计算方差图像python

Calculating variance image python

有没有一种简单的方法可以使用 Python/NumPy/Scipy 计算图像上的运行方差过滤器？通过运行方差图像，我的意思是计算图像中每个子窗口 I 的 sum((I - mean(I))^2)/nPixels 的结果。

由于图像非常大(12000x12000 像素)，我想避免在格式之间转换数组的开销，以便能够使用不同的库然后再转换回来。

我想我可以通过使用类似

的方法找到平均值来手动执行此操作

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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

但是如果有像 Matlab 中的 stdfilt 函数这样的东西会更好。

任何人都可以指出具有此功能并支持 numpy 数组的库的方向，或者提示/提供一种在 NumPy/SciPy 中执行此操作的方法吗？

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更简单的解决方案也更快：使用 SciPy\\'s ndimage.uniform_filter

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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

"跨步技巧"是个漂亮的技巧，但速度慢了 4 且不那么可读。
generic_filter 比步幅慢 20 倍...

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您可以使用 numpy.lib.stride_tricks.as_strided 来获得图像的窗口视图：

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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] 是 (win_rows, win_cols) 数组，左上角位于 [i, j] 位置：

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>>> 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]])

但是，您必须小心，不要将图像的窗口视图转换为它的窗口副本：在我的示例中，这将需要 25 倍的存储空间。我相信 numpy 1.7 可以让您选择多个轴，因此您可以简单地执行以下操作：

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

我被 numpy 1.6.2 卡住了，所以我无法测试它。如果我没记错我的数学，另一个选项可能会因窗口不太大而失败：

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>>> 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 是一个形状数组

1 2	>>> win_var.shape (496, 496)

和 win_var[i, j] 保存 (5, 5) 窗口的方差，左上角在 [i, j]。

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经过一些优化，我们想出了一个通用 3D 图像的函数：

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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')

您可以使用 scipy.ndimage.generic_filter。我无法使用 matlab 进行测试，但也许这可以为您提供所需的内容：

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import numpy as np
import scipy.ndimage as ndimage
subs = 10 # this is the size of the (square) sub-windows
img = np.random.rand(500, 500)
img_std = ndimage.filters.generic_filter(img, np.std, size=subs)

您可以使用 footprint 关键字制作任意大小的子窗口。有关示例，请参阅此问题。

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