# Hough transform

Hough transform
You are encouraged to solve this task according to the task description, using any language you may know.

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, ${\displaystyle (\rho ,\theta )}$, to the average color of the pixels on the corresponding line of the source image (in ${\displaystyle (x,y)}$-space, where the line corresponds to points of the form ${\displaystyle x\cos \theta +y\sin \theta =\rho }$). 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 ${\displaystyle \theta }$ and the other for ${\displaystyle \rho }$, 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.

## BBC BASIC

BBC BASIC uses Cartesian coordinates so the image is 'upside down' compared with some other solutions.

      Width% = 320      Height% = 240       VDU 23,22,Width%;Height%;8,16,16,128      *DISPLAY Pentagon.bmp      OFF       DIM hist%(Width%-1, Height%-1)       rs = 2 * SQR(Width%^2 + Height%^2) / Height% : REM Radial step      ts = PI / Width% : REM Angular step      h% = Height% / 2       REM Hough transform:      FOR y% = 0 TO Height%-1        FOR x% = 0 TO Width%-1          IF TINT(x%*2, y%*2) = 0 THEN            FOR t% = 0 TO Width%-1              th = t% * ts              r% = (x%*COS(th) + y%*SIN(th)) / rs + h% + 0.5              hist%(t%,r%) += 1            NEXT          ENDIF        NEXT      NEXT y%       REM Find max:      max% = 0      FOR y% = 0 TO Height%-1        FOR x% = 0 TO Width%-1          IF hist%(x%,y%) > max% max% = hist%(x%,y%)        NEXT      NEXT y%       REM Plot:      GCOL 1      FOR y% = 0 TO Height%-1        FOR x% = 0 TO Width%-1          c% = 255 * hist%(x%,y%) / max%          COLOUR 1, c%, c%, c%          LINE x%*2,y%*2,x%*2,y%*2        NEXT      NEXT y%       REPEAT        WAIT 1      UNTIL FALSE

## D

Translation of: Go

This uses the module from the Grayscale image Task. The output image is the same as in the Go solution.

import std.math, grayscale_image; Image!Gray houghTransform(in Image!Gray im,                          in size_t hx=460, in size_t hy=360)pure nothrow in {    assert(im !is null);    assert(hx > 0 && hy > 0);    assert((hy & 1) == 0, "hy argument must be even.");} body {    auto result = new Image!Gray(hx, hy);    result.clear(Gray.white);     immutable double rMax = hypot(im.nx, im.ny);    immutable double dr = rMax / (hy / 2.0);    immutable double dTh = PI / hx;     foreach (immutable y; 0 .. im.ny) {        foreach (immutable x; 0 .. im.nx) {            if (im[x, y] == Gray.white)                continue;            foreach (immutable iTh; 0 .. hx) {                immutable double th = dTh * iTh;                immutable double r = x * cos(th) + y * sin(th);                immutable iry = hy / 2 - cast(int)floor(r / dr + 0.5);                if (result[iTh, iry] > Gray(0))                    result[iTh, iry]--;            }        }    }    return result;} void main() {    (new Image!RGB)    .loadPPM6("Pentagon.ppm")    .rgb2grayImage()    .houghTransform()    .savePGM("Pentagon_hough.pgm");}

