特征白化生成相同的图像

Question

我正在查看此处显示的特征白化示例：How to implement ZCA Whitening? Python

我已经实现了下面的代码，但是每当我运行它时，我在所有 4 张图片中都得到了相同的图像，我不知道为什么：

读取数据的代码（工作正常）

import cv2
import matplotlib.pyplot as plt
from urllib.request import urlopen, Request
new_size = 50

urls = ['https://hips.hearstapps.com/hmg-prod.s3.amazonaws.com/images/dog-puppy-on-garden-royalty-free-image-1586966191.jpg',
        'https://dogtime.com/assets/uploads/2018/10/puppies-cover.jpg',
         'https://www.readersdigest.ca/wp-content/uploads/2013/03/6-facts-to-know-before-owning-a-puppy.jpg',
          'https://images.newscientist.com/wp-content/uploads/2021/06/03141753/03-june_puppies.jpg']

puppies = []
for url in urls:
    r = Request(url, headers={'User-Agent': 'Mozilla/5.0'})
    response = urlopen(r).read()
    arr = np.asarray(bytearray(response), dtype=np.uint8)
    puppies.append(cv2.imdecode(arr, 0)) # 'Load it as it is'

#item_pics = [cv2.imread( './pictures/picture_'+ str(x) + '.jpeg', 0) for x in range(1,5)]
puppies_scaled = [cv2.resize(x, [new_size,new_size], interpolation = cv2.INTER_AREA) for x in puppies]
puppies_vectors = [x.reshape(new_size * new_size) for x in puppies_scaled]

美白代码

#borrowed heavily from  https://stackoverflow.com/questions/31528800/how-to-implement-zca-whitening-python
def zca_whitening_matrix(X):
    """
    Function to compute ZCA whitening matrix (aka Mahalanobis whitening).
    INPUT:  X: [M x N] matrix.
        Rows: Variables
        Columns: Observations
    OUTPUT: ZCAMatrix: [M x M] matrix
    """
    # Covariance matrix [column-wise variables]: Sigma = (X-mu)' * (X-mu) / N
    sigma = np.cov(X, rowvar=True) # [M x M]
    # Singular Value Decomposition. X = U * np.diag(S) * V
    U,S,V = np.linalg.svd(sigma)
        # U: [M x M] eigenvectors of sigma.
        # S: [M x 1] eigenvalues of sigma.
        # V: [M x M] transpose of U
    # Whitening constant: prevents division by zero
    epsilon = 1e-25
    # ZCA Whitening matrix: U * Lambda * U'
    ZCAMatrix = np.dot(U, np.dot(np.diag(1.0/np.sqrt(S + epsilon)), U.T)) # [M x M]
    return ZCAMatrix

要美白的代码

combined_data = np.array(puppies_vectors).T
my_zca_transformer_image_stuff = zca_whitening_matrix(combined_data)
xZCAMatrix = np.dot(my_zca_transformer_image_stuff, combined_data)
reshaped_pics = [xZCAMatrix[:,i].reshape(new_size,new_size) for i in range(4)]

结果（所有图片相同）

Answer 1

对零均值数据执行白化。这意味着，矩阵是在零均值数据上计算的，并且它们也应该应用于零均值数据。如果你不这样做，你基本上会在所有图像中看到转换后的平均向量W*mean_image。如果这在数量上占主导地位，那么由于四舍五入的影响，图片看起来都一样。但是，如果您计算图像之间的差异，则它们不是。

在代码中，你可以看到所有这些

combined_data = np.array(puppies_vectors).T
my_zca_transformer_image_stuff = zca_whitening_matrix(combined_data)
mean_image = np.mean(combined_data,axis=1)
without_mean = (combined_data-mean_image[:,None])
xZCAMatrix = np.dot(my_zca_transformer_image_stuff, without_mean)
reshaped_pics = [xZCAMatrix[:,i].reshape(new_size,new_size) for i in range(4)]
for i in reshaped_pics:
    plt.imshow(i, cmap='gray')
    plt.show() # Should look good now
## What you essential saw is this transformed mean image
i = np.dot(my_zca_transformer_image_stuff, mean_image).reshape(new_size,new_size)
plt.imshow(i, cmap='gray')
plt.show()