# Hough transform

Hough transform
You are encouraged to solve this task according to the task description, using any language you may know.
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, ${\displaystyle (\rho ,\theta )}$, 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.

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

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

him := image.NewGray(image.Rect(0, 0, ntx, mry))
draw.Draw(him, him.Bounds(), image.NewUniform(color.White),
image.Point{}, 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)
}
}


## Haskell

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) -> a
dot (x1, y1) (x2, y2) = x1 * x2 + y1 * y2

mag
:: Floating a
=> (a, a) -> a
mag a = sqrt $dot a a sub :: Num a => (a, a) -> (a, a) -> (a, a) sub (x1, y1) (x2, y2) = (x1 - x2, y1 - y2) fromIntegralP :: (Integral a, Num b) => (a, a) -> (b, b) fromIntegralP (x, y) = (fromIntegral x, fromIntegral y) {- Create a Hough space image with y+ measuring the distance from the center of the input image on the range of 0 to half the hypotenuse and x+ measuring from [0, 2 * pi]. The origin is in the upper left, so y is increasing down. The image is scaled according to thetaSize and distSize. -} hough :: Image PixelRGB8 -> Int -> Int -> Image PixelRGB8 hough image thetaSize distSize = hImage where width = imageWidth image height = imageHeight image wMax = width - 1 hMax = height - 1 xCenter = wMax div 2 yCenter = hMax div 2 lumaMap = extractLumaPlane image gradient x y = let orig = pixelAt lumaMap x y x_ = pixelAt lumaMap (min (x + 1) wMax) y y_ = pixelAt lumaMap x (min (y + 1) hMax) in fromIntegralP (orig - x_, orig - y_) gradMap = [ ((x, y), gradient x y) | x <- [0 .. wMax] , y <- [0 .. hMax] ] -- The longest distance from the center, half the hypotenuse of the image. distMax :: Double distMax = (sqrt . fromIntegral$ 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 $"Usage: " ++ prog ++ " <image-file> <out-file.png> <width> <height>"  Example use: HoughTransform Pentagon.png hough.png 360 360  ## J Solution: NB.*houghTransform v Produces a density plot of image y in hough space NB. y is picture as an array with 1 at non-white points, NB. x is resolution (width,height) of resulting image houghTransform=: dyad define 'w h'=. x NB. width and height of target image theta=. o. (%~ 0.5+i.) w NB. theta in radians from 0 to π rho=. (4$.$. |.y) +/ .* 2 1 o./theta NB. rho for each pixel at each theta 'min max'=. (,~-) +/&.:*:$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
)


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;
}
}


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.BufferedImage
import java.io.File
import 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"]


## Nim

Translation of: D
Library: nimPNG

We use the modules from tasks “Bitmap” and “Grayscale image”, adding necessary conversions to read and write PNG files.

import lenientops, math
import grayscale_image

const White = 255

func houghTransform*(img: GrayImage; hx = 460; hy = 360): GrayImage =
assert not img.isNil
assert hx > 0 and hy > 0
assert (hy and 1) == 0, "hy argument must be even"

result = newGrayImage(hx, hy)
result.fill(White)

let rMax = hypot(img.w.toFloat, img.h.toFloat)
let dr = rMax / (hy / 2)
let dTh = PI / hx

for y in 0..<img.h:
for x in 0..<img.w:
if img[x, y] == White: continue
for iTh in 0..<hx:
let th = dTh * iTh
let r = x * cos(th) + y * sin(th)
let iry = hy div 2 - (r / dr).toInt
if result[iTh, iry] > 0:
result[iTh, iry] = result[iTh, iry] - 1

when isMainModule:
import nimPNG
import bitmap

const Input = "Pentagon.png"
const Output = "Hough.png"

let pngImage = loadPNG24(seq[byte], Input).get()
let grayImage = newGrayImage(pngImage.width, pngImage.height)

