如何获得加权高斯滤波器 [英] How to obtain a weighted gaussian filter

问题描述

我有一组加权 x,y点，如下所示(全套为这里):

I have a set of weighted x,y points, like shown below (the full set is here):

#  x       y     w
-0.038  2.0127  0.71
0.058   1.9557  1
0.067   2.0016  0.9
0.072   2.0316  0.83
...

我需要找到一条平滑的线，以根据分配给每个点的重要性来调整这些点，即:权重越大，则数据点应具有更大的相关性.

I need to find a smoothed line that adjusts these points according to the importance assigned to each, ie: more weight means the data point should have more relevance.

这是我到目前为止所拥有的代码，它基本上应用了 gaussian_filter1d 到数据(我从这个问题中得到了这个主意: python中的线平滑算法?):

This is the code I have so far, which basically applies a gaussian_filter1d to the data (I got the idea from this question: line smoothing algorithm in python?):

import matplotlib.pyplot as plt
import numpy as np
from scipy.ndimage import gaussian_filter1d

# Read data from file.
data = np.loadtxt('data_file', unpack=True)
x, y, w = data[0], data[1], data[2]

# Return evenly spaced numbers over a specified interval.
t = np.linspace(0, 1, len(x))
t2 = np.linspace(0, 1, 100)    
# One-dimensional linear interpolation.
x2 = np.interp(t2, t, x)
y2 = np.interp(t2, t, y)

# Obtain Gaussian filter with fixed sigma value.
sigma = 7
x3 = gaussian_filter1d(x2, sigma)
y3 = gaussian_filter1d(y2, sigma)

# Make plot.
cm = plt.cm.get_cmap('RdYlBu')
plt.scatter(x, y, marker="o", c=w, s=40, cmap=cm, lw=0.5, vmin=0, vmax=1)
plt.plot(x3, y3, "r", lw=2)
plt.show()

此代码生成以下图(蓝色点的权重值较高):

This code produces the following plot (bluer dots have a higher weight value):

问题在于，这种拟合不考虑分配给每个点的权重.如何将这些信息引入高斯滤波器?

The problem is that this fit does not consider the weights assigned to each point. How can I introduce that information into the gaussian filter?

推荐答案

请注意，以下想法不是解决方法，也不是确切的解决方案，但值得尝试.

Note that the following idea is workaround not an exact solution, but it is worth to try.

这个想法是使用w weight参数来重复x和y中的相应值.因此，例如，如果将w缩放到范围[1,10]，则x中的所有对应值，因此y中的所有对应值将被重复10次，而w等于10.即，新的x，将被创建.这样，我们实际上将权重作为x和y中值的频率合并.完成此操作后，将新的算法提供给您的算法有望带来所需的结果，如下面的工作示例所示.

The idea is to use w weight parameter to repeat corresponding values in x and y. So if you scale w for example into range [1,10] all corresponding values in x and so in y will be duplicated 10 times for w equal to 10. That is, new x, y will be created. In this way we incorporate the weight as frequency of values in x and y, indeed. Having this done, feeding the new ones to your algorithm hopefully gives you desired results as shown in the worked examples below.

• 对于第一个数字，蓝色到红色的光谱对应于从低到高的权重.标题编号是如上所述的复制因子.
• 第二个数字，您的数据，我们没有碰到您的颜色格式.

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