Smoothing a jagged path

I was participating in the thread Image/Graphic into a Shape the other day and made a hackish attempt to get the outline of an image by adding a Rectangle iteratively to an Area. That was very slow.

This example instead builds a GeneralPath and creates the Area from the GP. Much faster.

Sample images for processing

The image on the upper left is the 'source image'. The two on the right are various stages of processing the outline. Both of them have jagged edges around the circle and along the slanted sides of the triangle.

I'd like to gain a shape that has that jaggedness removed or reduced.

In ASCII art.

Case 1:

  1234
1 **
2 **
3 ***
4 ***
5 ****
6 ****

Corners are at:

(2,3) inner corner
(3,3)
(3,5) inner corner
(4,5)

Case 2:

  1234
1 ****
2 ****
3 **
4 **
5 ****
6 ****

Corners are at:

(4,2)
(2,2) inner corner
(2,5) inner corner
(4,5)

Assuming our path had the shapes shown, and the points as listed, I'd like to drop the 'inner corner' points of the first set, while retaining the 'pair' of inner corners (a bite out of the image) for the 2nd.

Can anybody suggest some clever inbuilt method to do the heavy lifting of this job?
Failing that, what would be a good approach to identifying the location & nature (pair/single) of the inner corners? (I'm guessing I could get a PathIterator and build a new GeneralPath dropping the singular inner corners - if only I could figure how to identify them!).

Here's the code to play with:

import java.awt.*;
import java.awt.event.*;
import java.awt.image.*;
import java.awt.geom.*;
import javax.swing.*;
import javax.swing.border.*;
import javax.swing.event.*;

/* Gain the outline of an image for further processing. */
class ImageOutline {

    private BufferedImage image;

    private TwoToneImageFilter twoToneFilter;
    private BufferedImage imageTwoTone;
    private JLabel labelTwoTone;

    private BufferedImage imageOutline;
    private Area areaOutline = null;
    private JLabel labelOutline;

    private JLabel targetColor;
    private JSlider tolerance;

    private JProgressBar progress;
    private SwingWorker sw;

    public ImageOutline(BufferedImage image) {
        this.image = image;
        imageTwoTone = new BufferedImage(
            image.getWidth(),
            image.getHeight(),
            BufferedImage.TYPE_INT_RGB);
    }

    public void drawOutline() {
        if (areaOutline!=null) {
            Graphics2D g = imageOutline.createGraphics();
            g.setColor(Color.WHITE);
            g.fillRect(0,0,imageOutline.getWidth(),imageOutline.getHeight());

            g.setColor(Color.RED);
            g.setClip(areaOutline);
            g.fillRect(0,0,imageOutline.getWidth(),imageOutline.getHeight());
            g.setColor(Color.BLACK);
            g.setClip(null);
            g.draw(areaOutline);

            g.dispose();
        }
    }

    public Area getOutline(Color target, BufferedImage bi) {
        // construct the GeneralPath
        GeneralPath gp = new GeneralPath();

        boolean cont = false;
        int targetRGB = target.getRGB();
        for (int xx=0; xx<bi.getWidth(); xx++) {
            for (int yy=0; yy<bi.getHeight(); yy++) {
                if (bi.getRGB(xx,yy)==targetRGB) {
                    if (cont) {
                        gp.lineTo(xx,yy);
                        gp.lineTo(xx,yy+1);
                        gp.lineTo(xx+1,yy+1);
                        gp.lineTo(xx+1,yy);
                        gp.lineTo(xx,yy);
                    } else {
                        gp.moveTo(xx,yy);
                    }
                    cont = true;
                } else {
                    cont = false;
                }
            }
            cont = false;
        }
        gp.closePath();

        // construct the Area from the GP & return it
        return new Area(gp);
    }

    public JPanel getGui() {
        JPanel images = new JPanel(new GridLayout(2,2,2,2));
        JPanel  gui = new JPanel(new BorderLayout(3,3));

