Python 3D 多项式曲面拟合，顺序相关 [英] Python 3D polynomial surface fit, order dependent

问题描述

我目前正在处理天文数据，其中包含彗星图像.由于捕获时间(黄昏)，我想删除这些图像中的背景天空渐变.我为此开发的第一个程序从 Matplotlib 的ginput"(x,y) 中获取用户选择的点，提取每个坐标 (z) 的数据，然后使用 SciPy 的griddata"将数据网格化到一个新数组中.

I am currently working with astronomical data among which I have comet images. I would like to remove the background sky gradient in these images due to the time of capture (twilight). The first program I developed to do so took user selected points from Matplotlib's "ginput" (x,y) pulled the data for each coordinate (z) and then gridded the data in a new array with SciPy's "griddata."

由于假设背景变化很小，我想将 3d 低阶多项式拟合到这组 (x,y,z) 点.但是，griddata"不允许输入顺序:

Since the background is assumed to vary only slightly, I would like to fit a 3d low order polynomial to this set of (x,y,z) points. However, the "griddata" does not allow for an input order:

griddata(points,values, (dimension_x,dimension_y), method='nearest/linear/cubic')

关于可能使用的另一个函数或开发最小二乘拟合的方法有什么想法可以让我控制顺序?

Any ideas on another function that may be used or a method for developing a leas-squares fit that will allow me to control the order?

推荐答案

Griddata 使用样条拟合.三阶样条与三阶多项式不同(相反，它在每一点都是不同的三阶多项式).

Griddata uses a spline fitting. A 3rd order spline is not the same thing as a 3rd order polynomial (instead, it's a different 3rd order polynomial at every point).

如果您只想将 2D、3 阶多项式拟合到您的数据中，请执行以下操作以使用所有数据点来估计 16 个系数.

If you just want to fit a 2D, 3rd order polynomial to your data, then do something like the following to estimate the 16 coefficients using all of your data points.

import itertools
import numpy as np
import matplotlib.pyplot as plt

def main():
    # Generate Data...
    numdata = 100
    x = np.random.random(numdata)
    y = np.random.random(numdata)
    z = x**2 + y**2 + 3*x**3 + y + np.random.random(numdata)

    # Fit a 3rd order, 2d polynomial
    m = polyfit2d(x,y,z)

    # Evaluate it on a grid...
    nx, ny = 20, 20
    xx, yy = np.meshgrid(np.linspace(x.min(), x.max(), nx), 
                         np.linspace(y.min(), y.max(), ny))
    zz = polyval2d(xx, yy, m)

    # Plot
    plt.imshow(zz, extent=(x.min(), y.max(), x.max(), y.min()))
    plt.scatter(x, y, c=z)
    plt.show()

def polyfit2d(x, y, z, order=3):
    ncols = (order + 1)**2
    G = np.zeros((x.size, ncols))
    ij = itertools.product(range(order+1), range(order+1))
    for k, (i,j) in enumerate(ij):
        G[:,k] = x**i * y**j
    m, _, _, _ = np.linalg.lstsq(G, z)
    return m

def polyval2d(x, y, m):
    order = int(np.sqrt(len(m))) - 1
    ij = itertools.product(range(order+1), range(order+1))
    z = np.zeros_like(x)
    for a, (i,j) in zip(m, ij):
        z += a * x**i * y**j
    return z

main()

这篇关于Python 3D 多项式曲面拟合，顺序相关的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！