如何使我的2D高斯适合我的图像

Question

我正在尝试将2D高斯拟合到图像中以找到其中最亮点的位置。我的代码如下所示：

import numpy as np
import astropy.io.fits as fits
import os
from astropy.stats import mad_std
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
from matplotlib.patches import Circle
from lmfit.models import GaussianModel
from astropy.modeling import models, fitting

def gaussian(xycoor,x0, y0, sigma, amp):
    '''This Function is the Gaussian Function'''

    x, y = xycoor # x and y taken from fit function.  Stars at 0, increases by 1, goes to length of axis
    A = 1 / (2*sigma**2)
    eq =  amp*np.exp(-A*((x-x0)**2 + (y-y0)**2)) #Gaussian
    return eq


def fit(image):
    med = np.median(image)
    image = image-med
    image = image[0,0,:,:]

    max_index = np.where(image >= np.max(image))
    x0 = max_index[1] #Middle of X axis
    y0 = max_index[0] #Middle of Y axis
    x = np.arange(0, image.shape[1], 1) #Stars at 0, increases by 1, goes to length of axis
    y = np.arange(0, image.shape[0], 1) #Stars at 0, increases by 1, goes to length of axis
    xx, yy = np.meshgrid(x, y) #creates a grid to plot the function over
    sigma = np.std(image) #The standard dev given in the Gaussian
    amp = np.max(image) #amplitude
    guess = [x0, y0, sigma, amp] #The initial guess for the gaussian fitting

    low = [0,0,0,0] #start of data array
    #Upper Bounds x0: length of x axis, y0: length of y axis, st dev: max value in image, amplitude: 2x the max value
    upper = [image.shape[0], image.shape[1], np.max(image), np.max(image)*2] 
    bounds = [low, upper]

    params, pcov = curve_fit(gaussian, (xx.ravel(), yy.ravel()), image.ravel(),p0 = guess, bounds = bounds) #optimal fit.  Not sure what pcov is. 

    return params


def plotting(image, params):
    fig, ax = plt.subplots()
    ax.imshow(image)
    ax.scatter(params[0], params[1],s = 10, c = 'red', marker = 'x')
    circle = Circle((params[0], params[1]), params[2], facecolor = 'none', edgecolor = 'red', linewidth = 1)

    ax.add_patch(circle)
    plt.show()

data = fits.getdata('AzTECC100.fits') #read in file
med = np.median(data) 
data = data - med

data = data[0,0,:,:]

parameters = fit(data)

#generates a gaussian based on the parameters given
plotting(data, parameters)

图像是绘图，代码没有错误，但是拟合不起作用。它只是在x和x0的任何地方放置y0。我图像中的像素值非常小。最大值为0.0007，std dev为0.0001，x和y大几个数量级。所以我相信我的问题是，因为这个我的eq到处都是零，所以curve_fit失败了。我想知道是否有更好的方法来构建我的高斯，以便正确绘制？

Answer 1

我无法访问您的图片。相反，我已经生成了一些测试＆＃34;图像＆＃34;如下：

y, x = np.indices((51,51))
x -= 25
y -= 25
data = 3 * np.exp(-0.7 * ((x+2)**2 + (y-1)**2))

此外，我修改了您的绘图代码，以便将圆的半径增加10：

circle = Circle((params[0], params[1]), 10 * params[2], ...)

我又注释了两行：

# image = image[0,0,:,:]
# data = data[0,0,:,:]

我得到的结果显示在附图中，对我来说看起来很合理：

问题在于您如何从FITS文件访问数据？ （例如，image = image[0,0,:,:]）数据是4D数组吗？为什么你有4个指数？

我还看到您在此处提出了类似的问题：Astropy.model 2DGaussian issue您尝试仅使用astropy.modeling。我会研究这个问题。

注意：您可以替换

等代码

max_index = np.where(image >= np.max(image))
x0 = max_index[1] #Middle of X axis
y0 = max_index[0] #Middle of Y axis

与

y0, x0 = np.unravel_index(np.argmax(data), data.shape)