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you just need to know which rows you want to remove and then you can just use the removeRow() function below:

void removeRow(InputOutputArray _matIn, int row, int method = METHOD::CV_RECT)
{
    CV_Assert( row >= 0 && row < _matIn.getMat().rows );

    Mat matIn = _matIn.getMat();
    cv::Size size = matIn.size();
    Mat matOut( matIn.rows - 1, matIn.cols, matIn.type());

    if ( row > 0 )
    {
        cv::Rect rect( 0, 0, size.width, row );
        matIn( rect ).copyTo( matOut( rect ) );
    }

    if ( row < size.height - 1 )
    {
        cv::Rect rect1( 0, row + 1, size.width, size.height - row - 1 );
        cv::Rect rect2( 0, row, size.width, size.height - row - 1 );
        matIn( rect1 ).copyTo( matOut( rect2 ) );
    }
    matOut.copyTo(_matIn);
}


int main()
{
    // Example case
    Mat mat = (Mat_<uchar>(5, 5) << 1, 2, 3, 4, 0,
                                  0, 0, 0, 0, 0,
                                  12, 13, 14, 15, 16,
                                  0, 0, 0, 0, 0,
                                  0, 0, 0, 8, 0);

    cout << "mat: " << endl << mat << endl;

    // Find all non zero rows and set in a vector as indexes
    Mat nonZeroCoordinates;
    findNonZero(mat, nonZeroCoordinates);

    vector<int> nonZeroRows;

    for(size_t i = 0; i < nonZeroCoordinates.rows; ++i)
    {
        int row = nonZeroCoordinates.at<Point>(i).y;
        if(!(std::find(nonZeroRows.begin(), nonZeroRows.end(), row) != nonZeroRows.end()))
        {
            //elem does not exists in the vector
            nonZeroRows.push_back(row);
        }
    }

    // Create a zeros rows indexer, according to the non zero indexes
    vector<int> zeroRows(mat.cols);
    std::iota(zeroRows.begin(), zeroRows.end(), 0);

    std::sort(nonZeroRows.begin(), nonZeroRows.end());

    for(int i = nonZeroRows.size() - 1; i >= 0; i--)
        zeroRows.erase( std::next( zeroRows.begin(), nonZeroRows[i] ) );

    // remove rows
    for(int i = 0; i < zeroRows.size(); ++i)
    {
        removeRow(mat, zeroRows[i]);
        // decrease index values since the form of the mat changes
        transform(zeroRows.begin(), zeroRows.end(), zeroRows.begin(), bind2nd(std::minus<int>(), 1));
    }

    cout << endl << "removedRowsMat: " << endl << mat << endl;

return 0;
}