是否有 python 包可以为我提供一种计算图像的偏斜度和峰度的方法？任何例子都会很棒。

非常感谢。

最佳答案

我假设您有一张显示某种峰的图像，并且您有兴趣获得该峰在 x 和 y 方向上的偏度和峰度(可能还有标准差和质心)。

我也在想这个问题。奇怪的是，我没有发现任何 python 图像分析包都实现了这一点。 OpenCV 有一个 moments function ，我们应该能够从中得到偏度，但是力矩只有三阶，我们需要四阶才能得到峰度。

为了使事情变得更容易和更快，我认为在 x 和 y 方向上对图像进行投影并从这些投影中找到统计数据在数学上等同于使用完整图像找到统计数据。在下面的代码中，我使用了这两种方法并表明它们对于这个流畅的示例是相同的。使用真实的、嘈杂的图像，我发现这两种方法也提供了相同的结果，但前提是您手动将图像数据转换为 float64(它导入为 float 32，“数字内容”导致结果略有不同。

下面是一个例子。您应该能够将“image_statistics()”函数剪切并粘贴到您自己的代码中。希望它对某人有用! :)

import numpy as np
import matplotlib.pyplot as plt
import time

plt.figure(figsize=(10,10))

ax1 = plt.subplot(221)
ax2 = plt.subplot(222)
ax4 = plt.subplot(224)

#Make some sample data as a sum of two elliptical gaussians:
x = range(200)
y = range(200)

X,Y = np.meshgrid(x,y)

def twoD_gaussian(X,Y,A=1,xo=100,yo=100,sx=20,sy=10):
    return A*np.exp(-(X-xo)**2/(2.*sx**2)-(Y-yo)**2/(2.*sy**2))

Z = twoD_gaussian(X,Y) + twoD_gaussian(X,Y,A=0.4,yo=75)

ax2.imshow(Z) #plot it

#calculate projections along the x and y axes for the plots
yp = np.sum(Z,axis=1)
xp = np.sum(Z,axis=0)

ax1.plot(yp,np.linspace(0,len(yp),len(yp)))
ax4.plot(np.linspace(0,len(xp),len(xp)),xp)

#Here is the business:
def image_statistics(Z):
    #Input: Z, a 2D array, hopefully containing some sort of peak
    #Output: cx,cy,sx,sy,skx,sky,kx,ky
    #cx and cy are the coordinates of the centroid
    #sx and sy are the stardard deviation in the x and y directions
    #skx and sky are the skewness in the x and y directions
    #kx and ky are the Kurtosis in the x and y directions
    #Note: this is not the excess kurtosis. For a normal distribution
    #you expect the kurtosis will be 3.0. Just subtract 3 to get the
    #excess kurtosis.
    import numpy as np

    h,w = np.shape(Z)

    x = range(w)
    y = range(h)


    #calculate projections along the x and y axes
    yp = np.sum(Z,axis=1)
    xp = np.sum(Z,axis=0)

    #centroid
    cx = np.sum(x*xp)/np.sum(xp)
    cy = np.sum(y*yp)/np.sum(yp)

    #standard deviation
    x2 = (x-cx)**2
    y2 = (y-cy)**2

    sx = np.sqrt( np.sum(x2*xp)/np.sum(xp) )
    sy = np.sqrt( np.sum(y2*yp)/np.sum(yp) )

    #skewness
    x3 = (x-cx)**3
    y3 = (y-cy)**3

    skx = np.sum(xp*x3)/(np.sum(xp) * sx**3)
    sky = np.sum(yp*y3)/(np.sum(yp) * sy**3)

    #Kurtosis
    x4 = (x-cx)**4
    y4 = (y-cy)**4
    kx = np.sum(xp*x4)/(np.sum(xp) * sx**4)
    ky = np.sum(yp*y4)/(np.sum(yp) * sy**4)


    return cx,cy,sx,sy,skx,sky,kx,ky

#We can check that the result is the same if we use the full 2D data array
def image_statistics_2D(Z):
    h,w = np.shape(Z)

    x = range(w)
    y = range(h)

    X,Y = np.meshgrid(x,y)

    #Centroid (mean)
    cx = np.sum(Z*X)/np.sum(Z)
    cy = np.sum(Z*Y)/np.sum(Z)

    ###Standard deviation
    x2 = (range(w) - cx)**2
    y2 = (range(h) - cy)**2

    X2,Y2 = np.meshgrid(x2,y2)

    #Find the variance
    vx = np.sum(Z*X2)/np.sum(Z)
    vy = np.sum(Z*Y2)/np.sum(Z)

    #SD is the sqrt of the variance
    sx,sy = np.sqrt(vx),np.sqrt(vy)

    ###Skewness
    x3 = (range(w) - cx)**3
    y3 = (range(h) - cy)**3

    X3,Y3 = np.meshgrid(x3,y3)

    #Find the thid central moment
    m3x = np.sum(Z*X3)/np.sum(Z)
    m3y = np.sum(Z*Y3)/np.sum(Z)

    #Skewness is the third central moment divided by SD cubed
    skx = m3x/sx**3
    sky = m3y/sy**3

    ###Kurtosis
    x4 = (range(w) - cx)**4
    y4 = (range(h) - cy)**4

    X4,Y4 = np.meshgrid(x4,y4)

    #Find the fourth central moment
    m4x = np.sum(Z*X4)/np.sum(Z)
    m4y = np.sum(Z*Y4)/np.sum(Z)

    #Kurtosis is the fourth central moment divided by SD to the fourth power
    kx = m4x/sx**4
    ky = m4y/sy**4

    return cx,cy,sx,sy,skx,sky,kx,ky


#Calculate the image statistics using the projection method
stats_pr = image_statistics(Z)

#Confirm that they are the same by using a 2D calculation
stats_2d = image_statistics_2D(Z)

names = ('Centroid x','Centroid y','StdDev x','StdDev y','Skewness x','Skewness y','Kurtosis x','Kurtosis y')

print 'Statistis\t1D\t2D'
for name,i1,i2 in zip(names, stats_2d,stats_pr):
    print '%s \t%.2f \t%.2f'%(name, i1,i2)

plt.show()

输出的屏幕截图，仅供娱乐:

还有一件事:根据您对图像所做的具体操作，您可能会考虑使用 ImageJ用于您的图像分析——但要小心! moments plugin会让你计算偏度、峰度等。ImageJ 在分析>>设置测量菜单中确实有一个“偏度”和“峰度”，但我认为这实际上找到了强度直方图的偏度和峰度(我被愚弄了一分钟)。

关于python - python中的图像偏度和峰度，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/13894631/