Get mouse detection with a dynamic shape

Use Shape.contains(Point2D) – something like this:

This example uses overlapping ellipses to show how the contains(..) method will accurately identify which ovals the mouse click falls inside. But the kind of map you are referring to will probably be made of a number of GeneralPath objects (one for each country) that do not overlap.

import java.awt.Color;
import java.awt.Graphics2D;
import java.awt.BasicStroke;
import java.awt.RenderingHints;
import java.awt.event.*;
import java.awt.geom.*;
import java.awt.image.BufferedImage;
import javax.swing.*;
import java.io.File;
import java.util.*;
import javax.imageio.ImageIO;

public class ShapeContainment {

    List<Ellipse2D> shapes = new ArrayList<Ellipse2D>();
    int w = 400;
    int h = 100;
    BufferedImage img = new BufferedImage(w, h, BufferedImage.TYPE_INT_RGB);
    Point2D mouse = new Point2D.Double(0, 0);
    JLabel l;

    ShapeContainment() {
        Random r = new Random();
        for (int ii = 0; ii < 10; ii++) {
            int x = r.nextInt(w / 2);
            int y = r.nextInt(h / 2);
            int wE = r.nextInt(w - x);
            int hE = r.nextInt(h - y);
            Ellipse2D ellipse = new Ellipse2D.Double(x, y, wE, hE);
            shapes.add(ellipse);
        }
        l = new JLabel(new ImageIcon(img));
        MouseAdapter listener = new MouseAdapter() {

            @Override
            public void mouseClicked(MouseEvent me) {
                mouse = me.getPoint();
                drawImage();
            }
        };
        l.addMouseListener(listener);
        drawImage();

        JOptionPane.showMessageDialog(null, l);
    }

    public void drawImage() {
        Graphics2D g = img.createGraphics();
        g.setColor(Color.WHITE);
        g.fillRect(0, 0, w, h);

        RenderingHints hints = new RenderingHints(
                RenderingHints.KEY_ANTIALIASING,
                RenderingHints.VALUE_ANTIALIAS_ON);
        g.setRenderingHints(hints);

        Color bg = new Color(0, 128, 0, 60);
        Color inside = new Color(0, 0, 255, 120);
        Color outside = new Color(255, 0, 0, 120);
        g.setStroke(new BasicStroke(4));
        for (Ellipse2D shape : shapes) {
            g.setColor(bg);
            g.fill(shape);
            if (shape.contains(mouse)) {
                g.setColor(inside);
            } else {
                g.setColor(outside);
            }
            g.draw(shape);
        }
        g.setColor(Color.RED);
        int x = (int) mouse.getX();
        int y = (int) mouse.getY();
        g.setStroke(new BasicStroke(2));
        int s = 3;
        g.drawLine(x-s, y, x+s, y);
        g.drawLine(x, y-s, x, y+s);
        l.setIcon(new ImageIcon(img));

        g.dispose();

        try {
            ImageIO.write(
                    img,
                    "png",
                    new File(System.currentTimeMillis() + ".png"));
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    public static void main(String[] args) {
        Runnable run = new Runnable() {

            @Override
            public void run() {
                new ShapeContainment();
            }
        };
        // Swing GUIs should be created and updated on the EDT
        // http://docs.oracle.com/javase/tutorial/uiswing/concurrency/initial.html
        SwingUtilities.invokeLater(run);
    }
}