I managed it to create a JPanel with a special picture as Background and put this JPanel in a JFrame. Everytime a resize the JFrame the JPanel and the picture in it with be also resized. The ComponentListener is registered to the JFrame which notifies modifications in its size.
Here's the code:
package examples;
import images.MyImage;
import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.RenderingHints;
import java.awt.event.ComponentAdapter;
import java.awt.event.ComponentEvent;
import javax.swing.BorderFactory;
import javax.swing.JFrame;
import javax.swing.JPanel;
public class example3 {
    private static JPanel panel = new MyPanel();
    private static JFrame frame = new JFrame();
    private static class MyPanel extends JPanel {
        private static final long serialVersionUID = 1L;
        private int width = 0;
        private int height = 0;
        public static final int DEFAULT_WIDTH = 400;
        public static final int DEFAULT_HEIGHT = 100;
        public MyPanel(int width, int heigth) {
            super.setLayout(new BorderLayout());
            setWidth(width);
            setHeigth(heigth);
        }
        public MyPanel() {
            super.setLayout(new BorderLayout());
            setWidth(DEFAULT_WIDTH);
            setHeigth(DEFAULT_HEIGHT);
        }
        @Override
        protected void paintComponent(Graphics g) {
            super.paintComponent(g);
            Graphics2D g2d = (Graphics2D) g;
            g2d.setRenderingHint(RenderingHints.KEY_INTERPOLATION,
                    RenderingHints.VALUE_INTERPOLATION_BILINEAR);
            g2d.setRenderingHint(RenderingHints.KEY_RENDERING,
                    RenderingHints.VALUE_RENDER_SPEED);
            g2d.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                    RenderingHints.VALUE_ANTIALIAS_ON);
            g2d.drawImage(MyImage.IMAGE_BLUE_BLACKGROUND, 0, 0,
                    getMyPanelWidth(), getMyPanelHeight(), null);
            g2d.dispose();
        }
        @Override
        public Dimension preferredSize() {
            return new Dimension(getMyPanelWidth(), getMyPanelHeight());
        }
        private void setWidth(int width) {
            this.width = width;
        }
        private void setHeigth(int height) {
            this.height = height;
        }
        private int getMyPanelHeight() {
            return height;
        }
        private int getMyPanelWidth() {
            return width;
        }
    }
    private static class ComponentHandler extends ComponentAdapter{
        @Override
        public void componentResized(ComponentEvent e) {
            super.componentResized(e);
            frame.remove(panel);
            frame.getContentPane().add(
                    new MyPanel(frame.getSize().width, frame.getSize().height),
                    BorderLayout.CENTER);
            frame.repaint();
            frame.revalidate();
        }
    }
    public static void main(String[] args) {
        panel.setBorder(BorderFactory.createLineBorder(Color.BLACK));
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.setLayout(new BorderLayout());
        frame.add(panel);
        frame.addComponentListener(new ComponentHandler());
        frame.pack();
        frame.setVisible(true);
    }
}
The problem is that I'm getting scaling errors:
 
Is it because the Event Dispatch Thread can not handle all the resize-Events which is fired by the resize-method? Is there any satisfying solution?