Combine two affine Transformations Matrices in OpenCV

Question

I have two 2x3 Matrices A and B - each one is for affine Transformation. I need to combine A and B into a thrid Matrix C which will combine the affine transformation from A and B into one Matrix.

How do I need to multiply them?

AB or BA ?

The difference is that either A or B gets transposed or does it make any difference at all?

I read a further solution is to use 3x3 matrices and copy into the first two rows and only use the first two rows in the result. But it comes down to the same question if it is AB or BA.

Furthermore, is there an easy way to implement this in OpenCV or do I need to implement every step as described above?

Answer 1

The following function combines this two matrices:

  Mat AffineTransform::concatenateMatrix(Mat first, Mat second){

        Mat mul1 = Mat::eye(3, 3, CV_64F);
        Mat mul2 = Mat::eye(3, 3, CV_64F);
        Mat x_;
        Mat temp_inv_;
        Mat mul_r;
        first.convertTo(temp_inv_, CV_64F);
        second.convertTo(x_, CV_64F);

        temp_inv_.row(0).copyTo(mul1.row(0));
        temp_inv_.row(1).copyTo(mul1.row(1));

        x_.row(1).copyTo(mul2.row(1));
        x_.row(0).copyTo(mul2.row(0));

        try{
            mul_r = mul1*mul2;
        }
        catch (Exception& e){
            const char* err_msg = e.what();
            cout << err_msg;
        }

        mul1.release();
        mul2.release();
        temp_inv_.release();

        return mul_r;
}