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opencv and numpy matrix multiplication vs element-wise multiplication

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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

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 !!!

code

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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;
}

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

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]])

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

>>> 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]])

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

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

History

  • 20190109: created.