# Convert to grayscale.
for i in 0..grayImage.pixels.high:
grayImage.pixels[i] = Luminance(0.2126 * pngImage.data[3 * i] +
0.7152 * pngImage.data[3 * i + 1] +
0.0722 * pngImage.data[3 * i + 2] + 0.5)

# Apply Hough transform and convert to an RGB image.
let houghImage = grayImage.houghTransform().toImage()

# Save into a PNG file.
# As nimPNG expects a sequence of bytes, not a sequence of colors, we have to make a copy.
var data = newSeqOfCap[byte](houghImage.pixels.len * 3)
for color in houghImage.pixels:
data.add([color.r, color.g, color.b])
discard savePNG24(Output, data, houghImage.w, houghImage.h)


## Perl

Translation of: Sidef
use strict;
use warnings;

use Imager;

use constant pi => 3.14159265;

sub hough {
my($im) = shift; my($width)  = shift || 460;
my($height) = shift || 360;$height = 2 * int $height/2;$height = 2 * int $height/2; my($xsize, $ysize) = ($im->getwidth, $im->getheight); my$ht = Imager->new(xsize => $width, ysize =>$height);
my @canvas;
for my $i (0..$height-1) { for my $j (0..$width-1) { $canvas[$i][$j] = 255 } }$ht->box(filled => 1, color => 'white');

my $rmax = sqrt($xsize**2 + $ysize**2); my$dr   = 2 * $rmax /$height;
my $dth = pi /$width;

for my $x (0..$xsize-1) {
for my $y (0..$ysize-1) {
my $col =$im->getpixel(x => $x, y =>$y);
my($r,$g,$b) =$col->rgba;
next if $r==255; # &&$g==255 && $b==255; for my$k (0..$width) { my$th = $dth*$k;
my $r2 = ($x*cos($th) +$y*sin($th)); my$iry = ($height/2 + int($r2/$dr + 0.5));$ht->setpixel(x => $k, y =>$iry, color => [ ($canvas[$iry][$k]--) x 3] ); } } } return$ht;
}

my $img = Imager->new;$img->read(file => 'ref/pentagon.png') or die "Cannot read: ", $img->errstr; my$ht = hough($img);$ht->write(file => 'hough_transform.png');


## Phix

Library: Phix/pGUI
Translation of: Sidef
-- demo\rosetta\Hough_transform.exw
without js -- IupImage, imImage, im_width/height/pixel, allocate,
-- imFileImageLoadBitmap, IupImageFromImImage
include 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_height(im)
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
if cik>=0 then
canvas[iry][k] = cik
end if
end for
end if
end for
end for
canvas = flatten(canvas) -- (needed by IupImage)
Ihandle new_img = IupImage(width, height, canvas)
for c=0 to 255 do
IupSetStrAttributeId(new_img,"",c,"%d %d %d",{c,c,c})
end for
return new_img
end function

IupOpen()

atom pError = allocate(machine_word())
imImage im1 = imFileImageLoadBitmap("Pentagon320.png",0,pError)
if im1=NULL then ?"error opening Pentagon320.png" abort(0) end if
Ihandln 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")
IupShow(dlg)
if platform()!=JS then -- (no chance...)
IupMainLoop()
IupClose()
end if


## 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, sin
from 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()


## Raku

(formerly 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;

(^$width).map: ->$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)

## 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
out
end


## Rust

//! Contributed by Gavin Baker <gavinb@antonym.org>
//! Adapted from the Go version

use std::fs::File;
use std::io::{self, BufRead, BufReader, BufWriter, Read, Write};
use std::iter::repeat;

/// Simple 8-bit grayscale image
struct ImageGray8 {
width: usize,
height: usize,
data: Vec<u8>,
}

fn load_pgm(filename: &str) -> io::Result<ImageGray8> {
// Open file
let mut file = BufReader::new(File::open(filename)?);

