如何在python中获得高斯滤波器

Question

我正在使用python创建一个大小为5x5的高斯滤波器.我在这里看到这篇文章,他们谈论类似的事情,但我没有找到获得相同的python代码到matlab函数的确切方法fspecial('gaussian', f_wid, sigma) 还有其他方法吗？我尝试使用以下代码:

size = 2
sizey = None
size = int(size)
if not sizey:
    sizey = size
else:
    sizey = int(sizey)
x, y = scipy.mgrid[-size: size + 1, -sizey: sizey + 1]
g = scipy.exp(- (x ** 2/float(size) + y ** 2 / float(sizey)))
print g / np.sqrt(2 * np.pi)

获得的输出是

[[ 0.00730688  0.03274718  0.05399097  0.03274718  0.00730688]
 [ 0.03274718  0.14676266  0.24197072  0.14676266  0.03274718]
 [ 0.05399097  0.24197072  0.39894228  0.24197072  0.05399097]
 [ 0.03274718  0.14676266  0.24197072  0.14676266  0.03274718]
 [ 0.00730688  0.03274718  0.05399097  0.03274718  0.00730688]]

我想要的是这样的:

   0.0029690   0.0133062   0.0219382   0.0133062   0.0029690
   0.0133062   0.0596343   0.0983203   0.0596343   0.0133062
   0.0219382   0.0983203   0.1621028   0.0983203   0.0219382
   0.0133062   0.0596343   0.0983203   0.0596343   0.0133062
   0.0029690   0.0133062   0.0219382   0.0133062   0.0029690

Answer 1

一般而言,如果你真的关心得到与MATLAB完全相同的结果,最简单的方法是直接查看MATLAB函数的来源.

在这种情况下,edit fspecial:

...
  case 'gaussian' % Gaussian filter

     siz   = (p2-1)/2;
     std   = p3;

     [x,y] = meshgrid(-siz(2):siz(2),-siz(1):siz(1));
     arg   = -(x.*x + y.*y)/(2*std*std);

     h     = exp(arg);
     h(h<eps*max(h(:))) = 0;

     sumh = sum(h(:));
     if sumh ~= 0,
       h  = h/sumh;
     end;
...

很简单,嗯？将此端口传输到Python是<10分钟的工作:

import numpy as np

def matlab_style_gauss2D(shape=(3,3),sigma=0.5):
    """
    2D gaussian mask - should give the same result as MATLAB's
    fspecial('gaussian',[shape],[sigma])
    """
    m,n = [(ss-1.)/2. for ss in shape]
    y,x = np.ogrid[-m:m+1,-n:n+1]
    h = np.exp( -(x*x + y*y) / (2.*sigma*sigma) )
    h[ h < np.finfo(h.dtype).eps*h.max() ] = 0
    sumh = h.sum()
    if sumh != 0:
        h /= sumh
    return h

这给出了与fspecial舍入误差相同的答案:

 >> fspecial('gaussian',5,1)

 0.002969     0.013306     0.021938     0.013306     0.002969
 0.013306     0.059634      0.09832     0.059634     0.013306
 0.021938      0.09832       0.1621      0.09832     0.021938
 0.013306     0.059634      0.09832     0.059634     0.013306
 0.002969     0.013306     0.021938     0.013306     0.002969

 : matlab_style_gauss2D((5,5),1)

array([[ 0.002969,  0.013306,  0.021938,  0.013306,  0.002969],
       [ 0.013306,  0.059634,  0.09832 ,  0.059634,  0.013306],
       [ 0.021938,  0.09832 ,  0.162103,  0.09832 ,  0.021938],
       [ 0.013306,  0.059634,  0.09832 ,  0.059634,  0.013306],
       [ 0.002969,  0.013306,  0.021938,  0.013306,  0.002969]])

Answer 2

您也可以尝试这样做（作为2个独立的1D高斯随机变量的乘积）以获得2D高斯内核：

from numpy import pi, exp, sqrt
s, k = 1, 2 #  generate a (2k+1)x(2k+1) gaussian kernel with mean=0 and sigma = s
probs = [exp(-z*z/(2*s*s))/sqrt(2*pi*s*s) for z in range(-k,k+1)] 
kernel = np.outer(probs, probs)
print kernel

#[[ 0.00291502  0.00792386  0.02153928  0.00792386  0.00291502]
#[ 0.00792386  0.02153928  0.05854983  0.02153928  0.00792386]
#[ 0.02153928  0.05854983  0.15915494  0.05854983  0.02153928]
#[ 0.00792386  0.02153928  0.05854983  0.02153928  0.00792386]
#[ 0.00291502  0.00792386  0.02153928  0.00792386  0.00291502]]

import matplotlib.pylab as plt
plt.imshow(kernel)
plt.colorbar()
plt.show()

Answer 3

我为这个问题找到了类似的解决方案：

def fspecial_gauss(size, sigma):

    """Function to mimic the 'fspecial' gaussian MATLAB function
    """

    x, y = numpy.mgrid[-size//2 + 1:size//2 + 1, -size//2 + 1:size//2 + 1]
    g = numpy.exp(-((x**2 + y**2)/(2.0*sigma**2)))
    return g/g.sum()