浦口区建设中学网站网站侧边栏代码

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. 该区域面积。

@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). 区域的边界框坐标。

@bbox_area: [int] Number of pixels of bounding box. 区域边界框内的矩形面积。

@centroid: [array] Centroid coordinate tuple (row, col). 

@convex_area: [int] Number of pixels of convex hull image. 凸包内像素点总数

@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. 离心率

@equivalent_diameter: [float] The diameter of a circle with the same area as the region. 和区域面积相同的圆的直径

@euler_number: [int] Euler characteristic of region. Computed as number of objects (= 1) subtracted by number of holes (8-connectivity). 区域欧拉数

@extent: [float] Ratio of pixels in the region to pixels in the total bounding box. Computed as area / (rows * cols) 区域面积和边界外接框面积的比率

@filled_area: [int] Number of pixels of filled region. 区域和外接框之间填充的像素点总数

@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.

原图： 

得到的image如下图所示：

@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. 椭圆的主轴长度

@max_intensity: [float] Value with the greatest intensity in the region. 区域内强度最大值

@mean_intensity: [float] Value with the mean intensity in the region. 区域内平均强度值

@min_intensity: [float] Value with the least intensity in the region. 区域内强度最小值

@minor_axis_length: [float] The length of the minor axis of the ellipse that has the same normalized second central moments as the region. 椭圆的短轴长度

@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. 椭圆的X轴和长轴之间的夹角，与区域具有相同的二阶矩。从-pi/2到pi/2的逆时针方向范围

@perimeter: [float] Perimeter of object which approximates the contour as a line through the centers of border pixels using a 4-connectivity. 区域周长

@solidity: [float] Ratio of pixels in the region to pixels of the convex hull image. 区域像素与凸包图像像素的比值

@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