// Read header
let mut magic_in = String::new();
let _ = file.read_line(&mut magic_in)?;
let mut width_in = String::new();
let _ = file.read_line(&mut width_in)?;
let mut height_in = String::new();
let _ = file.read_line(&mut height_in)?;
let mut maxval_in = String::new();
let _ = file.read_line(&mut maxval_in)?;

assert_eq!(magic_in, "P5\n");
assert_eq!(maxval_in, "255\n");

// Parse header
let width = width_in
.trim()
.parse::<usize>()
.map_err(|_| io::ErrorKind::InvalidData)?;
let height: usize = height_in
.trim()
.parse::<usize>()
.map_err(|_| io::ErrorKind::InvalidData)?;

println!("Reading pgm file {}: {} x {}", filename, width, height);

// Create image and allocate buffer
let mut img = ImageGray8 {
width,
height,
data: vec![],
};

// Read image data
let expected_bytes = width * height;
let bytes_read = file.read_to_end(&mut img.data)?;
if bytes_read != expected_bytes {
let kind = if bytes_read < expected_bytes {
io::ErrorKind::UnexpectedEof
} else {
io::ErrorKind::InvalidData
};
let msg = format!("expected {} bytes", expected_bytes);
return Err(io::Error::new(kind, msg));
}

Ok(img)
}

fn save_pgm(img: &ImageGray8, filename: &str) {
// Open file
let mut file = BufWriter::new(File::create(filename).unwrap());

// Write header
if let Err(e) = writeln!(&mut file, "P5\n{}\n{}\n255", img.width, img.height) {
println!("Failed to write header: {}", e);
}

println!(
"Writing pgm file {}: {} x {}",
filename, img.width, img.height
);

// Write binary image data
if let Err(e) = file.write_all(&(img.data[..])) {
println!("Failed to image data: {}", e);
}
}

#[allow(clippy::cast_precision_loss)]
#[allow(clippy::clippy::cast_possible_truncation)]
fn hough(image: &ImageGray8, out_width: usize, out_height: usize) -> ImageGray8 {
let in_width = image.width;
let in_height = image.height;

// Allocate accumulation buffer
let out_height = ((out_height / 2) * 2) as usize;
let mut accum = ImageGray8 {
width: out_width,
height: out_height,
data: repeat(255).take(out_width * out_height).collect(),
};

// Transform extents
let rmax = (in_width as f64).hypot(in_height as f64);
let dr = rmax / (out_height / 2) as f64;
let dth = std::f64::consts::PI / out_width as f64;

// Process input image in raster order
for y in 0..in_height {
for x in 0..in_width {
let in_idx = y * in_width + x;
let col = image.data[in_idx];
if col == 255 {
continue;
}

// Project into rho,theta space
for jtx in 0..out_width {
let th = dth * (jtx as f64);
let r = (x as f64) * (th.cos()) + (y as f64) * (th.sin());

let iry = out_height as i64 / 2 - (r / (dr as f64) + 0.5).floor() as i64;
#[allow(clippy::clippy::cast_sign_loss)]
let out_idx = (jtx as i64 + iry * out_width as i64) as usize;
let col = accum.data[out_idx];
if col > 0 {
accum.data[out_idx] = col - 1;
}
}
}
}
accum
}

fn main() -> io::Result<()> {
let image = load_pgm("resources/Pentagon.pgm")?;
let accum = hough(&image, 460, 360);
save_pgm(&accum, "hough.pgm");
Ok(())
}


## Scala

Translation of: Kotlin
import java.awt.image._
import java.io.File
import 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

