使用opencv和numpy實現矩陣相乘和按元素相乘 matrix multiplication vs element-wise multiplication

本文首發於我的博客kezunlin.me/post/1e37a6…，歡迎閱讀最新內容！

opencv and numpy matrix multiplication vs element-wise multiplication

Guide

opencv

Matrix multiplication is where two matrices are multiplied directly. This operation multiplies matrix A of size [a x b] with matrix B of size [b x c] to produce matrix C of size [a x c].

In OpenCV it is achieved using the simple * operator:

C = A * B  // Aab * Bbc = Cac
複製代碼

Element-wise multiplication is where each pixel in the output matrix is formed by multiplying that pixel in matrix A by its corresponding entry in matrix B. The input matrices should be the same size, and the output will be the same size as well. This is achieved using the mul() function:

output = A.mul(B); // A B must have same size !!!
複製代碼

code

cv::Mat cv_matmul(const cv::Mat& A, const cv::Mat& B)
{
    // matrix multipication    m*k,  k*n ===> m*n
    cv::Mat C = A * B; 
    return C; 
}

cv::Mat cv_mul(const cv::Mat& image, const cv::Mat& mask)
{
    // element-wise multiplication  output[i,j] = image[i,j] * mask[i,j]
    cv::Mat output = image.mul(mask, 1.0); // m*n,  m*n
    return output;
}

cv::Mat cv_multiply3x1(const cv::Mat& mat3, const cv::Mat& mat1)
{
    std::vector<cv::Mat> channels;
    cv::split(mat3, channels);

    std::vector<cv::Mat> result_channels;
    for(int i = 0; i < channels.size(); i++)
    {
        result_channels.push_back(channels[i].mul(mat1));
    }

    cv::Mat result3;
    cv::merge(result_channels, result3);
    return result3;
}

cv::Mat cv_multiply3x3(const cv::Mat& mat3_a, const cv::Mat& mat3_b)
{
    cv::Mat a;
    cv::Mat b;
    cv::Mat c;

    std::vector<cv::Mat> a_channels;
    std::vector<cv::Mat> b_channels;
    std::vector<cv::Mat> c_channels;

    cv::split(mat3_a, a_channels);
    cv::split(mat3_b, b_channels);

    for(int i = 0; i < a_channels.size() || b_channels.size(); i++)
    {
        c_channels.push_back(a_channels[i].mul(b_channels[i]));
    }

    cv::merge(c_channels, c);
    return c;
}複製代碼

numpy

numpy arrays are not matrices, and the standard operations *, +, -, / work element-wise on arrays.

Instead, you could try using numpy.matrix, and * will be treated like matrix multiplication.

code

Element-wise multiplication code

>>> img = np.array([1,2,3,4,5,6,7,8]).reshape(2,4)
    >>> mask = np.array([1,1,1,1,0,0,0,0]).reshape(2,4)
    >>> img * mask 
    array([[1, 2, 3, 4],
           [0, 0, 0, 0]])
    >>> 
    >>> np.multiply(img, mask)
    array([[1, 2, 3, 4],
           [0, 0, 0, 0]])
> for `numpy.array`, `*`and `multiply` work element-wise  
 複製代碼

matrix multiplication code

>>> a = np.array([1,2,3,4,5,6,7,8]).reshape(2,4)
    >>> b = np.array([1,1,1,1,0,0,0,0]).reshape(4,2)
    >>> np.matmul(a,b)
    array([[ 3,  3],
           [11, 11]])複製代碼

>>> np.dot(a,b)
    array([[ 3,  3],
           [11, 11]])複製代碼

>>> a = np.matrix([1,2,3,4,5,6,7,8]).reshape(2,4)
    >>> b = np.matrix([1,1,1,1,0,0,0,0]).reshape(4,2)
    >>> a
    matrix([[1, 2, 3, 4],
            [5, 6, 7, 8]])
    >>> b
    matrix([[1, 1],
            [1, 1],
            [0, 0],
            [0, 0]])
    >>> a*b
    matrix([[ 3,  3],
            [11, 11]])複製代碼

>>> np.matmul(a,b)
    matrix([[ 3,  3],
            [11, 11]])複製代碼

for 2-dim, np.dot equals np.matmul

for numpy.array, np.matmul means matrix multiplication;

for numpy.matrix, * and np.matmul means matrix multiplication;

Reference

• matrix-multiplication-in-opencv
• cvmat-element-matrix-multiplication

History

• 20190109: created.

Copyright

• Post author: kezunlin
• Post link: kezunlin.me/post/4bc343…
• Copyright Notice: All articles in this blog are licensed under CC BY-NC-SA 3.0 unless stating additionally.