Overview
对于二值图像来说，每个像素点的值只有类似0/1的两种可能性，一般为0(黑)/255(白)。 如果两个像素点位置相邻且取值相同，那么这两个像素点即处于同一个相互连通的区域内。 从视觉上看，彼此连通的点形成了一个区域，而该区域中所有连通点构成的集合，我们称之为一个连通区域。
在图像中，每个像素当以自身为中心时，周围一般存在8个邻接像素。
在判断两个像素是否属于同一连通区域时，根据邻接关系，通常存在两种判定方法：4连通或8连通。
4连通只考虑4个邻接像素，即上下左右，如下左图所示；
8连通则总共考虑8个邻接像素，额外还包括了对角线位置的点，如下右图所示。
值得注意的是，二值连通区域还具有简单而特殊的传递性： 如果像素点A与像素点B同值并邻接，我们称A与B连通，易得， 如果A与B连通，B与C连通，则A亦与C连通。
一个连通区域可能包含很多个像素点，而如果将同一个连通区域的所有像素点都用同一个数值/符号来进行标记，这个过程就成为连通区域标记。
Label
SciKit-Image是一种Python下的图像处理工具包，scikit-image — Image processing in Python：Official Site 在skimage包中，使用measure子模块下的label函数即可实现连通区域标记。 参数input表示需要处理的二值图像，connectivity表示判定连通的模式（1代表4连通，2代表8连通），输出labels为一个从0开始的标记数组。
skimage.measure.label(input, neighbors = None, background = None, return_num = False, connectivity = None)[source]
Parameters: @input : Image to label [ndarray of dtype int] @neighbors : Deprecated, use @connectivity instead [{4, 8}, int, optional] @background : Consider all pixels with this value as background pixels, and label them as 0. By default, 0-valued pixels are considered as background pixels. [int, optional] @return_num : Whether to return the number of assigned labels [bool, optional] @connectivity : Maximum number of orthogonal hops to consider a pixel/voxel as a neighbor. Accepted values are ranging from 1 to input.ndim. If None, a full connectivity of input.ndim is used. [int, optional] Returns: @labels : Labeled array, where all connected regions are assigned the same integer value. [ndarray of dtype int] @num : Number of labels, which equals the maximum label index and is only returned if return_num is True. [int, optional]
Examples:
>>> import numpy as np
>>> x = np.eye(3).astype(int)
>>> print(x)
[[1 0 0]
[0 1 0]
[0 0 1]]
>>> print(label(x, connectivity = 1))
[[1 0 0]
[0 2 0]
[0 0 3]]
>>> print(label(x, connectivity = 2))
[[1 0 0]
[0 1 0]
[0 0 1]]
>>> print(label(x, background = -1))
[[1 2 2]
[2 1 2]
[2 2 1]]
>>> x = np.array([[1, 0, 0],
... [1, 1, 5],
... [0, 0, 0]])
>>> print(label(x))
[[1 0 0]
[1 1 2]
[0 0 0]]Properties
此外，使用measure子模块中的regionprops()函数可以很方便地对每一个连通区域进行属性获取和操作，比如计算面积、外接矩形、凸包面积等等。 计算结果返回为所有连通区域的属性列表，列表长度为连通区域个数（第i个连通区域的attribute属性可以通过properties[i].attribute获取）。
skimage.measure.regionprops(label_image, intensity_image = None, cache = True)[source]
Parameters: @label_image : Labeled input image. Labels with value 0 are ignored. [(N, M) ndarray] @intensity_image : Intensity (i.e., input) image with same size as labeled image. Default is None. [(N, M) ndarray, optional] @cache : Determine whether to cache calculated properties. The computation is much faster for cached properties, whereas the memory consumption increases. [bool, optional] Returns: @properties : Each item describes one labeled region, and can be accessed using the attributes listed below. [list of RegionProperties]
Property Keys: The following properties can be accessed as attributes or keys: @area: [int] Number of pixels of region. @bbox: [tuple] Bounding box (min_row, min_col, max_row, max_col). Pixels belonging to the bounding box are in the half-open interval [min_row; max_row) and [min_col; max_col). @bbox_area: [int] Number of pixels of bounding box. @centroid: [array] Centroid coordinate tuple (row, col). @convex_area: [int] Number of pixels of convex hull image. @convex_image: [(H, J) ndarray] Binary convex hull image which has the same size as bounding box. @coords: [(N, 2) ndarray] Coordinate list (row, col) of the region. @eccentricity: [float] Eccentricity of the ellipse that has the same second-moments as the region. The eccentricity is the ratio of the focal distance (distance between focal points) over the major axis length. The value is in the interval [0, 1). When it is 0, the ellipse becomes a circle. @equivalent_diameter: [float] The diameter of a circle with the same area as the region. @euler_number: [int] Euler characteristic of region. Computed as number of objects (= 1) subtracted by number of holes (8-connectivity). @extent: [float] Ratio of pixels in the region to pixels in the