How to detect mouse over on drawn image with awt.Graphics.drawImage() when transformed

In a Java Swing panel I draw an image with arbitrary transfomation e.g.:

public void paintComponent(Graphics g){
    AffineTransform transform = AffineTransform.getTranslateInstance(x, y);
    AffineTransform rotateInstance AffineTransform.getRotateInstance(rotX, rotY);           
    transform.concatenate(rotateInstance);

    g.setTransform(transform);    
    g.drawImage(image, 0, 0 , null);
}

What is the best way to detect mouse over on such an image?

Even better: the best way to detect mouse over only on non-transparent pixels?