有效地计算图像蟒蛇的方差

Question

我正在开发一个需要获得图像方差的项目.目前我正采取两种方法(两种方法都有效,但速度很慢):

1. 分别计算每个像素的方差:

这是使用numpy的代码,varianceMatrix是输出

varianceMatrix = np.zeros(im.shape,np.uint8)
w = 1              # the radius of pixels neighbors 
ny = len(im)
nx = len(im[0])


for i in range(w,nx-w):
    for j in range(w,ny-w):

        sampleframe = im[j-w:j+w, i-w:i+w]
        variance    = np.var(sampleframe)
        varianceMatrix[j][i] = int(variance)

return varianceMatrix   

2. 使用现有的scipy函数:

这是scipy功能:

from scipy import ndimage

varianceMatrix = ndimage.generic_filter(im, np.var, size = 3)

scipy功能更快,但不是那么多.我正在寻找一种更好的替代方案来计算方差.

有任何想法吗？？？

Answer 1

这是使用OpenCV的快速解决方案:

import cv2

def winVar(img, wlen):
  wmean, wsqrmean = (cv2.boxFilter(x, -1, (wlen, wlen),
    borderType=cv2.BORDER_REFLECT) for x in (img, img*img))
  return wsqrmean - wmean*wmean

在我的机器上以及下面的示例中,winVar()比其快2915倍ndimage.generic_filter()和快10.8倍sliding_img_var()(参见光环的答案):

In [66]: img = np.random.randint(0, 256, (500,500)).astype(np.float)

In [67]: %timeit winVar(img, 3)
100 loops, best of 3: 1.76 ms per loop

In [68]: %timeit ndimage.generic_filter(img, np.var, size=3)
1 loops, best of 3: 5.13 s per loop

In [69]: %timeit sliding_img_var(img, 1)
100 loops, best of 3: 19 ms per loop

结果匹配ndimage.generic_filter():

In [70]: np.allclose(winVar(img, 3), ndimage.generic_filter(img, np.var, size=3))
Out[70]: True

Answer 2

您可以使用众所周知的滑动窗口跨步技巧来加速计算。它将两个“虚拟维度”添加到数组的末尾，而不复制数据，然后计算它们的方差。

请注意，在您的代码中，im[j-w:j+w, ..]遍历索引j-w,j-w+1,...,j+w-1，最后一个是排他的，这可能不是您的意思。此外，方差大于 uint8 范围，因此最终会得到整数环绕。

import numpy as np
import time
np.random.seed(1234)

img = (np.random.rand(200, 200)*256).astype(np.uint8)

def sliding_window(a, window, axis=-1):
    shape = list(a.shape) + [window]
    shape[axis] -= window - 1
    if shape[axis] < 0:
        raise ValueError("Array too small")
    strides = a.strides + (a.strides[axis],)
    return np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)

def sliding_img_var(img, window):
    if window <= 0:
        raise ValueError("invalid window size")
    buf = sliding_window(img, 2*window, 0)
    buf = sliding_window(buf, 2*window, 1)

    out = np.zeros(img.shape, dtype=np.float32)
    np.var(buf[:-1,:-1], axis=(-1,-2), out=out[window:-window,window:-window])
    return out

def looping_img_var(im, w):
    nx, ny = img.shape
    varianceMatrix = np.zeros(im.shape, np.float32)
    for i in range(w,nx-w):
        for j in range(w,ny-w):
            sampleframe = im[j-w:j+w, i-w:i+w]
            variance    = np.var(sampleframe)
            varianceMatrix[j][i] = variance
    return varianceMatrix

np.set_printoptions(linewidth=1000, edgeitems=5)
start = time.time()
print(sliding_img_var(img, 1))
time_sliding = time.time() - start
start = time.time()
print(looping_img_var(img, 1))
time_looping = time.time() - start
print("duration: sliding: {0} s, looping: {1} s".format(time_sliding, time_looping))