        JPanel originalImage =  new JPanel(new BorderLayout(2,2));
        final JLabel originalLabel = new JLabel(new ImageIcon(image));
        targetColor = new JLabel("Target Color");
        targetColor.setForeground(Color.RED);
        targetColor.setBackground(Color.WHITE);
        targetColor.setBorder(new LineBorder(Color.BLACK));
        targetColor.setOpaque(true);

        JPanel controls = new JPanel(new BorderLayout());
        controls.add(targetColor, BorderLayout.WEST);
        originalLabel.addMouseListener( new MouseAdapter() {
            @Override
            public void mouseEntered(MouseEvent me) {
                originalLabel.setCursor(
                    Cursor.getPredefinedCursor(Cursor.CROSSHAIR_CURSOR));
            }

            @Override
            public void mouseExited(MouseEvent me) {
                originalLabel.setCursor(Cursor.getDefaultCursor());
            }

            @Override
            public void mouseClicked(MouseEvent me) {
                int x = me.getX();
                int y = me.getY();

                Color c = new Color( image.getRGB(x,y) );
                targetColor.setBackground( c );

                updateImages();
            }
        });
        originalImage.add(originalLabel);

        tolerance = new JSlider(
            JSlider.HORIZONTAL,
            0,
            255,
            104
            );
        tolerance.addChangeListener( new ChangeListener() {
            public void stateChanged(ChangeEvent ce) {
                updateImages();
            }
        });
        controls.add(tolerance, BorderLayout.CENTER);
        gui.add(controls,BorderLayout.NORTH);

        images.add(originalImage);

        labelTwoTone = new JLabel(new ImageIcon(imageTwoTone));

        images.add(labelTwoTone);

        images.add(new JLabel("Smoothed Outline"));

        imageOutline = new BufferedImage(
            image.getWidth(),
            image.getHeight(),
            BufferedImage.TYPE_INT_RGB
            );

        labelOutline = new JLabel(new ImageIcon(imageOutline));
        images.add(labelOutline);

        updateImages();

        progress = new JProgressBar();

        gui.add(images, BorderLayout.CENTER);
        gui.add(progress, BorderLayout.SOUTH);

        return gui;
    }

    private void updateImages() {
        if (sw!=null) {
            sw.cancel(true);
        }
        sw = new SwingWorker() {
            @Override
            public String doInBackground() {
                progress.setIndeterminate(true);
                adjustTwoToneImage();
                labelTwoTone.repaint();
                areaOutline = getOutline(Color.BLACK, imageTwoTone);

                drawOutline();

                return "";
            }

            @Override
            protected void done() {
                labelOutline.repaint();
                progress.setIndeterminate(false);
            }
        };
        sw.execute();
    }

    public void adjustTwoToneImage() {
        twoToneFilter = new TwoToneImageFilter(
            targetColor.getBackground(),
            tolerance.getValue());

        Graphics2D g = imageTwoTone.createGraphics();
        g.drawImage(image, twoToneFilter, 0, 0);

        g.dispose();
    }

    public static void main(String[] args) throws Exception {
        int size = 150;
        final BufferedImage outline =
            new BufferedImage(size,size,BufferedImage.TYPE_INT_RGB);
        Graphics2D g = outline.createGraphics();
        g.setColor(Color.WHITE);
        g.fillRect(0,0,size,size);
        g.setRenderingHint(
            RenderingHints.KEY_DITHERING,
            RenderingHints.VALUE_DITHER_ENABLE);
        g.setRenderingHint(
            RenderingHints.KEY_ANTIALIASING,
            RenderingHints.VALUE_ANTIALIAS_ON);

        Polygon p = new Polygon();
        p.addPoint(size/2, size/10);
        p.addPoint(size-10, size-10);
        p.addPoint(10, size-10);
        Area a = new Area(p);

