I would like to have a background image in my QGraphicsView that is always scaled (and cropped if necessary) to the size of the viewport, without scrollbars and without scrolling with the keyboard and mouse. The example below is what I am doing to scale and crop an image in the viewport, but I am using random values for the cropping that are pulled out of the aether. I would like a logical solution?

MainWindow::MainWindow(QWidget *parent) :
    QMainWindow(parent),
    ui(new Ui::MainWindow)
{

    ui->setupUi(this);
    scene = new QGraphicsScene(this);

    ui->graphicsView->resize(800, 427); 
    // MainWindow is 800x480, GraphicsView is 800x427. I want an image that
    // is the size of the graphicsView.

    ui->graphicsView->setHorizontalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
    ui->graphicsView->setVerticalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
    // the graphicsView still scrolls if the image is too large, but 
    // displays no scrollbars. I would like it not to scroll (I want to 
    // add a scrolling widget into the QGraphicsScene later, on top of
    // the background image.)


    QPixmap *backgroundPixmap = new QPixmap(":/Valentino_Bar_Prague.jpg");
    QPixmap sized = backgroundPixmap->scaled(
            QSize(ui->graphicsView->width(), 
                  ui->graphicsView->height()),
            Qt::KeepAspectRatioByExpanding); // This scales the image too tall

    QImage sizedImage = QImage(sized.toImage());
    QImage sizedCroppedImage = QImage(sizedImage.copy(0,0,
       (ui->graphicsView->width() - 1.5),
       (ui->graphicsView->height() + 19))); 
    // so I try to crop using copy(), and I have to use these values
    // and I am unsure why.

    QGraphicsPixmapItem *sizedBackground = scene->addPixmap(
        QPixmap::fromImage(sizedCroppedImage));
    sizedBackground->setZValue(1);
    ui->graphicsView->setScene(this->scene);
}

I would like to know a way to scale and crop an image to the size of the QGraphicsView that will work even when I resize the QGraphicsView. Where are the 1.5 and 19 coming from?