total bounding box. Computed as area / (rows * cols) @filled_area: [int] Number of pixels of filled region. @filled_image: [(H, J) ndarray] Binary region image with filled holes which has the same size as bounding box. @image: [(H, J) ndarray] Sliced binary region image which has the same size as bounding box. @inertia_tensor: [(2, 2) ndarray] Inertia tensor of the region for the rotation around its mass. @inertia_tensor_eigvals: [tuple] The two eigen values of the inertia tensor in decreasing order. @intensity_image: [ndarray] Image inside region bounding box. @label: [int] The label in the labeled input image. @local_centroid: [array] Centroid coordinate tuple (row, col), relative to region bounding box. @major_axis_length: [float] The length of the major axis of the ellipse that has the same normalized second central moments as the region. @max_intensity: [float] Value with the greatest intensity in the region. @mean_intensity: [float] Value with the mean intensity in the region. @min_intensity: [float] Value with the least intensity in the region. @minor_axis_length: [float] The length of the minor axis of the ellipse that has the same normalized second central moments as the region. @moments: [(3, 3) ndarray] Spatial moments up to 3rd order: m_ji = sum{ array(x, y) * x^j * y^i } where the sum is over the x, y coordinates of the region. @moments_central: [(3, 3) ndarray] Central moments (translation invariant) up to 3rd order: mu_ji = sum{ array(x, y) * (x - x_c)^j * (y - y_c)^i } where the sum is over the x, y coordinates of the region, and x_c and y_c are the coordinates of the region’s centroid. @moments_hu: [tuple] Hu moments (translation, scale and rotation invariant). @moments_normalized: [(3, 3) ndarray] Normalized moments (translation and scale invariant) up to 3rd order: nu_ji = mu_ji / m_00^[(i+j)/2 + 1] where m_00 is the zeroth spatial moment. @orientation: [float] Angle between the X-axis and the major axis of the ellipse that has the same second-moments as the region. Ranging from -pi/2 to pi/2 in counter-clockwise direction. @perimeter: [float] Perimeter of object which approximates the contour as a line through the centers of border pixels using a 4-connectivity. @solidity: [float] Ratio of pixels in the region to pixels of the convex hull image. @weighted_centroid: [array] Centroid coordinate tuple (row, col) weighted with intensity image. @weighted_local_centroid: [array] Centroid coordinate tuple (row, col), relative to region bounding box, weighted with intensity image. @weighted_moments: [(3, 3) ndarray] Spatial moments of intensity image up to 3rd order: wm_ji = sum{ array(x, y) * x^j * y^i } where the sum is over the x, y coordinates of the region. @weighted_moments_central: [(3, 3) ndarray] Central moments (translation invariant) of intensity image up to 3rd order: wmu_ji = sum{ array(x, y) * (x - x_c)^j * (y - y_c)^i } where the sum is over the x, y coordinates of the region, and x_c and y_c are the coordinates of the region’s weighted centroid. @weighted_moments_hu: [tuple] Hu moments (translation, scale and rotation invariant) of intensity image. @weighted_moments_normalized: [(3, 3) ndarray] Normalized moments (translation and scale invariant) of intensity image up to 3rd order: wnu_ji = wmu_ji / wm_00^[(i+j)/2 + 1] where wm_00 is the zeroth spatial moment (intensity-weighted area).Examples:
>>> from skimage import data, util
>>> from skimage.measure import label
>>> img = util.img_as_ubyte(data.coins()) > 110
>>> label_img = label(img, connectivity = img.ndim)
>>> props = regionprops(label_img)
>>> # centroid of first labeled object
>>> props[0].centroid
(22.729879860483141, 81.912285234465827)
>>> # centroid of first labeled object
>>> props[0]['centroid']
(22.729879860483141, 81.912285234465827)Reference
[1] skimage.measure.label — skimage v0.13dev docs [2] skimage.measure.regionprops — skimage v0.13dev docs [3] python数字图像处理（18）：高级形态学处理 [4] 图像分析：二值图像连通域标记
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