## Go

Output png
Translation of: Python
package main import (    "fmt"    "image"    "image/color"    "image/draw"    "image/png"    "math"    "os") func hough(im image.Image, ntx, mry int) draw.Image {    nimx := im.Bounds().Max.X    mimy := im.Bounds().Max.Y    mry = int(mry/2) * 2    him := image.NewGray(image.Rect(0, 0, ntx, mry))    draw.Draw(him, him.Bounds(), image.NewUniform(color.White),        image.ZP, draw.Src)     rmax := math.Hypot(float64(nimx), float64(mimy))    dr := rmax / float64(mry/2)    dth := math.Pi / float64(ntx)     for jx := 0; jx < nimx; jx++ {        for iy := 0; iy < mimy; iy++ {            col := color.GrayModel.Convert(im.At(jx, iy)).(color.Gray)            if col.Y == 255 {                continue            }            for jtx := 0; jtx < ntx; jtx++ {                th := dth * float64(jtx)                r := float64(jx)*math.Cos(th) + float64(iy)*math.Sin(th)                iry := mry/2 - int(math.Floor(r/dr+.5))                col = him.At(jtx, iry).(color.Gray)                if col.Y > 0 {                    col.Y--                    him.SetGray(jtx, iry, col)                }            }        }    }    return him} func main() {    f, err := os.Open("Pentagon.png")    if err != nil {        fmt.Println(err)        return    }    pent, err := png.Decode(f)    if err != nil {        fmt.Println(err)        return    }    if err = f.Close(); err != nil {        fmt.Println(err)    }    h := hough(pent, 460, 360)    if f, err = os.Create("hough.png"); err != nil {        fmt.Println(err)        return    }    if err = png.Encode(f, h); err != nil {        fmt.Println(err)    }    if cErr := f.Close(); cErr != nil && err == nil {        fmt.Println(err)    }}

Library: JuicyPixels
import Control.Monad (forM_, when)import Data.Array ((!))import Data.Array.ST (newArray, writeArray, readArray, runSTArray)import qualified Data.Foldable as F (maximum)import System.Environment (getArgs, getProgName) -- Library JuicyPixels:import Codec.Picture       (DynamicImage(ImageRGB8, ImageRGBA8), Image, PixelRGB8(PixelRGB8),        PixelRGBA8(PixelRGBA8), imageWidth, imageHeight, pixelAt,        generateImage, readImage, pixelMap, savePngImage)import Codec.Picture.Types (extractLumaPlane, dropTransparency) dot  :: Num a  => (a, a) -> (a, a) -> adot (x1, y1) (x2, y2) = x1 * x2 + y1 * y2 mag  :: Floating a  => (a, a) -> amag a = sqrt $dot a a sub :: Num a => (a, a) -> (a, a) -> (a, a)sub (x1, y1) (x2, y2) = (x1 - x2, y1 - y2) fromIntegralP :: (Integral a, Num b) => (a, a) -> (b, b)fromIntegralP (x, y) = (fromIntegral x, fromIntegral y) {- Create a Hough space image with y+ measuring the distance from the center of the input image on the range of 0 to half the hypotenuse and x+ measuring from [0, 2 * pi]. The origin is in the upper left, so y is increasing down. The image is scaled according to thetaSize and distSize.