Mahotas 简明教程
Mahotas - Euler Number of an Image
想象一下，你有一幅上面有不同形状的图纸。欧拉数允许我们计算这些形状中有多少个孔，以及它们可以分成多少个独立部分（连通分量）。这有助于分析和表征图像的结构。
Imazine you have a drawing with different shapes on it. The Euler number allows us to count how many holes are in those shapes and how many separate parts they can be divided into (connected components). This can help in analyzing and characterizing the structure of the image.
在数学上，可以将其定义为：
Mathematically, it can be defined as −
E = C - H其中， E 是欧拉数， C 是连通分量的数量， H 是图像中的孔数。
where, E is the Euler number, C is the number of connected components, and H is the number of holes in the image.
Euler Number of an Image in Mahotas
在 Mahotas 中，你可以使用 mahotas.euler() 函数计算欧拉数。此函数将二值图像作为输入，其中关注的对象由白色像素表示，背景则由黑色像素表示。然后，它根据图像中存在的对象的连通性和孔洞来计算欧拉数。
In Mahotas, you can calculate the Euler number using the mahotas.euler() function. This function takes a binary image as input, where the objects of interest are represented by white pixels and the background is represented by black pixels. It then calculates the Euler number based on the connectivity and holes in the objects present in the image.
Using the mahotas.euler() Function
mahotas.euler() 函数将二值图像作为输入，并返回一个整数作为欧拉示性数。
The mahotas.euler() function takes a binary image as input and returns the Euler characteristic value as an integer.
欧拉示性数是一种拓扑度量，用于描述图像中对象之间的连通性和形状。它被定义为图像中连通部件数量与孔洞数量之间的差值。
The Euler characteristic is a topological measure that describes the connectivity and shape of objects in an image. It is defined as the difference between the number of connected components and the number of holes in the image.
Mahotas 中 euler() 函数的基本语法如下：
Following is the basic syntax of euler() function in mahotas −
mahotas.euler(f, n=8)其中， 'f' 是一个 2D 二值图像， 'n' 是整数形式的连接分量，取值 4 或 8（默认值为 8）。
Where, 'f' is a 2−D binary image and 'n' is the connected component in integer which is either 4 or 8 (default is 8).
在下面的示例中，我们通过将二值图像 'nature.jpeg' 作为灰度图像加载，然后再对其进行阈值处理以创建一个二值图像，进而计算其欧拉数：
In the following example, we are computing the Euler number of a binary image 'nature.jpeg' by loading it as a grayscale image and then thresholding it to create a binary image −
import mahotas as mh
import numpy as np
# Load binary image as a NumPy array
binary_image = mh.imread('nature.jpeg', as_grey=True) > 0
# Compute Euler number
euler_number = mh.euler(binary_image)
# Print result
print("Eu
ler Number:", euler_number)以下是上面代码的输出： -
Following is the output of the above code −
Euler Number: -2.75Euler Number with Different Connectivity
我们还可以使用 euler() 函数，以不同的连通性在 Mahotas 中计算欧拉数。连通性参数确定在计算中考虑哪些相邻像素。
We can also calculate the Euler number with different connectivity in Mahotas using the euler() function. The connectivity parameter determines which neighboring pixels are considered in the calculation.
例如，使用连通性-4 仅考虑直接的水平和垂直相邻像素，而连通性-8 同时也考虑对角相邻像素。
For example, using connectivity−4 considers only the immediate horizontal and vertical neighbors, while connectivity−8 includes diagonal neighbors as well.
Example
在此，我们使用不同的连通性计算 "nature.jpeg" 图像的欧拉数：
Here, we are calculating the Euler number with different connectivity for the "nature.jpeg" image −
import mahotas as mh
import numpy as np
# Load the image as a grayscale image
image = mh.imread('sun.png', as_grey=True)
# Threshold the image to create a binary image
thresholded_image = image > 0
# Compute the Euler number with 4-connectivity
euler_number_4conn = mh.euler(thresholded_image, 4)
# Compute the Euler number with 8-connectivity
euler_number_8conn = mh.euler(thresholded_image, 8)
# Print the results
print("Euler Number (4-connectivity):", euler_number_4conn)
print("Euler Number (8-connectivity):", euler_number_8conn)上述代码的输出如下：
Output of the above code is as follows −
Euler Number (4-connectivity): -4.75
Euler Number (8-connectivity): -4.75Euler Number Calculation with Labelled Image
标记图像将唯一的整数标签分配给二值图像中的连通组件。
A labeled image assigns unique integer labels to connected components in a binary image.
在 Mahotas 中，euler 函数将标记图像作为输入，并返回整个图像的欧拉数。计算考虑了对象数量、孔洞和对象之间的隧道。
In Mahotas, the euler function takes a labelled image as input and returns the Euler number for the entire image. The calculation takes into account the number of objects, holes, and tunnels between objects.
Example
在这里，我们计算从 "sea.bmp" 图像派生的标记图像的欧拉数：
In here, we are calculating the Euler number of a labeled image derived from the "sea.bmp" image −
import mahotas as mh
import numpy as np
# Load the image as a grayscale image
image = mh.imread('sea.bmp', as_grey=True)
# Threshold the image to create a binary image
thresholded_image = image > 0
# Label the connected components in the binary image
labeled_image, num_labels = mh.label(thresholded_image)
# Compute the Euler number of the labeled image
euler_number = mh.euler(labeled_image)
# Print the result
print("Euler Number:", euler_number)执行上面的代码后，我们得到以下输出： -
After executing the above code, we get the following output −
Euler Number: -44.75Euler Number Calculation with Binary Image
在 Mahotas 中，可以使用 euler() 函数计算二值图像的欧拉数。通过加载二值图像并将其转换为布尔格式，euler 函数接受图像作为输入，并返回整数形式的欧拉数。
In Mahotas, the Euler number of a binary image can be calculated using the euler() function. By loading the binary image and converting it to a boolean format, the euler function takes the image as input and returns the Euler number as an integer.
Example
在下面给出的示例中，我们使用 Mahotas 计算从 "nature.jpeg" 图像创建的二值图像的欧拉数：
In the example given below, we are calculating the Euler number of a binary image created from the "nature.jpeg" image using Mahotas −
import mahotas as mh
# load binary image and convert to boolean format
image = mh.imread('sun.png', as_grey= True)
image = image.astype(bool)
# calculate the Euler number
euler_number = mh.euler(image)
# print the result
print("Euler number of the binary image is:", euler_number)获得的结果如下 −
The result obtained is as follows −
Euler number of the binary image is: -4.75