属性运算符#

属性操作符（或连接操作符） [1] 是数学形态学中一组保持轮廓的滤波操作。它们可以通过最大树 [2] 实现，最大树是图像的紧凑层次表示。

在这里，我们展示了如何使用直径闭合 [3] [4]，这与形态学闭合进行了比较。比较两种结果，我们观察到图像与形态学闭合之间的差异也提取了长线。一条细但长的线不能包含结构元素。直径闭合一旦达到最大扩展就停止填充。因此，这条线没有被填充，因此也没有被差异提取。

import matplotlib.pyplot as plt
from skimage.morphology import diameter_closing
from skimage import data
from skimage.morphology import closing
from skimage.morphology import square

datasets = {
    'retina': {
        'image': data.microaneurysms(),
        'figsize': (15, 9),
        'diameter': 10,
        'vis_factor': 3,
        'title': 'Detection of microaneurysm',
    },
    'page': {
        'image': data.page(),
        'figsize': (15, 7),
        'diameter': 23,
        'vis_factor': 1,
        'title': 'Text detection',
    },
}

for dataset in datasets.values():
    # image with printed letters
    image = dataset['image']
    figsize = dataset['figsize']
    diameter = dataset['diameter']

    fig, ax = plt.subplots(2, 3, figsize=figsize)
    # Original image
    ax[0, 0].imshow(image, cmap='gray', aspect='equal', vmin=0, vmax=255)
    ax[0, 0].set_title('Original', fontsize=16)
    ax[0, 0].axis('off')

    ax[1, 0].imshow(image, cmap='gray', aspect='equal', vmin=0, vmax=255)
    ax[1, 0].set_title('Original', fontsize=16)
    ax[1, 0].axis('off')

    # Diameter closing : we remove all dark structures with a maximal
    # extension of less than <diameter> (12 or 23). I.e. in closed_attr, all
    # local minima have at least a maximal extension of <diameter>.
    closed_attr = diameter_closing(image, diameter, connectivity=2)

    # We then calculate the difference to the original image.
    tophat_attr = closed_attr - image

    ax[0, 1].imshow(closed_attr, cmap='gray', aspect='equal', vmin=0, vmax=255)
    ax[0, 1].set_title('Diameter Closing', fontsize=16)
    ax[0, 1].axis('off')

    ax[0, 2].imshow(
        dataset['vis_factor'] * tophat_attr,
        cmap='gray',
        aspect='equal',
        vmin=0,
        vmax=255,
    )
    ax[0, 2].set_title('Tophat (Difference)', fontsize=16)
    ax[0, 2].axis('off')

    # A morphological closing removes all dark structures that cannot
    # contain a structuring element of a certain size.
    closed = closing(image, square(diameter))

    # Again we calculate the difference to the original image.
    tophat = closed - image

    ax[1, 1].imshow(closed, cmap='gray', aspect='equal', vmin=0, vmax=255)
    ax[1, 1].set_title('Morphological Closing', fontsize=16)
    ax[1, 1].axis('off')

    ax[1, 2].imshow(
        dataset['vis_factor'] * tophat, cmap='gray', aspect='equal', vmin=0, vmax=255
    )
    ax[1, 2].set_title('Tophat (Difference)', fontsize=16)
    ax[1, 2].axis('off')
    fig.suptitle(dataset['title'], fontsize=18)
    fig.tight_layout(rect=(0, 0, 1, 0.88))

plt.show()

参考文献#

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