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

The image is shown out of the scene.


mainview.cpp
Qt Code: 
  1. MainView::MainView(QGraphicsView *parent)
  2.     : QGraphicsView(parent)
  3. {
  4.     view = new QGraphicsView();
  5.     scene = new QGraphicsScene(0,0,QApplication::desktop()->width(),QApplication::desktop()->height());
  6.  
  7.     image = new QImage("C:/fundo_01.png");
  8.     QImage lampada_on, lampada_off, lampada_on2, lampada_off2;
  9.     lampada_on.load("C:/lampada_on.png");
  10.     lampada_off.load("C:/lampada_off.png");
  11.     lampada_on2.load("C:/lampada_on2.png");
  12.     lampada_off2.load("C:/lampada_off2.png");
  13.  
  14.  
  15.     QAbstractGraphicsShapeItem* i = new Icon(lampada_on2, lampada_off2);
  16.     QAbstractGraphicsShapeItem* j = new Icon(lampada_on, lampada_off);
  17.     scene->addItem(i);
  18.     scene->addItem(j);
  19.  
  20.     setScene(scene);
  21.  
  22.     setVerticalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
  23.     setHorizontalScrollBarPolicy(Qt::ScrollBarAlwaysOff);
  24. }
  25.  
  26. void MainView::resizeEvent(QResizeEvent *event)
  27. {
  28.     QGraphicsView::resizeEvent(event);
  29.     fitInView(QRectF(0,0,scene->width(),scene->height()), Qt::IgnoreAspectRatio);
  30. }
  31.  
  32. void MainView::drawBackground(QPainter *painter, const QRectF &rect)
  33. {
  34.     painter->setRenderHint(QPainter::SmoothPixmapTransform);
  35.     QRectF r;
  36.  
  37.     r.setRect(0,0,image->width(),image->height());
  38.     painter->drawImage(r,*image);
  39. }
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mainview.h
Qt Code: 
  1. class MainView : public QGraphicsView
  2. {
  3.     Q_OBJECT
  4. public:
  5.     MainView(QGraphicsView *parent=0);
  6.     ~MainView() {};
  7.  
  8. private:
  11.     QImage *image;//, *lampada_on, *lampada_off, *lampada_on2, *lampada_off2;
  12.  
  13. protected:
  14.     void resizeEvent(QResizeEvent *event);
  15.     void drawBackground(QPainter *painter, const QRectF &rect);
  16. };
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