Global Contrast Normalization

1.作用

全局对比度归一化是为了防止图像的不同区域有不同量级的对比度。

2.计算方式

对于每个图像计算其像素均值，并根据其标准差归一化
表示宽高通道为的输入图像数组，

GCN的计算方式可表示为：

$$X_{ijk}^{{}^{\prime }}=s\frac{X_{ijk}-\overline{X}}{max\{ϵ,\sqrt{\lambda +\frac{1}{kwh}\sum _{i=1}^h\sum _{j=1}^w\sum _{k=1}^c(X_{ijk}-\overline{X}{)}^2}\}}$$

其中通常为10,通常为一个很小的数，以免除以0.

3.示例代码

import numpy
import scipy
import scipy.misc
from PIL import Image

def global_contrast_normalization(filename, s, lmda, epsilon):
    X = numpy.array(Image.open(filename))

    # replacement for the loop
    X_average = numpy.mean(X)
    print('Mean: ', X_average)
    X = X - X_average

    # `su` is here the mean, instead of the sum
    contrast = numpy.sqrt(lmda + numpy.mean(X**2))

    X = s * X / max(contrast, epsilon)

    # scipy can handle it
    scipy.misc.imsave('result.jpg', X)


global_contrast_normalization("cat.jpg", 1, 10, 0.000000001)

补充

GCN的应用可见Deep SVDD的代码 (opens new window)，其中对数据Normalize之前，先对数据进行了GCN，按类别求出了GCN后每个图像像素数据的最大最小值。

# Deep-SVDD-PyTorch/src/datasets/mnist.py line:20-30
# Pre-computed min and max values (after applying GCN) from train data per class
min_max = [(-0.8826567065619495, 9.001545489292527),
          (-0.6661464580883915, 20.108062262467364),
          (-0.7820454743183202, 11.665100841080346),
          (-0.7645772083211267, 12.895051191467457),
          (-0.7253923114302238, 12.683235701611533),
          (-0.7698501867861425, 13.103278415430502),
          (-0.778418217980696, 10.457837397569108),
          (-0.7129780970522351, 12.057777597673047),
          (-0.8280402650205075, 10.581538445782988),
          (-0.7369959242164307, 10.697039838804978)]

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参考资料

• 1.How to implement global contrast normalization in python? (opens new window)
• 2.Global Contrast Normalization
  (opens new window)