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This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
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{{task|Image processing}} [[Category:Graphics algorithms]]
;Task: Implement the [[wp:Hough transform|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, , to the average color of the pixels on the corresponding line of the source image (in -space, where the line corresponds to points of the form ). 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.
[[Image:Pentagon.png|thumb|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 and the other for , 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
{{works with|BBC BASIC for Windows}} BBC BASIC uses Cartesian coordinates so the image is 'upside down' compared with some other solutions. [[Image:hough_bbc.gif|right]]
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
C
- see [[Example:Hough transform/C]]
D
{{trans|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
[[file:GoHough.png|right|thumb|Output png]] {{trans|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)
}
}
Haskell
{{libheader|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:'''
## J
'''Solution:'''
```j
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
)
[[Image:JHoughTransform.png|320px200px|thumb|right|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;
}
}
[[Image:JavaHoughTransform.png|640px480px|thumb|right|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
{{trans|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));
=={{header|Mathematica}} / {{header|Wolfram Language}}==
Radon[image, Method -> "Hough"]
MATLAB
- see [[Example:Hough transform/MATLAB]]
Perl
{{trans|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;
$height = 2 * int $height/2;
my($xsize, $ysize) = ($im->getwidth, $im->getheight);
my $ht = Imager->new(xsize => $width, ysize => $height);
for my $i (0..$height-1) { for my $j (0..$width-1) { $canvas[$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;
}
my $img = Imager->new;
$img->read(file => 'ref/pentagon.png') or die "Cannot read: ", $img->errstr;
$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.
{{trans|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 [https://github.com/thundergnat/rc/blob/master/img/hough-transform.png Hough Transform] (offsite .png image)
Phix
{{libheader|pGUI}} {{trans|Sidef}}
-- demo\rosetta\Hough_transform.exw
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_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_img
end 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 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")
IupCloseOnEscape(dlg)
IupShow(dlg)
IupMainLoop()
IupClose()
Python
{{libheader|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()
{{omit from|PARI/GP}}
Racket
- see [[Example:Hough transform/Racket]]
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
Scala
{{trans|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
{{trans|Java}} '''Tail-Recursive SequenceL Code:'''
;
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:'''
{{libheader|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;
}
{{out}} [http://i.imgur.com/McCuZP3.png Output Screenshot]
Sidef
{{trans|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')
Tcl
{{libheader|Tk}}
- See [[Example:Hough transform/Tcl]]
zkl
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl {{trans|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"));
{{out}} The output image looks the same as in the Go solution.
http://www.zenkinetic.com/Images/RosettaCode/pentagon_hough.jpg
{{omit from|PARI/GP}}
[[Category:Geometry]]