, y-1:y+2]
      
        # Apply IF |? 1 ?| OR |? 0 ?| THEN origin(x,y) == 0
        #          |0 1 0|    |1 1 1|
        #          |? 1 ?|    |? 0 ?|
        if ((kernel[1,0:3]).all() == 1 and kernel[0,1] == 0 and kernel[2,1] == 0 
            or (kernel[0:3,1]).all() == 1 and kernel[1,0] == 0 and kernel[1,2] == 0):
            example_array[x,y] = 0
                
# Identify discrete regions and assign unique IDs
current_output, num_ids = ndimage.label(example_array, structure=np.ones((3,3)))

# Plot outputs
plt.imshow(example_array, cmap="spectral", interpolation='nearest')
plt.imshow(current_output, cmap="spectral", interpolation='nearest')

结果：