Rosetta Code

Hough transform: Difference between revisions

Page Discussion

Hough transform (view source)

Revision as of 21:10, 9 December 2023

52,268 bytes added ,  6 months ago
m
→‎{{header|Wren}}: Minor tidy
(Fixed a problem with the MATLAB output image)
m (→‎{{header|Wren}}: Minor tidy)
 
(74 intermediate revisions by 38 users not shown)
Line 1:
{{task|Image processing}}[[Category:Graphics algorithms]]
[[Category:Graphics algorithms]]
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.
 
;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, <math>(\rho,\theta)</math>, to the average color of the pixels on the corresponding line of the source image (in <math>(x,y)</math>-space, where the line corresponds to points of the form <math>x\cos\theta + y\sin\theta = \rho</math>). 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.
Line 8 ⟶ 13:
 
There is also a spherical Hough transform, which is more suited to identifying planes in 3D data.
<br><br>
 
=={{header|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]]
<syntaxhighlight lang="bbcbasic"> 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</syntaxhighlight>
 
=={{header|C}}==
{{trans|tcl}}
 
* see [[Example:Hough transform/C]]
{{libheader|cairo}}
 
=={{header|D}}==
(Tested only with the pentagon image given)
{{trans|Go}}
<lang c>#include <stdio.h>
This uses the module from the Grayscale image Task. The output image is the same as in the Go solution.
#include <stdlib.h>
<syntaxhighlight lang="d">import std.math, grayscale_image;
#include <stdint.h>
#include <string.h>
#include <math.h>
 
Image!Gray houghTransform(in Image!Gray im,
#include <cairo.h>
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);
#ifndef M_PI
immutable double dr = rMax / (hy / 2.0);
#define M_PI 3.1415927
immutable double dTh = PI / hx;
#endif
 
foreach (immutable y; 0 .. im.ny) {
#define GR(X,Y) (d[(*s)*(Y)+bpp*(X)+((2)%bpp)])
foreach (immutable x; 0 .. im.nx) {
#define GG(X,Y) (d[(*s)*(Y)+bpp*(X)+((1)%bpp)])
if (im[x, y] == Gray.white)
#define GB(X,Y) (d[(*s)*(Y)+bpp*(X)+((0)%bpp)])
continue;
#define SR(X,Y) (ht[4*tw*((Y)%th)+4*((X)%tw)+2])
foreach (immutable iTh; 0 .. hx) {
#define SG(X,Y) (ht[4*tw*((Y)%th)+4*((X)%tw)+1])
immutable double th = dTh * iTh;
#define SB(X,Y) (ht[4*tw*((Y)%th)+4*((X)%tw)+0])
immutable double r = x * cos(th) + y * sin(th);
#define RAD(A) (M_PI*((double)(A))/180.0)
immutable iry = hy / 2 - cast(int)floor(r / dr + 0.5);
uint8_t *houghtransform(uint8_t *d, int *w, int *h, int *s, int bpp)
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");
}</syntaxhighlight>
 
=={{header|Go}}==
[[file:GoHough.png|right|thumb|Output png]]
{{trans|Python}}
<syntaxhighlight lang="go">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)
}
}</syntaxhighlight>
 
=={{header|Haskell}}==
{{libheader|JuicyPixels}}
<syntaxhighlight lang="haskell">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>"</syntaxhighlight>
'''Example use:'''
<syntaxhighlight lang="text">HoughTransform Pentagon.png hough.png 360 360</syntaxhighlight>
 
=={{header|J}}==
'''Solution:'''
<syntaxhighlight lang="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
)</syntaxhighlight>
[[Image:JHoughTransform.png|320px200px|thumb|right|Resulting viewmat image from J implementation of Hough Transform on sample pentagon image]]'''Example use:'''
<syntaxhighlight lang="j"> require 'viewmat'
require 'media/platimg' NB. addon required pre J8
Img=: readimg_jqtide_ jpath '~temp/pentagon.png'
viewmat 460 360 houghTransform _1 > Img</syntaxhighlight>
<br style="clear:both" />
 
