python - 对于 PIL.ImageFilter.GaussianBlur 如何使用内核以及半径参数与标准偏差有关吗？

Question

使用 PIL 读取图像后，我通常使用 scipy.ndimage 执行高斯滤波器，如下所示

import PIL
from scipy import ndimage

PIL_image = PIL.Image.open(filename)
data = PIL_image.getdata()
array = np.array(list(data)).reshape(data.size[::-1]+(-1,))
img = array.astype(float)
fimg = ndimage.gaussian_filter(img, sigma=sigma, mode='mirror', order=0)

PIL 中有如下高斯模糊函数(来自 this answer )，但我不知道它究竟是如何工作的，也不知道它使用的是什么内核:

from PIL import ImageFilter
fimgPIL = PIL_image.filter(ImageFilter.GaussianBlur(radius=r)

This documentation does not provide details .
问题 关于 PIL.ImageFilter.GaussianBlur :

半径参数到底是什么；是否相当于standard deviation σ?

对于给定的半径，它计算内核有多远？ 2σ? 3σ? 6σ?

This comment关于高斯模糊的答案 - 标准偏差、半径和内核大小说明如下，但我还没有找到 PIL 的信息。

OpenCV uses kernel radius of (sigma * 3) while scipy.ndimage.gaussian_filter uses kernel radius of int(4 * sigma + 0.5)

Answer 1

来自 source code ，看起来像 PIL.ImageFilter.GaussianBlur用途 PIL.ImageFilter.BoxBlur .但我无法弄清楚半径和西格玛是如何相关的。
我写了一个脚本来检查 scipy.ndimage.gaussian_filter 之间的区别和 PIL.ImageFilter.GaussianBlur .

import numpy as np
from scipy import misc
from scipy.ndimage import gaussian_filter
import PIL
from PIL import ImageFilter
import matplotlib.pyplot as plt


# Load test color image
img = misc.face()

# Scipy gaussian filter
sigma = 5
img_scipy = gaussian_filter(img, sigma=(sigma,sigma,0), mode='nearest')

# PIL gaussian filter
radius = 5
PIL_image = PIL.Image.fromarray(img)
img_PIL = PIL_image.filter(ImageFilter.GaussianBlur(radius=radius))
data = img_PIL.getdata()
img_PIL = np.array(data).reshape(data.size[::-1]+(-1,))
img_PIL = img_PIL.astype(np.uint8)

# Image difference
img_diff = np.abs(np.float_(img_scipy) - np.float_(img_PIL))
img_diff = np.uint8(img_diff)

# Stats
mean_diff = np.mean(img_diff)
median_diff = np.median(img_diff)
max_diff = np.max(img_diff)

# Plot results
plt.subplot(221)
plt.imshow(img_scipy)
plt.title('SciPy (sigma = {})'.format(sigma))
plt.axis('off')

plt.subplot(222)
plt.imshow(img_PIL)
plt.title('PIL (radius = {})'.format(radius))
plt.axis('off')

plt.subplot(223)
plt.imshow(img_diff)
plt.title('Image difference \n (Mean = {:.2f}, Median = {:.2f}, Max = {:.2f})'
          .format(mean_diff, median_diff, max_diff))
plt.colorbar()
plt.axis('off')

# Plot histogram
d = img_diff.flatten()
bins = list(range(int(max_diff)))

plt.subplot(224)
plt.title('Histogram of Image difference')

h = plt.hist(d, bins=bins)
for i in range(len(h[0])):
    plt.text(h[1][i], h[0][i], str(int(h[0][i])))

sigma=5, radius=5 的输出:
sigma=30, radius=30 的输出:
scipy.ndimage.gaussian_filter 的输出和 PIL.ImageFilter.GaussianBlur非常相似，差异可以忽略不计。超过 95% 的差异值 <= 2。
PIL 版本:7.2.0，SciPy 版本:1.5.0