        Rectangle r = new Rectangle(size/4, 8*size/10, size/2, 2*size/10);
        a.subtract(new Area(r));

        int radius = size/10;
        Ellipse2D.Double c = new Ellipse2D.Double(
            (size/2)-radius,
            (size/2)-radius,
            2*radius,
            2*radius
            );
        a.subtract(new Area(c));

        g.setColor(Color.BLACK);
        g.fill(a);

        ImageOutline io = new ImageOutline(outline);

        JFrame f = new JFrame("Image Outline");
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.add(io.getGui());
        f.pack();
        f.setResizable(false);
        f.setLocationByPlatform(true);
        f.setVisible(true);
    }
}

class TwoToneImageFilter implements BufferedImageOp {

    Color target;
    int tolerance;

    TwoToneImageFilter(Color target, int tolerance) {
        this.target = target;
        this.tolerance = tolerance;
    }

    private boolean isIncluded(Color pixel) {
        int rT = target.getRed();
        int gT = target.getGreen();
        int bT = target.getBlue();
        int rP = pixel.getRed();
        int gP = pixel.getGreen();
        int bP = pixel.getBlue();
        return(
            (rP-tolerance<=rT) && (rT<=rP+tolerance) &&
            (gP-tolerance<=gT) && (gT<=gP+tolerance) &&
            (bP-tolerance<=bT) && (bT<=bP+tolerance) );
    }

    public BufferedImage createCompatibleDestImage(
        BufferedImage src,
        ColorModel destCM) {
        BufferedImage bi = new BufferedImage(
            src.getWidth(),
            src.getHeight(),
            BufferedImage.TYPE_INT_RGB);
        return bi;
    }

    public BufferedImage filter(
        BufferedImage src,
        BufferedImage dest) {

        if (dest==null) {
            dest = createCompatibleDestImage(src, null);
        }

        for (int x=0; x<src.getWidth(); x++) {
            for (int y=0; y<src.getHeight(); y++) {
                Color pixel = new Color(src.getRGB(x,y));
                Color write = Color.BLACK;
                if (isIncluded(pixel)) {
                    write = Color.WHITE;
                }
                dest.setRGB(x,y,write.getRGB());
            }
        }

        return dest;
    }

    public Rectangle2D getBounds2D(BufferedImage src) {
        return new Rectangle2D.Double(0, 0, src.getWidth(), src.getHeight());
    }

    public Point2D getPoint2D(
        Point2D srcPt,
        Point2D dstPt) {
        // no co-ord translation
        return srcPt;
    }

    public RenderingHints getRenderingHints() {
        return null;
    }
}

This is a big subject. You might find Depixelizing Pixel Art¹ by Johannes Kopf & Dani Lischinski useful: it's readable, recent, includes a summary of previous work, and explains their approach in detail.

See also slides covering similar background and video(!).

Here are some screenshots from the document of 'nearest neighbor' vs. 'their technique'.

The most general version of this problem is one of the initial stages in most computer vision pipelines. It's called Image Segementation. It splits an image into regions of pixels considered to be visually identical. These regions are separated by "contours" (see for example this article), which amount to paths through the image running along pixel boundaries.

There is a simple recursive algorithm for representing contours as a polyline defined such that no point in it deviates more than some fixed amount (say max_dev) you get to pick. Normally it's 1/2 to 2 pixels.

function getPolyline(points [p0, p1, p2... pn] in a contour, max_dev) {
  if n <= 1 (there are only one or two pixels), return the whole contour
  Let pi, 0 <= i <= n, be the point farthest from the line segment p0<->pn
  if distance(pi, p0<->pn) < max_dev 
    return [ p0 -> pn ]
  else
    return concat(getPolyline [ p0, ..., pi ],  getPolyline [ pi, ..., pn] )

The thought behind this is that you seem to have cartoon-like images that are already segmented. So if you code a simple search that assembles the edge pixels into chains, you can use the algorithm above to convert them into line segment chains that will will be smooth. They can even be drawn with anti-aliasing.

Smoothing a jagged path

In ASCII art.

Case 1:

Case 2:

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