图像变换 2: 小波变换（Python）

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1. pyWavelets小波工具包安装：

pip install PyWavelets -i https://pypi.douban.com/simple  --default-timeout=1000

pyWavelets工具包的安装及使用
pyWavelets参考资料

2. pyWavelets例子

二维Haar小波

import cv2
import pywt
import numpy as np
import matplotlib.pyplot as plt

img_gray = cv2.imread("baboon.bmp", cv2.IMREAD_GRAYSCALE).astype(np.float32)

cA_l1, (cH_l1, cV_l1, cD_l1) = pywt.dwt2(img_gray, 'haar')
cA_l2, (cH_l2, cV_l2, cD_l2) = pywt.dwt2(cA_l1, 'haar')


# 将各个子图进行拼接，最后得到一张图
AH_l2 = np.concatenate([cA_l2, cH_l2], axis=1)
VD_l2 = np.concatenate([cV_l2, cD_l2], axis=1)
img_wt_l1 = np.concatenate([AH_l2, VD_l2], axis=0)

AH_l1 = np.concatenate([img_wt_l1, cH_l1], axis=1)
VD_l1 = np.concatenate([cV_l1, cD_l1], axis=1)
img_wt = np.concatenate([AH_l1, VD_l1], axis=0)

print(cV_l1)
cV_l1[:, :] = 0
VD_l1 = np.concatenate([cV_l1, cD_l1], axis=1)
img_wt_marked = np.concatenate([AH_l1, VD_l1], axis=0)
img_marked = pywt.idwt2((cA_l1, (cH_l1, cV_l1, cD_l1)), 'haar')

plt.figure('二维Haar小波L2')
plt.subplot(221), plt.imshow(img_gray, cmap='gray'), plt.title('Cover'), plt.axis('off')
plt.subplot(222), plt.imshow(img_wt, cmap='gray'), plt.title('Cover Haar L2'), plt.axis('off')
plt.subplot(223), plt.imshow(img_wt_marked, cmap='gray'), plt.title('Haar cV_l1 = 0'), plt.axis('off')
plt.subplot(224), plt.imshow(img_marked, cmap='gray'), plt.title('Modified'), plt.axis('off'), plt.axis('off')
plt.tight_layout()
plt.show()

3. 基于DWT的水印

This is only a demo.

基于DWT的水印

import cv2
import pywt
import numpy as np 
import matplotlib.pyplot as plt 
import random

 
def dwt_embed(img_gray, img_watermark, seed=2020):
    "An illustration of how data are embedded in pair-wise DCT coefficients,"
    " img_gray - of grayscale"
    " img_watermark - the to be embedded msg composed of 0 and 1 only"
    " seed - the encryption password"
    
    if len(img_gray.shape) > 2 or len(img_watermark.shape) > 2:
        print("Parameter img should be of grayscale")
        return img_gray
    
    # Step 1: DWT in level 2 Haar coefficients cH_l2 and cV_l2
    cA_l1, (cH_l1, cV_l1, cD_l1) = pywt.dwt2(img_gray.astype(np.float32), 'haar')
    cA_l2, (cH_l2, cV_l2, cD_l2) = pywt.dwt2(cA_l1, 'haar')
    
    # Step 2: Embed
    height, width = img_gray.shape
    img_watermark = cv2.resize(img_watermark, (width>>2, height>>2))
    img_watermark = img_watermark.astype(np.float32)
    
    # change 0 to -1
    # img_watermark[img_watermark<1] = -1
    alpha = 3 # The strength of watermark
    cH_l2 = alpha*img_watermark
    cV_l2 = alpha*img_watermark

    # Step 3: IDWT
    cA_l1 = pywt.idwt2((cA_l2, (cH_l2, cV_l2, cD_l2)), 'haar')
    img_marked = pywt.idwt2((cA_l1, (cH_l1, cV_l1, cD_l1)), 'haar')
    
    return img_marked.astype(np.uint8)

# Non-blind detection, requires the original watermark
def dwt_extract(img_marked, img_watermark, seed=2020):
    "An illustration of data extraction to the previous embedding,"
    " img_marked - of grayscale"
    " img_watermark - Non-blind detection, requires the original watermark"
    " seed - the password for decryption"
    
    if len(img_marked.shape) > 2:
        print("Parameter img should be of grayscale")
        return img_marked
    
    # Step 1: DWT in level 2 Haar coefficients cH_l2 and cV_l2
    cA_l1, (cH_l1, cV_l1, cD_l1) = pywt.dwt2(img_marked.astype(np.float32), 'haar')
    cA_l2, (cH_l2, cV_l2, cD_l2) = pywt.dwt2(cA_l1, 'haar')
    
    # Step 2: Extract
    height, width = img_marked.shape
    img_watermark = cv2.resize(img_watermark, (width>>2, height>>2))
    img_watermark = img_watermark.astype(np.float32)
    # img_watermark[img_watermark<1] = -1
    alpha = 3
    img_watermark_extracted = cH_l2*img_watermark + cV_l2*img_watermark
    img_watermark_extracted = 255*img_watermark_extracted/np.max(img_watermark_extracted)
    img_watermark_extracted[img_watermark_extracted<alpha] = 0
    img_watermark_extracted[img_watermark_extracted>=alpha] = 255
    return img_watermark_extracted.astype(np.uint8)


if __name__ == '__main__':

    img_gray = cv2.imread('./baboon.bmp', cv2.IMREAD_GRAYSCALE)
    
    img_watermark = cv2.imread('./lenna.bmp', cv2.IMREAD_GRAYSCALE)
    _, img_watermark = cv2.threshold(img_watermark, 0, 1, cv2.THRESH_BINARY + cv2.THRESH_OTSU)
    img_marked = dwt_embed(img_gray, img_watermark, 20200417)

    cv2.imwrite('baboon_marked.png', img_marked)


    # print(img_marked.shape, type(img_marked), type(img_marked[0,0]))
    img_stego = cv2.imread('baboon_marked.png', cv2.IMREAD_GRAYSCALE)
    img_watermark = cv2.imread('./lenna.bmp', cv2.IMREAD_GRAYSCALE)
    _, img_watermark = cv2.threshold(img_watermark, 0, 1, cv2.THRESH_BINARY + cv2.THRESH_OTSU)
    img_watermark_extracted = dwt_extract(img_stego, img_watermark, 20200417)

    plt.figure(figsize=(4,3))
    plt.subplot(221), plt.imshow(img_gray, cmap='gray'), plt.title('Cover'), plt.axis('off')
    plt.subplot(222), plt.imshow(img_marked, cmap='gray'), plt.title('Marked'), plt.axis('off')
    plt.subplot(223), plt.imshow(img_watermark, cmap='gray'), plt.title('Watermark'), plt.axis('off')
    plt.subplot(224), plt.imshow(img_watermark_extracted, cmap='hot'), plt.title('Watermark Extracted'), plt.axis('off')
    plt.tight_layout()
    plt.show()

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