Matlab中的一维高斯卷积函数 [英] one Dimensional gauss convolution function in Matlab

问题描述

我正在尝试编写一个返回一个二维高斯滤波器的函数.该函数将sigma作为参数.问题在于该函数为所有sigma返回相同的数组.

I am trying to write a function that returns a one dimentional gauss filter. the function took sigma as a parameter. The problem is that the function returns the same array for all sigmas.

  function gaussFilter=gauss(sigma)  
  width = 3 * sigma;  
  support = (-width :sigma: width);  
  gaussFilter= exp( - (support).^2 / (2*sigma^2));   
  gaussFilter = gaussFilter/ sum(gaussFilter);  

请注意，支持数组的计算正确，但是应用exp时会出现问题.

Note that support array is calculated correctly but the problem arise when applying the exp.

推荐答案

想法是，滤波器的宽度必须足以表示高斯函数.经验法则是使用至少6*sigma的过滤器大小.

The idea is that the filter needs to be wide enough to represent the Gaussian function. The rule of thumb is to use filter size of at least 6*sigma.

由于支撑需要以零为中心，所以您可以在-3*sigma到+3*sigma的范围内(更准确地说，在中间将零表示为-/+ round(6*sigma - 1)/2).因此:

Since the support needs to be centered around zero, that would give you the range of -3*sigma to +3*sigma (to be more accurate, it is -/+ round(6*sigma - 1)/2 to account for the zero in the middle). Hence:

function gaussFilter = gauss(sigma)
    width = round((6*sigma - 1)/2);
    support = (-width:width);
    gaussFilter = exp( -(support).^2 ./ (2*sigma^2) );
    gaussFilter = gaussFilter/ sum(gaussFilter);

示例 :(以下各项均等效)

Example: (all the following are equivalent)

sigma = 1.2;
width = round((6*sigma - 1)/2);

gauss(sigma)

normpdf( -width:width, 0, sigma )

fspecial('gaussian', [1 2*width+1], sigma)

h = gausswin(2*width+1)';
h = h / sum(h)

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