-}hough :: Image PixelRGB8 -> Int -> Int -> Image PixelRGB8hough image thetaSize distSize = hImage where width = imageWidth image height = imageHeight image wMax = width - 1 hMax = height - 1 xCenter = wMax div 2 yCenter = hMax div 2 lumaMap = extractLumaPlane image gradient x y = let orig = pixelAt lumaMap x y x_ = pixelAt lumaMap (min (x + 1) wMax) y y_ = pixelAt lumaMap x (min (y + 1) hMax) in fromIntegralP (orig - x_, orig - y_) gradMap = [ ((x, y), gradient x y) | x <- [0 .. wMax] , y <- [0 .. hMax] ] -- The longest distance from the center, half the hypotenuse of the image. distMax :: Double distMax = (sqrt . fromIntegral$ height ^ 2 + width ^ 2) / 2    {-      The accumulation bins of the polar values.      For each value in the gradient image, if the gradient length exceeds      some threshold, consider it evidence of a line and plot all of the      lines that go through that point in Hough space.    -}    accBin =      runSTArray $do arr <- newArray ((0, 0), (thetaSize, distSize)) 0 forM_ gradMap$           \((x, y), grad) -> do             let (x_, y_) = fromIntegralP $(xCenter, yCenter) sub (x, y) when (mag grad > 127)$               forM_ [0 .. thetaSize] $\theta -> do let theta_ = fromIntegral theta * 360 / fromIntegral thetaSize / 180 * pi :: Double dist = cos theta_ * x_ + sin theta_ * y_ dist_ = truncate$ dist * fromIntegral distSize / distMax                     idx = (theta, dist_)                 when (dist_ >= 0 && dist_ < distSize) $do old <- readArray arr idx writeArray arr idx$ old + 1         return arr    maxAcc = F.maximum accBin    -- The image representation of the accumulation bins.    hTransform x y =      let l = 255 - truncate ((accBin ! (x, y)) / maxAcc * 255)      in PixelRGB8 l l l    hImage = generateImage hTransform thetaSize distSize houghIO :: FilePath -> FilePath -> Int -> Int -> IO ()houghIO path outpath thetaSize distSize = do  image <- readImage path  case image of    Left err -> putStrLn err    Right (ImageRGB8 image_) -> doImage image_    Right (ImageRGBA8 image_) -> doImage $pixelMap dropTransparency image_ _ -> putStrLn "Expecting RGB8 or RGBA8 image" where doImage image = do let houghImage = hough image thetaSize distSize savePngImage outpath$ ImageRGB8 houghImage main :: IO ()main = do  args <- getArgs  prog <- getProgName  case args of    [path, outpath, thetaSize, distSize] ->      houghIO path outpath (read thetaSize) (read distSize)    _ ->      putStrLn $"Usage: " ++ prog ++ " <image-file> <out-file.png> <width> <height>" Example use: HoughTransform Pentagon.png hough.png 360 360 ## J Solution: NB.*houghTransform v Produces a density plot of image y in hough spaceNB. y is picture as an array with 1 at non-white points,NB. x is resolution (width,height) of resulting imagehoughTransform=: dyad define 'w h'=. x NB. width and height of target image theta=. o. (%~ 0.5+i.) w NB. theta in radians from 0 to π rho=. (4$.$. |.y) +/ .* 2 1 o./theta NB. rho for each pixel at each theta 'min max'=. (,~-) +/&.:*:$y            NB. min/max possible rho  rho=. <. 0.5+ h * (rho-min) % max-min   NB. Rescale rho from 0 to h and round to int  |.([: <:@(#/.~) (i.h)&,)"1&.|: rho      NB. consolidate into picture)
Resulting viewmat image from J implementation of Hough Transform on sample pentagon image
Example use:
   require 'viewmat'   require 'media/platimg'       NB. addon required pre J8   Img=: readimg_jqtide_ jpath '~temp/pentagon.png'   viewmat 460 360 houghTransform _1 > Img

