Question

我正在研究一些代码，这些代码需要能够执行2d高斯拟合。我的代码主要基于以下问题：Fitting a 2D Gaussian function using scipy.optimize.curve_fit - ValueError and minpack.error。现在的问题是，我实际上对所需使用的不同参数没有一个初步的猜测。

我已经尝试过：

def twoD_Gaussian(x_data_tuple, amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
    (x,y) = x_data_tuple
    xo = float(xo)
    yo = float(yo)    
    a = (np.cos(theta)**2)/(2*sigma_x**2) + (np.sin(theta)**2)/(2*sigma_y**2)
    b = -(np.sin(2*theta))/(4*sigma_x**2) + (np.sin(2*theta))/(4*sigma_y**2)
    c = (np.sin(theta)**2)/(2*sigma_x**2) + (np.cos(theta)**2)/(2*sigma_y**2)
    g = offset + amplitude*np.exp( - (a*((x-xo)**2) + 2*b*(x-xo)*(y-yo) 
                            + c*((y-yo)**2)))
    return g.ravel()

data.reshape（201,201）只是我从上述问题中得到的。

mean_gauss_x = sum(x * data.reshape(201,201)) / sum(data.reshape(201,201))
sigma_gauss_x = np.sqrt(sum(data.reshape(201,201) * (x - mean_gauss_x)**2) / sum(data.reshape(201,201)))

mean_gauss_y = sum(y * data.reshape(201,201)) / sum(data.reshape(201,201))
sigma_gauss_y = np.sqrt(sum(data.reshape(201,201) * (y - mean_gauss_y)**2) / sum(data.reshape(201,201)))


initial_guess = (np.max(data), mean_gauss_x, mean_gauss_y, sigma_gauss_x, sigma_gauss_y,0,10)


popt, pcov = curve_fit(twoD_Gaussian, (x, y), data, p0=initial_guess)

data_fitted = twoD_Gaussian((x, y), *popt)

如果尝试这样做，则会收到以下错误消息：ValueError：设置具有序列的数组元素。

有关begin参数的推理正确吗？为什么我会收到此错误？

Answer 1

如果我使用linked question中的可运行代码并替换为initial_guess的定义：

mean_gauss_x = sum(x * data.reshape(201,201)) / sum(data.reshape(201,201))
sigma_gauss_x = np.sqrt(sum(data.reshape(201,201) * (x - mean_gauss_x)**2) / sum(data.reshape(201,201)))

mean_gauss_y = sum(y * data.reshape(201,201)) / sum(data.reshape(201,201))
sigma_gauss_y = np.sqrt(sum(data.reshape(201,201) * (y - mean_gauss_y)**2) / sum(data.reshape(201,201)))

initial_guess = (np.max(data), mean_gauss_x, mean_gauss_y, sigma_gauss_x, sigma_gauss_y,0,10)

然后

print(inital_guess)

收益

(13.0, array([...]), array([...]), array([...]), array([...]), 0, 10)

请注意，initial_guess中的某些值是数组。 optimize.curve_fit函数期望initial_guess是标量的元组。这是问题的根源。

错误消息

ValueError: setting an array element with a sequence

通常在期望标量值的情况下提供类数组时出现。这提示问题的根源可能与维数错误的数组有关。例如，如果将一维数组传递给需要标量的函数，则可能会出现这种情况。

让我们看看摘自linked question的这段代码：

x = np.linspace(0, 200, 201)
y = np.linspace(0, 200, 201)
X, Y = np.meshgrid(x, y)

x和y是一维数组，而X和Y是2D数组。（我将所有2D数组大写，以帮助将它们与1D数组区分开。）

现在请注意，将Python sum和NumPy的sum方法应用于2D数组时，其行为有所不同：

In [146]: sum(X)
Out[146]: 
array([    0.,   201.,   402.,   603.,   804.,  1005.,  1206.,  1407.,
        1608.,  1809.,  2010.,  2211.,  2412.,  2613.,  2814.,  3015.,
        ...
       38592., 38793., 38994., 39195., 39396., 39597., 39798., 39999.,
       40200.])

In [147]: X.sum()
Out[147]: 4040100.0

Python sum功能等效于

total = 0
for item in X:
    total += item

由于X是2D数组，因此循环for item in X在X的行上进行迭代。因此，每个item是代表X行的一维数组。因此，total最终是一维数组。

相反，X.sum()对X中的所有元素求和并返回标量。

由于initial_guess应该是标量的元组，在使用sum的任何地方，都应改用NumPy sum方法。例如，替换

mean_gauss_x = sum(x * data) / sum(data)

使用

mean_gauss_x = (X * DATA).sum() / (DATA.sum())

import numpy as np import scipy.optimize as optimize import matplotlib.pyplot as plt # define model function and pass independant variables x and y as a list def twoD_Gaussian(data, amplitude, xo, yo, sigma_x, sigma_y, theta, offset): X, Y = data xo = float(xo) yo = float(yo) a = (np.cos(theta) ** 2) / (2 * sigma_x ** 2) + (np.sin(theta) ** 2) / ( 2 * sigma_y ** 2 ) b = -(np.sin(2 * theta)) / (4 * sigma_x ** 2) + (np.sin(2 * theta)) / ( 4 * sigma_y ** 2 ) c = (np.sin(theta) ** 2) / (2 * sigma_x ** 2) + (np.cos(theta) ** 2) / ( 2 * sigma_y ** 2 ) g = offset + amplitude * np.exp( -(a * ((X - xo) ** 2) + 2 * b * (X - xo) * (Y - yo) + c * ((Y - yo) ** 2)) ) return g.ravel() # Create x and y indices x = np.linspace(0, 200, 201) y = np.linspace(0, 200, 201) X, Y = np.meshgrid(x, y) # create data data = twoD_Gaussian((X, Y), 3, 100, 100, 20, 40, 0, 10) data_noisy = data + 0.2 * np.random.normal(size=data.shape) DATA = data.reshape(201, 201) # add some noise to the data and try to fit the data generated beforehand mean_gauss_x = (X * DATA).sum() / (DATA.sum()) sigma_gauss_x = np.sqrt((DATA * (X - mean_gauss_x) ** 2).sum() / (DATA.sum())) mean_gauss_y = (Y * DATA).sum() / (DATA.sum()) sigma_gauss_y = np.sqrt((DATA * (Y - mean_gauss_y) ** 2).sum() / (DATA.sum())) initial_guess = ( np.max(data), mean_gauss_x, mean_gauss_y, sigma_gauss_x, sigma_gauss_y, 0, 10, ) print(initial_guess) # (13.0, 100.00000000000001, 100.00000000000001, 57.106515650488404, 57.43620227324201, 0, 10) # initial_guess = (3,100,100,20,40,0,10) popt, pcov = optimize.curve_fit(twoD_Gaussian, (X, Y), data_noisy, p0=initial_guess) data_fitted = twoD_Gaussian((X, Y), *popt) fig, ax = plt.subplots(1, 1) ax.imshow( data_noisy.reshape(201, 201), cmap=plt.cm.jet, origin="bottom", extent=(X.min(), X.max(), Y.min(), Y.max()), ) ax.contour(X, Y, data_fitted.reshape(201, 201), 8, colors="w") plt.show()

确定开始参数2D高斯拟合

1 个答案: