def SVD_embed(im, wm, strength, blk_size): U, S, V = block_SVD(im, blk_size) S_new = embed(S, wm, strength) im_wm = block_ISVD(U, S_new, V, blk_size) return im_wm def SVD_extract(im_wm, im, strength, block_size): _, S, _ = block_SVD(im, block_size) _, S_wm, _ = block_SVD(im_wm, block_size) tmp = S_wm - S wm_ex = np.empty_like(tmp, dtype=int) for i in range(tmp.shape[0]): for j in range(tmp.shape[1]): wm_ex[i, j] = np.sum(tmp[i, j]) wm_ex = wm_ex / block_size[0] / strength return wm_ex def embed(S, wm, strength): wm = wm.flatten() row, col = S.shape S = S.flatten() for i in range(S.size): S[i] = S[i] + strength * wm[i] S = S.reshape(row, col) return S这段代码什么意思
时间: 2023-12-04 12:06:27 浏览: 32
这段代码实现了基于SVD的数字水印嵌入和提取算法。具体来说,它包括以下两个函数:
- SVD_embed(im, wm, strength, blk_size): 该函数输入原始图像im,数字水印wm,嵌入强度strength和块大小blk_size,输出嵌入数字水印后的图像im_wm。
- SVD_extract(im_wm, im, strength, block_size): 该函数输入嵌有数字水印的图像im_wm,原始图像im,嵌入强度strength和块大小block_size,输出提取出的数字水印wm_ex。
具体来说,SVD_embed函数首先将原始图像im分成大小为blk_size的块,对每个块进行SVD分解,并将数字水印嵌入到分解后的S矩阵中。然后通过逆SVD变换,将嵌有数字水印的块合并成嵌入数字水印后的图像im_wm。
SVD_extract函数则是将原始图像im和嵌有数字水印的图像im_wm都分成大小为block_size的块,对每个块进行SVD分解,计算出嵌有数字水印的块和原始块的S矩阵之差,并将差值除以块大小和嵌入强度得到数字水印。最后将数字水印wm_ex返回。
相关问题
def block_SVD(M, blk_size): row_block = M.shape[0] // blk_size[0] col_block = M.shape[1] // blk_size[1] U = np.empty((row_block, col_block), dtype=object) S = np.empty((row_block, col_block), dtype=object) V = np.empty((row_block, col_block), dtype=object) M = M[:M.shape[0] - M.shape[0] % blk_size[0], :M.shape[1] - M.shape[1] % blk_size[1]] rows = [] for i in range(0, M.shape[0], blk_size[0]): cols = [] for j in range(0, M.shape[1], blk_size[1]): max_ndx = (min(i + blk_size[0], M.shape[0]), min(j + blk_size[1], M.shape[1])) u, s, v = np.linalg.svd(M[i:max_ndx[0], j:max_ndx[1]]) U[i // blk_size[0], j // blk_size[1]] = u S[i // blk_size[0], j // blk_size[1]] = s V[i // blk_size[0], j // blk_size[1]] = v return U, S, V def block_ISVD(U, S, V, blk_size): row_U, col_U = U.shape U = U.flatten() S = S.flatten() V = V.flatten() im_tmp = np.empty_like(U) im_wm = np.empty((row_U*blk_size[0],col_U*blk_size[1])) for i in range(U.size): tmp = np.matmul(U[i],np.diag(S[i])) im_tmp[i] = np.matmul(tmp,V[i]) im_tmp = im_tmp.reshape(row_U, col_U) for i in range(row_U): for j in range(col_U): im_wm[i*blk_size[0]:(i+1)*blk_size[0], j*blk_size[1]:(j+1)*blk_size[1]] = im_tmp[i,j] return im_wm 这段代码什么意思
这段代码实现了基于块的 SVD(奇异值分解)和逆 SVD 操作。具体地,它分为两个函数:
1. block_SVD(M, blk_size):输入一个矩阵 M 和一个块大小 blk_size,输出 M 的基于块的 SVD 分解结果,包括 U、S、V 三个矩阵。其中 U 和 V 是正交矩阵,S 是对角线上的奇异值向量。
2. block_ISVD(U, S, V, blk_size):输入基于块的 SVD 分解结果 U、S、V 和块大小 blk_size,输出原始矩阵 M。这个函数实际上是对 U、S、V 分别进行逆 SVD 操作,然后将结果拼接成原始矩阵 M。
整个过程中,矩阵 M 被分成多个大小为 blk_size 的块,每个块分别进行 SVD 分解和逆 SVD 操作,最终得到整个矩阵的 SVD 分解结果和原始矩阵。这种基于块的 SVD 分解和逆 SVD 操作可以在处理大型矩阵时提高计算效率,并且适用于分布式计算环境。
cv::SVD::V_T
cv::SVD::V_T is a member function of the cv::SVD class in OpenCV library. It returns the transpose of the matrix of right singular vectors of the input matrix. The right singular vectors are the eigenvectors of the transpose of the input matrix multiplied by the input matrix. The transpose of the right singular vectors matrix is also known as the matrix of left singular vectors.
In other words, if we have a matrix A, and we perform the Singular Value Decomposition (SVD) on it: A=U*S*V_T, then cv::SVD::V_T returns the matrix of right singular vectors V_T.
Syntax:
cv::Mat cv::SVD::V_T
Returns:
A cv::Mat object representing the transpose of the matrix of right singular vectors of the input matrix.
Example:
```
cv::Mat A = (cv::Mat_<double>(3,3) << 1, 2, 3, 4, 5, 6, 7, 8, 9);
cv::SVD svd(A);
cv::Mat V_T = svd.vt;
```
This code snippet calculates the SVD of a 3x3 matrix A and returns the transpose of the right singular vectors matrix in V_T.
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