How to Correctly Overlay Text onto a BufferedImage using Java\'s Graphics2D?

import java.awt.Color;
import java.awt.Dimension;
import java.awt.Font;
import java.awt.FontMetrics;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.image.BufferedImage;
import java.io.IOException;
import java.net.URL;
import javax.imageio.ImageIO;
import javax.swing.JFrame;
import javax.swing.JPanel;

public class TextOverlay extends JPanel {

    private BufferedImage image;

    public TextOverlay() {
        try {
            image = ImageIO.read(new URL(
                "http://cdn.sstatic.net/stackexchange/img/logos/so/so-logo.png"));
        } catch (IOException e) {
            e.printStackTrace();
        }
        image = process(image);
    }

    @Override
    public Dimension getPreferredSize() {
        return new Dimension(image.getWidth(), image.getHeight());
    }

    private BufferedImage process(BufferedImage old) {
        int w = old.getWidth() / 3;
        int h = old.getHeight() / 3;
        BufferedImage img = new BufferedImage(
            w, h,BufferedImage.TYPE_INT_ARGB);
        Graphics2D g2d = img.createGraphics();
        g2d.drawImage(old, 0, 0, w, h, this);
        g2d.setPaint(Color.red);
        g2d.setFont(new Font("Serif", Font.BOLD, 20));
        String s = "Hello, world!";
        FontMetrics fm = g2d.getFontMetrics();
        int x = img.getWidth() - fm.stringWidth(s) - 5;
        int y = fm.getHeight();
        g2d.drawString(s, x, y);
        g2d.dispose();
        return img;
    }

    @Override
    protected void paintComponent(Graphics g) {
        super.paintComponent(g);
        g.drawImage(image, 0, 0, null);
    }

    private static void create() {
        JFrame f = new JFrame();
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.add(new TextOverlay());
        f.pack();
        f.setVisible(true);
    }

    public static void main(String[] args) {
        javax.swing.SwingUtilities.invokeLater(new Runnable() {

            @Override
            public void run() {
                create();
            }
        });
    }
}