用2D方程在Python中拟合图像

Question

我有一张图片，我想把它适配到一个二维方程上，以便提取出nx和ny这两个参数。首先，我定义了一个二维函数和拟合的残差，然后我读取了图片文件，接着我尝试使用leastsq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，我收到了这个错误信息：

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.

请问有人能建议一下解决方案吗？我哪里出错了？

谢谢大家！

Answer 1

只需将 residuals() 替换成下面的内容，就可以解决你的问题：

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

基本上，我怀疑调用 residuals(p0, meas, nx, ny) 这个函数会返回一个形状为 (nx, ny) 的 二维数组，这会导致出现 minpack.error 的错误。你需要传递一个 一维数组（或者一个 浮点数）给 leastsq()。