scipy中的高斯滤波器 [英] Gaussian filter in scipy

问题描述

我想在512x512像素的图像上应用尺寸为5x5像素的高斯滤镜。我发现了一个scipy函数：

I want to apply a Gaussian filter of dimension 5x5 pixels on an image of 512x512 pixels. I found a scipy function to do that:

scipy.ndimage.filters.gaussian_filter(input, sigma, truncate=3.0)

我如何选择西格玛参数以确保我的高斯窗口为5x5像素？

How I choose the parameter of sigma to make sure that my Gaussian window is 5x5 pixels?

推荐答案

在这里查看源代码：https://github.com/scipy/scipy/blob/master/scipy/ndimage/filters.py

你会看到 gaussian_filter 为每个轴调用 gaussian_filter1d 。在 gaussian_filter1d 中，过滤器的宽度由 sigma 和 truncate的值隐式确定。实际上，宽度 w 是

You'll see that gaussian_filter calls gaussian_filter1d for each axis. In gaussian_filter1d, the width of the filter is determined implicitly by the values of sigma and truncate. In effect, the width w is

w = 2*int(truncate*sigma + 0.5) + 1

所以

(w - 1)/2 = int(truncate*sigma + 0.5)

对于w = 5，左边是2.右边是2，如果

For w = 5, the left side is 2. The right side is 2 if

2 <= truncate*sigma + 0.5 < 3

或

1.5 <= truncate*sigma < 2.5

如果选择 truncate = 3 （覆盖默认值4），你得到

If you choose truncate = 3 (overriding the default of 4), you get

0.5 <= sigma < 0.83333...

我们可以通过过滤一个全0的输入来检查这个，除了一个1 （即找到滤波器的脉冲响应）并计算滤波输出中的非零值的数量。 （在下面， np 是 numpy 。）

We can check this by filtering an input that is all 0 except for a single 1 (i.e. find the impulse response of the filter) and counting the number of nonzero values in the filtered output. (In the following, np is numpy.)

首先使用单个1创建输入：

First create an input with a single 1:

In [248]: x = np.zeros(9)

In [249]: x[4] = 1

检查中的变化大小 sigma = 0.5 ...

Check the change in the size at sigma = 0.5...

In [250]: np.count_nonzero(gaussian_filter1d(x, 0.49, truncate=3))
Out[250]: 3

In [251]: np.count_nonzero(gaussian_filter1d(x, 0.5, truncate=3))
Out[251]: 5

...和 sigma = 0.8333 ... ：

In [252]: np.count_nonzero(gaussian_filter1d(x, 0.8333, truncate=3))
Out[252]: 5

In [253]: np.count_nonzero(gaussian_filter1d(x, 0.8334, truncate=3))
Out[253]: 7

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