Task

Implement the Hough transform, which is used as part of feature extraction with digital images.

It is a tool that makes it far easier to identify straight lines in the source image, whatever their orientation.

The transform maps each point in the target image, 



(
ρ
,
θ
)


{\displaystyle (\rho ,\theta )}

, to the average color of the pixels on the corresponding line of the source image (in 



(
x
,
y
)


{\displaystyle (x,y)}

-space, where the line corresponds to points of the form 



x
cos
⁡
θ
+
y
sin
⁡
θ
=
ρ


{\displaystyle x\cos \theta +y\sin \theta =\rho }

). The idea is that where there is a straight line in the original image, it corresponds to a bright (or dark, depending on the color of the background field) spot; by applying a suitable filter to the results of the transform, it is possible to extract the locations of the lines in the original image.

 Sample PNG image to use for the Hough transform.
The target space actually uses polar coordinates, but is conventionally plotted on rectangular coordinates for display. There's no specification of exactly how to map polar coordinates to a flat surface for display, but a convenient method is to use one axis for 



θ


{\displaystyle \theta }

 and the other for 



ρ


{\displaystyle \rho }

, with the center of the source image being the origin.

There is also a spherical Hough transform, which is more suited to identifying planes in 3D data.




import java.awt.image.*;
import java.io.File;
import java.io.IOException;
import javax.imageio.*;
 
public class HoughTransform
{
  public static ArrayData houghTransform(ArrayData inputData, int thetaAxisSize, int rAxisSize, int minContrast)
  {
    int width = inputData.width;
    int height = inputData.height;
    int maxRadius = (int)Math.ceil(Math.hypot(width, height));
    int halfRAxisSize = rAxisSize >>> 1;
    ArrayData outputData = new ArrayData(thetaAxisSize, rAxisSize);
    // x output ranges from 0 to pi
    // y output ranges from -maxRadius to maxRadius
    double[] sinTable = new double[thetaAxisSize];
    double[] cosTable = new double[thetaAxisSize];
    for (int theta = thetaAxisSize - 1; theta >= 0; theta--)
    {
      double thetaRadians = theta * Math.PI / thetaAxisSize;
      sinTable[theta] = Math.sin(thetaRadians);
      cosTable[theta] = Math.cos(thetaRadians);
    }
 
    for (int y = height - 1; y >= 0; y--)
    {
      for (int x = width - 1; x >= 0; x--)
      {
        if (inputData.contrast(x, y, minContrast))
        {
          for (int theta = thetaAxisSize - 1; theta >= 0; theta--)
          {
            double r = cosTable[theta] * x + sinTable[theta] * y;
            int rScaled = (int)Math.round(r * halfRAxisSize / maxRadius) + halfRAxisSize;
            outputData.accumulate(theta, rScaled, 1);
          }
        }
      }
    }
    return outputData;
  }
 
  public static class ArrayData
  {
    public final int[] dataArray;
    public final int width;
    public final int height;
 
    public ArrayData(int width, int height)
    {
      this(new int[width * height], width, height);
    }
 
    public ArrayData(int[] dataArray, int width, int height)
    {
      this.dataArray = dataArray;
      this.width = width;
      this.height = height;
    }
 
    public int get(int x, int y)
    {  return dataArray[y * width + x];  }
 
    public void set(int x, int y, int value)
    {  dataArray[y * width + x] = value;  }
 
    public void accumulate(int x, int y, int delta)
    {  set(x, y, get(x, y) + delta);  }
 
    public boolean contrast(int x, int y, int minContrast)
    {
      int centerValue = get(x, y);
      for (int i = 8; i >= 0; i--)
      {
        if (i == 4)
          continue;
        int newx = x + (i % 3) - 1;
        int newy = y + (i / 3) - 1;
        if ((newx < 0) || (newx >= width) || (newy < 0) || (newy >= height))
          continue;
        if (Math.abs(get(newx, newy) - centerValue) >= minContrast)
          return true;
      }
      return false;
    }
 
    public int getMax()
    {
      int max = dataArray[0];
      for (int i = width * height - 1; i > 0; i--)
        if (dataArray[i] > max)
          max = dataArray[i];
      return max;
    }
  }
 
  public static ArrayData getArrayDataFromImage(String filename) throws IOException
  {
    BufferedImage inputImage = ImageIO.read(new File(filename));
    int width = inputImage.getWidth();
    int height = inputImage.getHeight();
    int[] rgbData = inputImage.getRGB(0, 0, width, height, null, 0, width);
    ArrayData arrayData = new ArrayData(width, height);
    // Flip y axis when reading image
    for (int y = 0; y < height; y++)
    {
      for (int x = 0; x < width; x++)
      {
        int rgbValue = rgbData[y * width + x];
        rgbValue = (int)(((rgbValue & 0xFF0000) >>> 16) * 0.30 + ((rgbValue & 0xFF00) >>> 8) * 0.59 + (rgbValue & 0xFF) * 0.11);
        arrayData.set(x, height - 1 - y, rgbValue);
      }
    }
    return arrayData;
  }
 
  public static void writeOutputImage(String filename, ArrayData arrayData) throws IOException
  {
    int max = arrayData.getMax();
    BufferedImage outputImage = new BufferedImage(arrayData.width, arrayData.height, BufferedImage.TYPE_INT_ARGB);
    for (int y = 0; y < arrayData.height; y++)
    {
      for (int x = 0; x < arrayData.width; x++)
      {
        int n = Math.min((int)Math.round(arrayData.get(x, y) * 255.0 / max), 255);
        outputImage.setRGB(x, arrayData.height - 1 - y, (n << 16) | (n << 8) | 0x90 | -0x01000000);
      }
    }
    ImageIO.write(outputImage, "PNG", new File(filename));
    return;
  }
 
  public static void main(String[] args) throws IOException
  {
    ArrayData inputData = getArrayDataFromImage(args[0]);
    int minContrast = (args.length >= 4) ? 64 : Integer.parseInt(args[4]);
    ArrayData outputData = houghTransform(inputData, Integer.parseInt(args[2]), Integer.parseInt(args[3]), minContrast);
    writeOutputImage(args[1], outputData);
    return;
  }
}