## Java

Code:

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;  }}
Output from example pentagon image
Example use:
java HoughTransform pentagon.png JavaHoughTransform.png 640 480 100

## Julia

using ImageFeatures img = fill(false,5,5)img[3,:] .= true println(hough_transform_standard(img))
Output:

Tuple{Float64,Float64}[(3.0, 1.5708)]



## Kotlin

Translation of: Java
import java.awt.image.BufferedImageimport java.io.Fileimport javax.imageio.ImageIO internal class ArrayData(val dataArray: IntArray, val width: Int, val height: Int) {     constructor(width: Int, height: Int) : this(IntArray(width * height), width, height)     operator fun get(x: Int, y: Int) = dataArray[y * width + x]     operator fun set(x: Int, y: Int, value: Int) {        dataArray[y * width + x] = value    }     operator fun invoke(thetaAxisSize: Int, rAxisSize: Int, minContrast: Int): ArrayData {        val maxRadius = Math.ceil(Math.hypot(width.toDouble(), height.toDouble())).toInt()        val halfRAxisSize = rAxisSize.ushr(1)        val outputData = ArrayData(thetaAxisSize, rAxisSize)        // x output ranges from 0 to pi        // y output ranges from -maxRadius to maxRadius        val sinTable = DoubleArray(thetaAxisSize)        val cosTable = DoubleArray(thetaAxisSize)        for (theta in thetaAxisSize - 1 downTo 0) {            val thetaRadians = theta * Math.PI / thetaAxisSize            sinTable[theta] = Math.sin(thetaRadians)            cosTable[theta] = Math.cos(thetaRadians)        }         for (y in height - 1 downTo 0)            for (x in width - 1 downTo 0)                if (contrast(x, y, minContrast))                    for (theta in thetaAxisSize - 1 downTo 0) {                        val r = cosTable[theta] * x + sinTable[theta] * y                        val rScaled = Math.round(r * halfRAxisSize / maxRadius).toInt() + halfRAxisSize                        outputData.accumulate(theta, rScaled, 1)                    }         return outputData    }     fun writeOutputImage(filename: String) {        val max = dataArray.max()!!        val image = BufferedImage(width, height, BufferedImage.TYPE_INT_ARGB)        for (y in 0..height - 1)            for (x in 0..width - 1) {                val n = Math.min(Math.round(this[x, y] * 255.0 / max).toInt(), 255)                image.setRGB(x, height - 1 - y, n shl 16 or (n shl 8) or 0x90 or -0x01000000)            }         ImageIO.write(image, "PNG", File(filename))    }     private fun accumulate(x: Int, y: Int, delta: Int) {        set(x, y, get(x, y) + delta)    }     private fun contrast(x: Int, y: Int, minContrast: Int): Boolean {        val centerValue = get(x, y)        for (i in 8 downTo 0)            if (i != 4) {                val newx = x + i % 3 - 1                val newy = y + i / 3 - 1                if (newx >= 0 && newx < width && newy >= 0 && newy < height                        && Math.abs(get(newx, newy) - centerValue) >= minContrast)                    return true            }        return false    }} internal fun readInputFromImage(filename: String): ArrayData {    val image = ImageIO.read(File(filename))    val w = image.width    val h = image.height    val rgbData = image.getRGB(0, 0, w, h, null, 0, w)    // flip y axis when reading image    val array = ArrayData(w, h)    for (y in 0..h - 1)        for (x in 0..w - 1) {            var rgb = rgbData[y * w + x]            rgb = ((rgb and 0xFF0000).ushr(16) * 0.30 + (rgb and 0xFF00).ushr(8) * 0.59 + (rgb and 0xFF) * 0.11).toInt()            array[x, h - 1 - y] = rgb        }     return array} fun main(args: Array<out String>) {    val inputData = readInputFromImage(args[0])    val minContrast = if (args.size >= 4) 64 else args[4].toInt()    inputData(args[2].toInt(), args[3].toInt(), minContrast).writeOutputImage(args[1])}

## Maple

with(ImageTools):img := Read("pentagon.png")[..,..,1]:img_x := Convolution (img, Matrix ([[1,2,1], [0,0,0],[-1,-2,-1]])):img_y := Convolution (img, Matrix ([[-1,0,1],[-2,0,2],[-1,0,1]])):img := Array (abs (img_x) + abs (img_y), datatype=float[8]):countPixels := proc(M)	local r,c,i,j,row,col:	row := Array([]);	col := Array([]);	r,c := LinearAlgebra:-Dimensions(M);	for i from 1 to r do		for j from 1 to c do			if M[i,j] <> 0 then 				ArrayTools:-Append(row, i, inplace=true):				ArrayTools:-Append(col, j, inplace=true):			end if:		end do:	end do:	return row,col:end proc:row,col := countPixels(img);pTheta := proc(acc,r,c,x,y)	local j, pos:	for j from 1 to c do		pos := ceil(x*cos((j-1)*Pi/180)+y*sin((j-1)*Pi/180)+r/2):		acc[pos,j] := acc[pos,j]+1;	end do:end proc:HoughTransform := proc(img,row,col)   local r,c,pMax,theta,numThetas,numPs,acc,i:   r,c := LinearAlgebra:-Dimensions(img);   pMax := ceil(sqrt(r^2+c^2)):   theta := [seq(evalf(i), i = 1..181, 1)]:   numThetas := numelems(theta):   numPs := 2*pMax+1:   acc := Matrix(numPs, numThetas, fill=0,datatype=integer[4]):   for i from 1 to numelems(row) do   	pTheta(acc,numPs,numThetas,col[i],row[i]):   end do:   return acc;end proc:result :=HoughTransform(img,row,col);Embed(Scale(FitIntensity(Create(result)), 1..500,1..500));

