Downscaling an image for grabCut

edit

I've an input image (around 24 MP). Feeding such a large image to grabCut in OpenCV is time consuming, so first I want to downscale the image then I want to upscale the mask. So, in grabCut function I'm downscaling the image as follows:

//Downsampling
    double c_ratio = 0.0;
    double r_ratio = 0.0;
    double ratio = 0.0;
    bool donwSampled = false;
    if (img.cols > 800 || img.rows > 600){
        c_ratio = img.cols/800.0;
        r_ratio = img.rows/600.0;
        ratio = (c_ratio > r_ratio)?r_ratio:c_ratio;
        printf("downscaled by: %f\n", ratio);
        fflush(stdout);
        resize( img, img, Size( img.cols/ratio, img.rows/ratio ),0,0,INTER_LANCZOS4);
        resize( mask, mask, Size( mask.cols/ratio, mask.rows/ratio ),0,0,INTER_LANCZOS4);
        donwSampled = true;
    }

And the end of this function I'm upscaling as follows:

//Upsampling
if(donwSampled){
    resize( img, img, Size( img.cols*ratio, img.rows*ratio ));
    resize( mask, mask, Size( mask.cols*ratio, mask.rows*ratio ));
}

The input mask is as follows:

The output is this:

As one can see in the output image the little area around the brush are marked wrong both in foreground and background selection.