将图像与python中的2D方程式拟合

Question

我有一个图像，我想将其适合2D方程，以提取NX和NY参数。首先，我定义了2D函数和fit的残差，然后读取图像文件，然后尝试使用最小值的方法进行拟合，这是我的代码：

#!/usr/bin/python
import pyfits
import numpy as np
import numpy.random as npr
import matplotlib.pyplot as plt
import scipy.optimize

nx=870
ny=901
# define 2D function
def fun(nx,ny):
   n=(1+((nx**2+ny**2)**0.5/150)**2)**-3.7
   return n
vfun=np.vectorize(fun)
nxlist=np.linspace(-nx,nx,870)
nylist=np.linspace(-ny,ny,901)
X,Y=np.meshgrid(nxlist,nylist)
Z=vfun(X,Y)

def residuals(p,y,nx,ny):
    nx,ny = p
    err = y-fun(nx,ny)
    return err
def peval (nx,ny,p):
    nx,ny=p
    return fun(nx,ny)

# read image file
def image():
    h = pyfits.open('image.fits')
    IM = h[0].data      # copy the image data into a numpy (numerical python) array
    return IM
y_true = image()
y_meas = y_true+0.1*np.random.randn(ny,nx)         # add noise
colmap = plt.get_cmap('CMRmap') # load CMRmap colormap
plt.imshow(y_meas, cmap=colmap, origin='lower') # plot image using gray colorbar
plt.show()

# initial values
p0=[300,500]
plsq = scipy.optimize.leastsq(residuals,p0,args=(y_meas,nx,ny))
print plsq

但是，我收到了此错误消息

File "image_fit_test.py", line 51, in <module>    
plsq =   scipy.optimize.leastsq(residuals,p0,args=(y_meas,nx,ny))
File "/.../anaconda/lib/python2.7/site-packages/scipy/optimize/minpack.py", line 364,
in leastsq
gtol, maxfev, epsfcn, factor, diag)
minpack.error: Result from function call is not a proper array of floats.

请有人建议任何解决方案，这是在哪里出错？

预先感谢您。

Answer 1

只需用以下内容替换residuals()即可解决您的问题：

def residuals(p,y,nx,ny):
    nx,ny = p
    err = y-fun(nx,ny)
    return err.flatten()

基本上，我怀疑residuals(p0, meas, nx, ny)的功能调用会返回(nx, ny)形状的2d array，从而导致minpack.error异常。您需要将1d array（或float）传递给leastsq()。