## Mathematica / Wolfram Language

 Radon[image, Method -> "Hough"]

## Perl

Translation of: Sidef
use Imager; use constant pi => 3.14159265; sub hough {    my($im) = shift; my($width)  = shift || 460;    my($height) = shift || 360;$height = 2 * int $height/2;$xsize = $im->getwidth();$ysize = $im->getheight();$ht = Imager->new(xsize => $width, ysize =>$height);    for $i (0..$height) { for $j (0..$width) { $canvas[$i][$j] = 255 } }$ht->box(filled => 1, color => 'white');     $rmax = sqrt($xsize**2 + $ysize**2);$dr   = 2 * $rmax /$height;    $dth = pi /$width;     for $x (0..$xsize-1) {      for $y (0..$ysize-1) {        my $col =$im->getpixel(x => $x, y =>$y);        my($r,$g,$b) =$col->rgba;        next if $r==255; # &&$g==255 && $b==255; for$k (0..$width) {$th = $dth*$k;            $r = ($x*cos($th) +$y*sin($th));$iry = ($height/2 + int($r/$dr + 0.5));$ht->setpixel(x => $k, y =>$iry, color => [ ($canvas[$iry][$k]--) x 3] ); } } } return$ht;} $img = Imager->new(file => 'pentagon.png');$ht  = hough($img);$ht->write(file => 'hough_transform.png');

## Perl 6

The GD module the output palette to 255 colors, so only transform darker pixels in the image.

Translation of: Perl
use GD; my $filename = 'pentagon.ppm';my$in = open($filename, :r, :enc<iso-8859-1>);my ($type, $dim,$depth) = $in.lines[^3];my ($xsize,$ysize) = split ' ',$dim; my ($width,$height) = 460, 360;my $image = GD::Image.new($width, $height); my @canvas = [255 xx$width] xx $height; my$rmax = sqrt($xsize**2 +$ysize**2);my $dr = 2 *$rmax / $height;my$dth  = π / $width; my$pixel = 0;my %cstore;for $in.lines.ords ->$r, $g,$b {    $pixel++; next if$r > 130;     my $x =$pixel % $xsize; my$y = floor $pixel /$xsize;     (0..^$width).race.map: ->$k {        my $th =$dth*$k; my$r = ($x*cos($th) + $y*sin($th));        my $iry = ($height/2 + ($r/$dr).round(1)).Int;        my $c = '#' ~ (@canvas[$iry][$k]--).base(16) x 3; %cstore{$c} = $image.colorAllocate($c) if %cstore{$c}:!exists;$image.pixel($k,$iry, %cstore{$c}); }} my$png_fh = $image.open("hough-transform.png", "wb");$image.output($png_fh, GD_PNG);$png_fh.close;

See Hough Transform (offsite .png image)

## Phix

Translation of: Sidef
-- demo\rosetta\Hough_transform.exwinclude pGUI.e function hypot(atom a,b) return sqrt(a*a+b*b) end function function hough_transform(imImage im, integer width=460, height=360)    height = 2*floor(height / 2)    integer xsize = im_width(im),            ysize = im_width(im)    sequence ht = repeat(repeat(repeat(255,3),width),height)    sequence canvas = repeat(repeat(255,width),height)    atom rmax = hypot(xsize, ysize),         dr = 2*(rmax / height),         dth = (PI / width)    for y=0 to ysize-1 do        for x=0 to xsize-1 do            integer {r,g,b} = im_pixel(im, x, y)            if r!=255 then                for k=1 to width do                    atom th = dth*(k-1),                         r2 = (x*cos(th) + y*sin(th))                    integer iry = (height/2 + floor(r2/dr + 0.5))+1,                            cik = canvas[iry][k] - 1                    canvas[iry][k] = cik                    ht[iry][k] = repeat(cik,3)                end for            end if        end for    end for    ht = flatten(ht) -- (needed by IupImageRGB)    Ihandle new_img = IupImageRGB(width, height, ht)     return new_imgend function IupOpen() atom pError = allocate(machine_word())imImage im1 = imFileImageLoadBitmap("Pentagon.png",0,pError)if im1=NULL then ?"error opening Pentagon.png" abort(0) end ifIhandln image1 = IupImageFromImImage(im1),        image2 = hough_transform(im1),        label1 = IupLabel(),        label2 = IupLabel()IupSetAttributeHandle(label1, "IMAGE", image1)IupSetAttributeHandle(label2, "IMAGE", image2) Ihandle dlg = IupDialog(IupHbox({label1, label2}))IupSetAttribute(dlg, "TITLE", "Hough transform")IupCloseOnEscape(dlg)IupShow(dlg) IupMainLoop()IupClose()

