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I like quadric :

int main( int argc, char** argv )
{
    Mat z    = imread("1449862093156643.jpg",CV_LOAD_IMAGE_GRAYSCALE);

    Mat M = Mat_<double>(z.rows*z.cols,6);
    Mat I=Mat_<double>(z.rows*z.cols,1);
    for (int i=0;i<z.rows;i++)
        for (int j = 0; j < z.cols; j++)
        {
            double x=(j - z.cols / 2) / double(z.cols),y= (i - z.rows / 2) / double(z.rows);
            M.at<double>(i*z.cols+j, 0) = x*x;
            M.at<double>(i*z.cols+j, 1) = y*y;
            M.at<double>(i*z.cols+j, 2) = x*y;
            M.at<double>(i*z.cols+j, 3) = x;
            M.at<double>(i*z.cols+j, 4) = y;
            M.at<double>(i*z.cols+j, 5) = 1;
            I.at<double>(i*z.cols+j, 0) = z.at<uchar>(i,j);
        }
    SVD s(M);
    Mat q;
    s.backSubst(I,q);
    cout<<q;
    imshow("Orignal",z);
    cout<<q.at<double>(2,0);
    Mat background(z.rows,z.cols,CV_8UC1);
    for (int i=0;i<z.rows;i++)
        for (int j = 0; j < z.cols; j++)
        {
            double x=(j - z.cols / 2) / double(z.cols),y= (i - z.rows / 2) / double(z.rows);
            double quad=q.at<double>(0,0)*x*x+q.at<double>(1,0)*y*y+q.at<double>(2,0)*x*y;
            quad+=q.at<double>(3,0)*x+q.at<double>(4,0)*y+q.at<double>(5,0);
            background.at<uchar>(i,j) = saturate_cast<uchar>(quad);
        }
    imshow("Simulated background",background);
    Mat diff;
    absdiff(background,z,diff);
    double mind,maxd;
    minMaxLoc(diff,&mind,&maxd);
    imshow("background_original",diff*(256/(maxd-mind)));


    waitKey();
    return 0;
}

results are simulated background

and difference bakground original is

With last image you can make hypothesis that bias is due camera gain...