How to resize a background imagem in the QGraphicsScene?

How can I resize the background image to fit in the scene background?

The image is shown out of the scene.

mainview.cpp

Code:

MainView::MainView(QGraphicsView *parent)
    : QGraphicsView(parent)
{
    view = new QGraphicsView();
    scene = new QGraphicsScene(0,0,QApplication::desktop()->width(),QApplication::desktop()->height());
 
    image = new QImage("C:/fundo_01.png");
    QImage lampada_on, lampada_off, lampada_on2, lampada_off2;
    lampada_on.load("C:/lampada_on.png");
    lampada_off.load("C:/lampada_off.png");
    lampada_on2.load("C:/lampada_on2.png");
    lampada_off2.load("C:/lampada_off2.png");
 
 
    QAbstractGraphicsShapeItem* i = new Icon(lampada_on2, lampada_off2);
    QAbstractGraphicsShapeItem* j = new Icon(lampada_on, lampada_off);
    scene->addItem(i);
    scene->addItem(j);
 
    setScene(scene);
 
    setVerticalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
    setHorizontalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
}
 
void MainView::resizeEvent(QResizeEvent *event)
{
    QGraphicsView::resizeEvent(event);
    fitInView(QRectF(0,0,scene->width(),scene->height()), Qt::IgnoreAspectRatio);
}
 
void MainView::drawBackground(QPainter *painter, const QRectF &rect)
{
    painter->setRenderHint(QPainter::SmoothPixmapTransform);
    QRectF r;
 
    r.setRect(0,0,image->width(),image->height());
    painter->drawImage(r,*image);
}

mainview.h

Code:

class MainView : public QGraphicsView
{
    Q_OBJECT
public:
    MainView(QGraphicsView *parent=0);
    ~MainView() {};
 
private:
    QGraphicsView *view;
    QGraphicsScene *scene;
    QImage *image;//, *lampada_on, *lampada_off, *lampada_on2, *lampada_off2;
 
protected:
    void resizeEvent(QResizeEvent *event);
    void drawBackground(QPainter *painter, const QRectF &rect);
};