python高斯滤波和降噪_高斯滤波器和高斯滤波器中sigma与带宽的关系

例如，我可以通过在gaussian_filter(左图)中设置sigma=2.和在{}(右绘图)中设置bw_method=sigma/30.来获得以下绘图：

(MWE在问题的底部)

很明显，这些参数之间有一个关系，因为一个是高斯滤波器，另一个是高斯核密度估计。在

每个参数的定义是：sigma : scalar or sequence of scalars Standard deviation for Gaussian

kernel. The standard deviations of the Gaussian filter are given for

each axis as a sequence, or as a single number, in which case it is

equal for all axes.

根据高斯算子的定义，我可以理解这一点：

bw_method : str, scalar or callable, optional The method used to

calculate the estimator bandwidth. This can be ‘scott’, ‘silverman’, a

scalar constant or a callable. If a scalar, this will be used directly

as kde.factor. If a callable, it should take a gaussian_kde instance

as only parameter and return a scalar. If None (default), ‘scott’ is

used. See Notes for more details.

在本例中，假设bw_method的输入是标量(float)，以便与sigma相比较。这里是我迷路的地方，因为我在任何地方都找不到关于这个kde.factor参数的信息。在

我想知道的是，如果可能的话，连接这两个参数的精确数学方程(即：当使用float时，sigma和{})。在

MWE:import numpy as np

from scipy.stats import gaussian_kde

from scipy.ndimage.filters import gaussian_filter

import matplotlib.pyplot as plt

def rand_data():

return np.random.uniform(low=1., high=200., size=(1000,))

# Generate 2D data.

x_data, y_data = rand_data(), rand_data()

xmin, xmax = min(x_data), max(x_data)

ymin, ymax = min(y_data), max(y_data)

# Define grid density.

gd = 100

# Define bandwidth

bw = 2.

# Using gaussian_filter

# Obtain 2D histogram.

rang = [[xmin, xmax], [ymin, ymax]]

binsxy = [gd, gd]

hist1, xedges, yedges = np.histogram2d(x_data, y_data, range=rang, bins=binsxy)

# Gaussian filtered histogram.

h_g = gaussian_filter(hist1, bw)

# Using gaussian_kde

values = np.vstack([x_data, y_data])

# Data 2D kernel density estimate.

kernel = gaussian_kde(values, bw_method=bw / 30.)

# Define x,y grid.

gd_c = complex(0, gd)

x, y = np.mgrid[xmin:xmax:gd_c, ymin:ymax:gd_c]

positions = np.vstack([x.ravel(), y.ravel()])

# Evaluate KDE.

z = kernel(positions)

# Re-shape for plotting

z = z.reshape(gd, gd)

# Make plots.

fig, (ax1, ax2) = plt.subplots(1, 2)

# Gaussian filtered 2D histograms.

ax1.imshow(h_g.transpose(), origin='lower')

ax2.imshow(z.transpose(), origin='lower')

plt.show()