## Python

Library: PIL

This is the classical Hough transform as described in wikipedia. The code does not compute averages; it merely makes a point on the transformed image darker if a lot of points on the original image lie on the corresponding line. The output is almost identical to that of the Tcl code. The code works only with gray-scale images, but it is easy to extend to RGB.

 from math import hypot, pi, cos, sinfrom PIL import Image  def hough(im, ntx=460, mry=360):    "Calculate Hough transform."    pim = im.load()    nimx, mimy = im.size    mry = int(mry/2)*2          #Make sure that this is even    him = Image.new("L", (ntx, mry), 255)    phim = him.load()     rmax = hypot(nimx, mimy)    dr = rmax / (mry/2)    dth = pi / ntx     for jx in xrange(nimx):        for iy in xrange(mimy):            col = pim[jx, iy]            if col == 255: continue            for jtx in xrange(ntx):                th = dth * jtx                r = jx*cos(th) + iy*sin(th)                iry = mry/2 + int(r/dr+0.5)                phim[jtx, iry] -= 1    return him  def test():    "Test Hough transform with pentagon."    im = Image.open("pentagon.png").convert("L")    him = hough(im)    him.save("ho5.bmp")  if __name__ == "__main__": test()

## Ruby

 require 'mathn'require 'rubygems'require 'gd2'include GD2 def hough_transform(img)  mx, my = img.w*0.5, img.h*0.5  max_d = Math.sqrt(mx**2 + my**2)  min_d = max_d * -1  hough = Hash.new(0)  (0..img.w).each do |x|    puts "#{x} of #{img.w}"    (0..img.h).each do |y|      if img.pixel2color(img.get_pixel(x,y)).g > 32        (0...180).each do |a|          rad = a * (Math::PI / 180.0)          d = (x-mx) * Math.cos(rad) + (y-my) * Math.sin(rad)          hough["#{a.to_i}_#{d.to_i}"] = hough["#{a.to_i}_#{d.to_i}"] + 1        end      end    end  end  heat = GD2::Image.import 'heatmap.png'  out = GD2::Image::TrueColor.new(180,max_d*2)  max = hough.values.max  p max  hough.each_pair do |k,v|    a,d = k.split('_').map(&:to_i)    c = (v / max) * 255    c = heat.get_pixel(c,0)    out.set_pixel(a, max_d + d, c)  end  outend

