How to convert a BufferedImage to black and white?

How can I convert an existing colored BufferedImage to monochrome? I want the image to be completely split between only two rgb codes, black and white. So if there's a border around the image which is a lighter or darker shade of the background, and the background is being converted to white, then I want the border to be converted to white as well, and so on.

How can I do this?

If its necessary to save the image / load it from disk, I can do that if necessary.

Edit: Code to test this:

package test;

import java.awt.Graphics2D;
import java.awt.image.BufferedImage;
import java.io.File;
import java.util.HashSet;
import javax.imageio.ImageIO;

public class Test
{
    public static void main(String[] args)
    {
        try
        {
            BufferedImage img = ImageIO.read(new File("http://i.stack.imgur.com/yhCnH.png") );
            BufferedImage gray = new BufferedImage(img.getWidth(), img.getHeight(),
                    BufferedImage.TYPE_BYTE_GRAY);

            Graphics2D g = gray.createGraphics();
            g.drawImage(img, 0, 0, null);

            HashSet<Integer> colors = new HashSet<>();
            int color = 0;
            for (int y = 0; y < gray.getHeight(); y++)
            {
                for (int x = 0; x < gray.getWidth(); x++)
                {
                    color = gray.getRGB(x, y);
                    System.out.println(color);
                    colors.add(color);
                }
            }

            System.out.println(colors.size() );
        }
        catch (Exception e)
        {
            e.printStackTrace();
        }
    }
}

Image used:

Using this, I get the output of 24 as the last output, i.e there were 24 colors found in this image, when there should be 2.

The solution was to use BufferedImage.TYPE_BYTE_BINARY as the type rather than TYPE_BYTE_GRAY. Using BINARY causes a pure black & white copy of the image to be created, with no colors except b & w. Not pretty looking, but perfect for things like OCR where the colors need to be exact.