OpenCV: Matrix multiplication with a matrix containing Vec3d and a matrix containing doubles

Question

I am using OpenCV for some time and now I hit the point where I need a multiplication of this type:

Define a matrix T, which contains elements of the type Vec3d¹ . Matrix T has the size: M X N. Matrix T has to be multiplied with a Vector Phi, which has the size: N X 1, containing doubles as values. Each element of the result has to be the result of a matrix multiplication of both matrices.

I don't want to do a component-wise multiplication, but a "real" matrix multiplication, e.g. multiplying the first element of T² with the first element of matrix J, then multiplying the second element of matrix T³ with the second element of matrix J. Do this until you completed the first row of T and then sum up the results. The result is a M X 1.

For example, if T would be a 3 X 2 matrix and Phi a 2 X 1 matrix, then the calculation should be T_11 * phi_11 + T_12 * phi_21 for the first value of the result. Currently I'm using two for loops which are slow:

for (int i = 0; i<M; ++i){
    cv::Mat summedResult = cv::Mat(3, 1, CV_64F, double(0));
    for (uint32 j = 0; j<N; ++j){
        summedResult = summedResult + 
        (cv::Mat(mMatrixT.at<cv::Vec3d>(i, j)) * mMatrixPhi.at<double>(j));
    }
    // The result matrix contains values of type Vec3d again
    mResultMatrix.at<cv::Vec3d>(i) = cv::Vec3d(summedResult);
}

More generally: Is it possible to efficiently multiply matrices containing Vec3ds and doubles in OpenCV?

^{1. three dimensional vector containing doubles.}

^{2. coordinate: 1,1}

^{3. coordinate: 1,2}

Don't try to "help" the compiler, mMatrixT.at(i, j) is just fine (i.e., do not explicitly give the template parameter if it has already been deduced) — Brandlingo
Your matrix T seems to have the size MxNx3. Then you want to multiply this T with the vector phi of size Nx1. But in the next sentence you state that there is a matrix matrix multiplication involved. But there are no two matrices. (Except matrix J which appears out of nowhere) Please elaborate. Btw "real" matrix multiplication involving two 2D matrices with fitting dimensions can be done simply by using A * B. — Brandlingo
Thank you, this seems to reduce a lot of allocations, but it still does not hit a suitable performance. A good improvement though :). — Thomas Kosch
@MatthäusBrandl You're right, I was mixing matrix J and Phi. In this case matrix J and matrix Phi are both the same. I know that two matrices containing double values can be simply multiplied using the star operator. Now I have a matrix T containing vec3d values and a matrix Phi which contains regular double values. Now I want to multiply the vectors from T with the scalar values from Phi, so that the resulting vectors from each multiplication sum up with each row of matrix T. Sorry for confusing you mixing up matrices. — Thomas Kosch
what should be the result? what's the matrix multiplication of a 1xn matrix of Vec3d with a nx1 matrix of type double? should that be the sum of double_i * Vec3d_i? I don't think you can use matrix multiplication directly there because 3-channeled matrices aren't defined mathematically for matrix multiplication with single channel matrices. — Micka

Micka Micka · Accepted Answer · 2015-10-02T14:09:46

I still don't know what kind of result you expect, but maybe try this:

Assuming that you have a MxN matrix of Vec3d and a Nx1 Matrix of type double, your result will be a Mx1 matrix of type Vec3d:

for (int i = 0; i<M; ++i)
    {
        cv::Vec3d summedResult; // here this must be a Vec3d instead of a matrix, if I assume the right result expection
        for (uint32 j = 0; j<N; ++j)
        {
            summedResult = summedResult + (mMatrixT.at<cv::Vec3d>(i, j) * mMatrixPhi.at<double>(j));
        }
        // The result matrix contains values of type Vec3d again
        mResultMatrix.at<cv::Vec3d>(i) = summedResult;
    }

EDIT:

ah sorry, didnt read to the end that your provided code works but is too slow... well, I expect that there is no optimization for that because mathematically this isnt defined. What you can do is to convert your Vec3d mat to a Mx(3*N) matrix and convert your Nx1 mat to a (3*N)x1 mat (3 times the same value before the next value) and use the OpenCV matrix product directly. But probably that's not faster because of the 3* bigger size of both matrices ;)

EDIT: will be a different result, since each element will be the sum of the Vec3d elements...

OpenCV: Matrix multiplication with a matrix containing Vec3d and a matrix containing doubles

1 Answers