## Wren

Translation of: Kotlin
Library: DOME
import "graphics" for Canvas, Color, ImageData
import "dome" for Window, Process
import "math" for Math

var Hypot = Fn.new { |x, y| (x*x + y*y).sqrt }

class ArrayData {
construct new(width, height) {
_width  = width
_height = height
_dataArray = List.filled(width * height, 0)
}

width  { _width }
height { _height }

[x, y] { _dataArray[y * _width + x] }

[x, y]=(v) { _dataArray[y * _width + x] = v }

transform(thetaAxisSize, rAxisSize, minContrast) {
var maxRadius = Math.ceil(Hypot.call(_width, _height))
var halfRAxisSize = rAxisSize >> 1
var outputData = ArrayData.new(thetaAxisSize, rAxisSize)
// x output ranges from 0 to pi
// y output ranges from -maxRadius to maxRadius
var sinTable = List.filled(thetaAxisSize, 0)
var cosTable = List.filled(thetaAxisSize, 0)
for (theta in thetaAxisSize - 1..0) {
var thetaRadians = theta * Num.pi / thetaAxisSize
sinTable[theta] = Math.sin(thetaRadians)
cosTable[theta] = Math.cos(thetaRadians)
}
for (y in _height - 1..0) {
for (x in _width - 1..0) {
if (contrast(x, y, minContrast)) {
for (theta in thetaAxisSize - 1..0) {
var r = cosTable[theta] * x + sinTable[theta] * y
var rScaled = Math.round(r * halfRAxisSize / maxRadius) + halfRAxisSize
outputData.accumulate(theta, rScaled, 1)
}
}
}
}
return outputData
}

accumulate(x, y, delta) { this[x, y] = this[x, y] + delta }

contrast(x, y, minContrast) {
var centerValue = this[x, y]
for (i in 8..0) {
if (i != 4) {
var newx = x + i % 3 - 1
var newy = y + (i / 3).truncate - 1
if (newx >= 0 && newx < width && newy >= 0 && newy < height &&
Math.abs(this[newx, newy] - centerValue) >= minContrast) return true
}
}
return false
}

max {
var max = _dataArray[0]
for (i in width * height - 1..1) {
if (_dataArray[i] > max) max = _dataArray[i]
}
return max
}
}

class HoughTransform {
construct new(inFile, outFile, width, height, minCont) {
Window.title = "Hough Transform"
Window.resize(width, height)
Canvas.resize(width, height)
_width   = width
_height  = height
_inFile  = inFile
_outFile = outFile
_minCont = minCont
}

init() {
var dataArray = readInputFromImage(_inFile)
dataArray = dataArray.transform(_width, _height, _minCont)
writeOutputImage(_outFile, dataArray)
}

readInputFromImage(filename) {
var inputImage = ImageData.load(filename)
var width  = inputImage.width
var height = inputImage.height
var rgbData = []
for (y in 0...height) {
for (x in 0...width) rgbData.add(inputImage.pget(x, y))
}
var arrayData = ArrayData.new(width, height)
// Flip y axis when reading image
for (y in 0...height) {
for (x in 0...width) {
var rgbValue = rgbData[y * width + x]
rgbValue = (rgbValue.r * 0.3 + rgbValue.g * 0.59 + rgbValue.b * 0.11).floor
arrayData[x, height - 1 - y] = rgbValue
}
}
return arrayData
}

writeOutputImage(filename, arrayData) {
var max = arrayData.max
var outputImage = ImageData.create(filename, arrayData.width, arrayData.height)
for (y in 0...arrayData.height) {
for (x in 0...arrayData.width) {
var n = Math.min(Math.round(arrayData[x, y] * 255 / max), 255)
var c = Color.new(n, n, 0x90)
outputImage.pset(x, arrayData.height - 1 - y, c)
}
}
outputImage.draw(0, 0)
outputImage.saveToFile(filename)
}

update() {}

draw(alpha) {}
}

var args = Process.args
System.print(args)
if (args.count != 7) Fiber.abort("There should be exactly 5 command line arguments.")
var inFile  = args[2]
var outFile = args[3]
var width   = Num.fromString(args[4])
var height  = Num.fromString(args[5])
var minCont = Num.fromString(args[6])
var Game = HoughTransform.new(inFile, outFile, width, height, minCont)

Output:
When called with: 'dome hough_transform.wren Pentagon.png Pentagon2.png 640 480 100' the resulting image is similar to that of the Java entry.


## 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.