## Scala

Translation of: Kotlin
import java.awt.image._import java.io.Fileimport javax.imageio._ object HoughTransform extends App {    override def main(args: Array[String]) {        val inputData = readDataFromImage(args(0))        val minContrast = if (args.length >= 4) 64 else args(4).toInt        inputData(args(2).toInt, args(3).toInt, minContrast).writeOutputImage(args(1))    }     private def readDataFromImage(filename: String) = {        val image = ImageIO.read(new File(filename))        val width = image.getWidth        val height = image.getHeight        val rgbData = image.getRGB(0, 0, width, height, null, 0, width)        val arrayData = new ArrayData(width, height)        for (y <- 0 until height; x <- 0 until width) {            var rgb = rgbData(y * width + x)            rgb = (((rgb & 0xFF0000) >>> 16) * 0.30 + ((rgb & 0xFF00) >>> 8) * 0.59 +                    (rgb & 0xFF) * 0.11).toInt            arrayData(x, height - 1 - y) = rgb        }        arrayData    }} class ArrayData(val width: Int, val height: Int) {    def update(x: Int, y: Int, value: Int) {        dataArray(x)(y) = value    }     def apply(thetaAxisSize: Int, rAxisSize: Int, minContrast: Int) = {        val maxRadius = Math.ceil(Math.hypot(width, height)).toInt        val halfRAxisSize = rAxisSize >>> 1        val outputData = new ArrayData(thetaAxisSize, rAxisSize)        val sinTable = Array.ofDim[Double](thetaAxisSize)        val cosTable = sinTable.clone()        for (theta <- thetaAxisSize - 1 until -1 by -1) {            val thetaRadians = theta * Math.PI / thetaAxisSize            sinTable(theta) = Math.sin(thetaRadians)            cosTable(theta) = Math.cos(thetaRadians)        }        for (y <- height - 1 until -1 by -1; x <- width - 1 until -1 by -1)            if (contrast(x, y, minContrast))                for (theta <- thetaAxisSize - 1 until -1 by -1) {                    val r = cosTable(theta) * x + sinTable(theta) * y                    val rScaled = Math.round(r * halfRAxisSize / maxRadius).toInt + halfRAxisSize                    outputData.dataArray(theta)(rScaled) += 1                }         outputData    }     def writeOutputImage(filename: String) {        var max = Int.MinValue        for (y <- 0 until height; x <- 0 until width) {            val v = dataArray(x)(y)            if (v > max) max = v        }        val image = new BufferedImage(width, height, BufferedImage.TYPE_INT_ARGB)        for (y <- 0 until height; x <- 0 until width) {            val n = Math.min(Math.round(dataArray(x)(y) * 255.0 / max).toInt, 255)            image.setRGB(x, height - 1 - y, (n << 16) | (n << 8) | 0x90 | -0x01000000)        }        ImageIO.write(image, "PNG", new File(filename))    }     private def contrast(x: Int, y: Int, minContrast: Int): Boolean = {        val centerValue = dataArray(x)(y)        for (i <- 8 until -1 by -1 if i != 4) {            val newx = x + (i % 3) - 1            val newy = y + (i / 3) - 1            if (newx >= 0 && newx < width && newy >= 0 && newy < height &&                    Math.abs(dataArray(newx)(newy) - centerValue) >= minContrast)                return true        }         false    }     private val dataArray = Array.ofDim[Int](width, height)}

## SequenceL

Translation of: Java

Tail-Recursive SequenceL Code:

import <Utilities/Sequence.sl>;import <Utilities/Math.sl>; hough: int(2) * int * int * int -> int(2);hough(image(2), thetaAxisSize, rAxisSize, minContrast) :=    let        initialResult[r,theta] := 0 foreach r within 1 ... rAxisSize, theta within 1 ... thetaAxisSize;         result := houghHelper(image, minContrast, 1, 1, initialResult);         max := vectorMax(vectorMax(result));    in        255 - min(round((result * 255 / max)), 255); houghHelper(image(2), minContrast, x, y, result(2)) :=    let        thetaAxisSize := size(head(result));        rAxisSize := size(result);         width := size(head(image));        height := size(image);        maxRadius := ceiling(sqrt(width^2 + height^2));        halfRAxisSize := rAxisSize / 2;         rs[theta] := round((cos(theta) * x + sin(theta) * y) * halfRAxisSize / maxRadius) + halfRAxisSize                     foreach theta within (0 ... (thetaAxisSize-1)) * pi / thetaAxisSize;         newResult[r,theta] := result[r,theta] + 1 when rs[theta] = r-1 else result[r,theta];         nextResult := result when not checkContrast(image, x, y, minContrast) else newResult;         nextX := 1 when x = width else x + 1;        nextY := y + 1 when x = width else y;    in        nextResult when x = width and y = height    else        houghHelper(image, minContrast, nextX, nextY, nextResult); checkContrast(image(2), x, y, minContrast) :=     let        neighbors[i,j] := image[i,j] when i > 0 and i < size(image) and j > 0 and j < size(image[i])                          foreach i within y-1 ... y+1,                                   j within x-1 ... x+1;    in        some(some(abs(image[y,x] - neighbors) >= minContrast));

