Sobel Edge Detection

import java.awt.*;
import java.awt.image.*;
import javax.swing.*;
class Test {

    private static int[][] sobelx = {{-1, 0, 1}, {-2, 0, 2}, {-1, 0, 1}};
    private static int[][] sobely = {{1, 2, 1}, {0, 0, 0}, {-1, -2, -1}};

    public static int lum(int r, int g, int b) {
    return (r + r + r + b + g + g + g + g) >> 3;
    }

    public static int rgb_to_luminance(int rgb) {
    int r = (rgb & 0xff0000) >> 16;
    int g = (rgb & 0xff00) >> 8;
    int b = (rgb & 0xff);
    //System.out.println(r + ", " + g + ", " + b);
    return lum(r, g, b);
    }

    public static int level_to_greyscale(int level) {
    return (level << 16) | (level << 8) | level;
    }

    public static BufferedImage cloneImage(BufferedImage image) {
    return new BufferedImage(image.getColorModel(), image.copyData(null), image.isAlphaPremultiplied(), null);
    }

    public static BufferedImage sobelEdgeDetection(BufferedImage image) {
    BufferedImage ret = cloneImage(image);
    int width = image.getWidth();
    int height = image.getHeight();
    for (int x = 0; x < width; x++) {
        for (int y = 0; y < height; y++) {
        int level = 255;
        if ((x > 0) && (x < (width - 1)) && (y > 0) && (y < (height - 1))) {
            int sumX = 0;
            int sumY = 0;
            for (int i = -1; i < 2; i++) {
            for (int j = -1; j < 2; j++) {
                sumX += rgb_to_luminance(image.getRGB(x+i, y+j)) * sobelx[i+1][j+1];
                sumY += rgb_to_luminance(image.getRGB(x+i, y+j)) * sobely[i+1][j+1];
                System.out.println(sumX + " " + sumY);
            }
            }
            level = Math.abs(sumX) + Math.abs(sumY);
            if (level < 0) {
            level = 0;
            } else if (level > 255) {
            level = 255;
            }
            level = 255 - level;
        }
        ret.setRGB(x, y, level_to_greyscale(level));
        }
    }
    return ret;
    }

    public static class MyPanel extends JPanel {
    private BufferedImage _image;
    public MyPanel (BufferedImage image) {
        super();
        _image = image;
        setPreferredSize(new Dimension(image.getWidth(), image.getHeight()));
    }
    protected void paintComponent(Graphics g) {
        g.drawImage(_image, 0, 0, null);
    }
    }

    public static void main(String[] args) throws Exception {
    DisplayMode dm = GraphicsEnvironment.getLocalGraphicsEnvironment().getDefaultScreenDevice().getDisplayMode();
    BufferedImage image = new Robot().createScreenCapture(new Rectangle(dm.getWidth(), dm.getHeight()));;
    BufferedImage edImage = sobelEdgeDetection(image);

    JFrame frame = new JFrame();
    long startTime = System.currentTimeMillis();
    JPanel panel = new MyPanel(edImage);
    long endTime = System.currentTimeMillis();
    System.out.println("xform took: " + (endTime - startTime) + "ms");
    frame.add(panel);
    frame.pack();
    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    frame.show();

    }
}