使用Python计算方差图像

Question

有没有简单的方法可以用Python/NumPy/Scipy来计算图像的运行方差滤波？这里的运行方差图像是指对图像中每个小窗口I计算的结果，公式是sum((I - mean(I))^2)/nPixels。

因为这些图像非常大（12000x12000像素），我想避免为了使用不同的库而在格式之间转换数组，然后再转换回来，这样会很麻烦。

我想我可以手动计算平均值，使用类似下面的代码：

kernel = np.ones((winSize, winSize))/winSize**2
image_mean = scipy.ndimage.convolve(image, kernel)
diff = (image - image_mean)**2
# Calculate sum over winSize*winSize sub-images
# Subsample result

但如果能有像Matlab中的stdfilt函数那样的功能就好了。

有没有人能推荐一个支持numpy数组并且有这种功能的库，或者给我一些在NumPy/SciPy中实现这个功能的提示或方法？

Answer 1

经过一些优化，我们想出了这个适用于通用3D图像的函数：

def variance_filter( img, VAR_FILTER_SIZE ):
  from numpy.lib.stride_tricks import as_strided

  WIN_SIZE=(2*VAR_FILTER_SIZE)+1
  if ~ VAR_FILTER_SIZE%2==1:
      print 'Warning, VAR_FILTER_SIZE must be ODD Integer number  '
  # hack -- this could probably be an input to the function but Alessandro is lazy
  WIN_DIMS = [ WIN_SIZE, WIN_SIZE, WIN_SIZE ]


  # Check that there is a 3D image input.
  if len( img.shape ) != 3:
      print "\t variance_filter: Are you sure that you passed me a 3D image?"
      return -1
  else:
      DIMS = img.shape

  # Set up a windowed view on the data... this will have a border removed compared to the img_in
  img_strided = as_strided(img, shape=(DIMS[0]-WIN_DIMS[0]+1, DIMS[1]-WIN_DIMS[1]+1, DIMS[2]-WIN_DIMS[2]+1, WIN_DIMS[0], WIN_DIMS[1], WIN_DIMS[2] ), strides=img.strides*2)

  # Calculate variance, vectorially
  win_mean = numpy.sum(numpy.sum(numpy.sum(img_strided, axis=-1), axis=-1), axis=-1) / (WIN_DIMS[0]*WIN_DIMS[1]*WIN_DIMS[2])

  # As per http://en.wikipedia.org/wiki/Variance, we are removing the mean from every window,
  #   then squaring the result.
  # Casting to 64 bit float inside, because the numbers (at least for our images) get pretty big
  win_var = numpy.sum(numpy.sum(numpy.sum((( img_strided.T.astype('<f8') - win_mean.T.astype('<f8') )**2).T, axis=-1), axis=-1), axis=-1) / (WIN_DIMS[0]*WIN_DIMS[1]*WIN_DIMS[2])

  # Prepare an output image of the right size, in order to replace the border removed with the windowed view call
  out_img = numpy.zeros( DIMS, dtype='<f8' )
  # copy borders out...
  out_img[ WIN_DIMS[0]/2:DIMS[0]-WIN_DIMS[0]+1+WIN_DIMS[0]/2, WIN_DIMS[1]/2:DIMS[1]-WIN_DIMS[1]+1+WIN_DIMS[1]/2, WIN_DIMS[2]/2:DIMS[2]-WIN_DIMS[2]+1+WIN_DIMS[2]/2, ] = win_var

  # output
  return out_img.astype('>f4')

Answer 2

你可以使用 numpy.lib.stride_tricks.as_strided 来获取你图像的窗口视图：

import numpy as np
from numpy.lib.stride_tricks import as_strided

rows, cols = 500, 500
win_rows, win_cols = 5, 5

img = np.random.rand(rows, cols)

win_img = as_strided(img, shape=(rows-win_rows+1, cols-win_cols+1,
                                 win_rows, win_cols),
                     strides=img.strides*2)

现在 win_img[i, j] 就是一个大小为 (win_rows, win_cols) 的数组，它的左上角位于 [i, j] 这个位置：

>>> img[100:105, 100:105]
array([[ 0.34150754,  0.17888323,  0.67222354,  0.9020784 ,  0.48826682],
       [ 0.68451774,  0.14887515,  0.44892615,  0.33352743,  0.22090103],
       [ 0.41114758,  0.82608407,  0.77190533,  0.42830363,  0.57300759],
       [ 0.68435626,  0.94874394,  0.55238567,  0.40367885,  0.42955156],
       [ 0.59359203,  0.62237553,  0.58428725,  0.58608119,  0.29157555]])
>>> win_img[100,100]
array([[ 0.34150754,  0.17888323,  0.67222354,  0.9020784 ,  0.48826682],
       [ 0.68451774,  0.14887515,  0.44892615,  0.33352743,  0.22090103],
       [ 0.41114758,  0.82608407,  0.77190533,  0.42830363,  0.57300759],
       [ 0.68435626,  0.94874394,  0.55238567,  0.40367885,  0.42955156],
       [ 0.59359203,  0.62237553,  0.58428725,  0.58608119,  0.29157555]])

不过你要小心，不要把你窗口的视图转变成它的窗口副本：在我的例子中，这样会需要多25倍的存储空间。我记得 numpy 1.7 允许你选择多个轴，这样你就可以简单地这样做：

>>> np.var(win_img, axis=(-1, -2))

我现在用的是 numpy 1.6.2，所以无法测试这个。另一个选择是，如果我没记错我的数学的话，可能会在窗口不大的情况下失败：

>>> win_mean = np.sum(np.sum(win_img, axis=-1), axis=-1)/win_rows/win_cols
>>> win_sqr_mean = np.sum(np.sum(win_img**2, axis=-1), axis=-1)/win_rows/win_cols
>>> win_var = win_sqr_mean - win_mean**2

现在 win_var 是一个形状为

>>> win_var.shape
(496, 496)

的数组，而 win_var[i, j] 存储的是左上角在 [i, j] 的 (5, 5) 窗口的方差。

Answer 3

更简单的解决方案，而且速度更快：使用SciPy的 ndimage.uniform_filter

import numpy as np
from scipy import ndimage 
rows, cols = 500, 500
win_rows, win_cols = 5, 5

img = np.random.rand(rows, cols)
win_mean = ndimage.uniform_filter(img, (win_rows, win_cols))
win_sqr_mean = ndimage.uniform_filter(img**2, (win_rows, win_cols))
win_var = win_sqr_mean - win_mean**2

所谓的“步幅技巧”确实很巧妙，但速度慢了4倍，而且不太容易理解。generic_filter的速度比步幅技巧慢20倍……