C++ Driver Code:

Library: CImg
#include "SL_Generated.h"#include "CImg.h" using namespace cimg_library; int main( int argc, char** argv ){    string fileName = "Pentagon.bmp";    if(argc > 1) fileName = argv[1];    int thetaAxisSize = 640; if(argc > 2) thetaAxisSize = atoi(argv[2]);    int rAxisSize = 480; if(argc > 3) rAxisSize = atoi(argv[3]);    int minContrast = 64; if(argc > 4) minContrast = atoi(argv[4]);    int threads = 0; if(argc > 5) threads = atoi(argv[5]);    char titleBuffer[200];    SLTimer t;     CImg<int> image(fileName.c_str());    int imageDimensions[] = {image.height(), image.width(), 0};    Sequence<Sequence<int> > imageSeq((void*) image.data(), imageDimensions);    Sequence< Sequence<int> > result;     sl_init(threads);     t.start();    sl_hough(imageSeq, thetaAxisSize, rAxisSize, minContrast, threads, result);    t.stop();     CImg<int> resultImage(result[1].size(), result.size());    for(int y = 0; y < result.size(); y++)        for(int x = 0; x < result[y+1].size(); x++)            resultImage(x,result.size() - 1 - y) = result[y+1][x+1];     sprintf(titleBuffer, "SequenceL Hough Transformation: %d X %d Image to %d X %d Result | %d Cores | Processed in %f sec\0",                          image.width(), image.height(), resultImage.width(), resultImage.height(), threads, t.getTime());    resultImage.display(titleBuffer);     sl_done();    return 0;}
Output:

## Sidef

Translation of: Python
require('Imager') func hough(im, width=460, height=360) {     height = 2*floor(height / 2)     var xsize = im.getwidth    var ysize = im.getheight     var ht = %s|Imager|.new(xsize => width, ysize => height)    var canvas = height.of { width.of(255) }     ht.box(filled => true, color => 'white')     var rmax = hypot(xsize, ysize)    var dr = 2*(rmax / height)    var dth = (Num.pi / width)     for y,x in (^ysize ~X ^xsize) {        var col = im.getpixel(x => x, y => y)        var (r,g,b) = col.rgba        (r==255 && g==255 && b==255) && next        for k in ^width {            var th = dth*k            var r = (x*cos(th) + y*sin(th))            var iry = (height/2 + int(r/dr + 0.5))            ht.setpixel(x => k, y => iry, color => 3.of(--canvas[iry][k]))        }    }     return ht} var img = %s|Imager|.new(file => 'Pentagon.png')var ht = hough(img)ht.write(file => 'Hough transform.png')

Library: Tk

## zkl

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl

Translation of: D
const WHITE=0xffFFff, X=0x010101;fcn houghTransform(image,hx=460,hy=360){   if(hy.isOdd) hy-=1; // hy argument must be even   out:=PPM(hx,hy,WHITE);   rMax:=image.w.toFloat().hypot(image.h);   dr,dTh:=rMax/(hy/2), (0.0).pi/hx;    foreach y,x in (image.h,image.w){      if(image[x,y]==WHITE) continue;      foreach iTh in (hx){         th,r:=dTh*iTh, th.cos()*x + th.sin()*y;	 iry:=hy/2 + (r/dr + 0.5).floor();  // y==0 is top 	 if(out[iTh,iry]>0) out[iTh,iry]=out[iTh,iry] - X;      }   }   out}
fcn readPNG2PPM(fileName){   p:=System.popen("convert \"%s\" ppm:-".fmt(fileName),"r");      img:=PPM.readPPM(p);   p.close();   img}houghTransform(readPNG2PPM("pentagon.png")).write(File("pentagon_hough.ppm","wb"));
Output:

The output image looks the same as in the Go solution.