=={{header|Java}}==
'''Code:'''
<syntaxhighlight lang="java">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 rho, theta, y, x, W = *w, H = *h;
{
int th = sqrt(W*W + H*H)/2.0;
int twwidth = 360inputData.width;
int height = inputData.height;
uint8_t *ht = malloc(th*tw*4);
int maxRadius = (int)Math.ceil(Math.hypot(width, height));
memset(ht, 0, 4*th*tw); // black bg
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
for(rho = 0; rho < th; rho++)
{
public final int[] dataArray;
for(theta = 0; theta < tw/*720*/; theta++)
public final int width;
public final int height;
public ArrayData(int width, int height)
{
doublethis(new Cint[width =* cos(RAD(theta)height], width, height);
}
double S = sin(RAD(theta));
uint32_t totalred = 0;
public ArrayData(int[] dataArray, int width, int height)
uint32_t totalgreen = 0;
{
uint32_t totalblue = 0;
uint32_t totalpixthis.dataArray = 0dataArray;
this.width = width;
if ( theta < 45 || (theta > 135 && theta < 225) || theta > 315) {
this.height = height;
for(y = 0; y < H; y++) {
}
double dx = W/2.0 + (rho - (H/2.0-y)*S)/C;
if ( dx < 0 || dx >= W ) continue;
public int get(int x, int y)
x = floor(dx+.5);
{ return dataArray[y * width + x]; }
if (x == W) continue;
totalpix++;
public void set(int x, int y, int value)
totalred += GR(x, y);
{ dataArray[y * width + x] = value; }
totalgreen += GG(x, y);
totalblue += GB(x, y);
public void accumulate(int x, int y, int delta)
}
{ set(x, y, get(x, y) + delta); }
} else {
for(x = 0; x < W; x++) {
public boolean contrast(int x, int y, int minContrast)
double dy = H/2.0 - (rho - (x - W/2.0)*C)/S;
{
if ( dy < 0 || dy >= H ) continue;
y int centerValue = floorget(dy+.5x, y);
if for (yint i == H)8; continuei >= 0; i--)
{
totalpix++;
totalred += GR if (x,i == y4);
continue;
totalgreen += GG(x, y);
int newx = x + (i % 3) - 1;
totalblue += GB(x, y);
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;
}
ifreturn ( totalpix > 0 ) {false;
}
double dp = totalpix;
SR(theta, rho) = (int)(totalred/dp) &0xff;
public int getMax()
SG(theta, rho) = (int)(totalgreen/dp) &0xff;
{
SB(theta, rho) = (int)(totalblue/dp) &0xff;
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;
}
 
*h = th; // sqrt(W*W+H*H)/2
*w = tw; // 360
*s = 4*tw;
return ht;
}
 
int main(int argc, char **argv)
{
cairo_surface_t *inputimg = NULL;
cairo_surface_t *houghimg = NULL;
public static void writeOutputImage(String filename, ArrayData arrayData) throws IOException
uint8_t *houghdata = NULL, *inputdata = NULL;
{
int w, h, s, bpp;
int max = arrayData.getMax();
 
BufferedImage outputImage = new BufferedImage(arrayData.width, arrayData.height, BufferedImage.TYPE_INT_ARGB);
if ( argc < 3 ) return EXIT_FAILURE;
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
inputimg = cairo_image_surface_create_from_png(argv[1]);
w = cairo_image_surface_get_width(inputimg);
h = cairo_image_surface_get_height(inputimg);
s = cairo_image_surface_get_stride(inputimg);
bpp = cairo_image_surface_get_format(inputimg);
switch(bpp)
{
ArrayData inputData = getArrayDataFromImage(args[0]);
case CAIRO_FORMAT_ARGB32: bpp = 4; break;
int minContrast = (args.length >= 4) ? 64 : Integer.parseInt(args[4]);
case CAIRO_FORMAT_RGB24: bpp = 3; break;
ArrayData outputData = houghTransform(inputData, Integer.parseInt(args[2]), Integer.parseInt(args[3]), minContrast);
case CAIRO_FORMAT_A8: bpp = 1; break;
writeOutputImage(args[1], outputData);
default:
return;
fprintf(stderr, "unsupported\n");
goto destroy;
}
}</syntaxhighlight>
 
[[Image:JavaHoughTransform.png|640px480px|thumb|right|Output from example pentagon image]]'''Example use:'''
inputdata = cairo_image_surface_get_data(inputimg);
<pre>java HoughTransform pentagon.png JavaHoughTransform.png 640 480 100</pre>
houghdata = houghtransform(inputdata, &w, &h, &s, bpp);
<br style="clear:both" />
printf("w=%d, h=%d\n", w, h);
houghimg = cairo_image_surface_create_for_data(houghdata,
CAIRO_FORMAT_RGB24,
w, h, s);
cairo_surface_write_to_png(houghimg, argv[2]);
destroy:
if (inputimg != NULL) cairo_surface_destroy(inputimg);
if (houghimg != NULL) cairo_surface_destroy(houghimg);
 
=={{header|Julia}}==
return EXIT_SUCCESS;
<syntaxhighlight lang="julia">using ImageFeatures
}</lang>
 
img = fill(false,5,5)
img[3,:] .= true
 
println(hough_transform_standard(img))
</syntaxhighlight> {{output}} <pre>
Tuple{Float64,Float64}[(3.0, 1.5708)]
</pre>
 
=={{header|Kotlin}}==
{{trans|Java}}
<syntaxhighlight lang="scala">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])
}</syntaxhighlight>
 
=={{header|Maple}}==
<syntaxhighlight lang="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));</syntaxhighlight>
 
=={{header|Mathematica}} / {{header|Wolfram Language}}==
 
<syntaxhighlight lang="mathematica">
Radon[image, Method -> "Hough"]
</syntaxhighlight>
 
=={{header|MATLAB}}==
This solution takes an image and the theta resolution as inputs. The image itself must be a 2-D boolean array. This array is constructed such that all of the pixels on an edge have the value "true." This can be done for a normal image using an "edge finding" algorithm to preprocess the image. In the case of the example image the hexagon "edges" are black pixels. So when the image is imported into MATLAB simply say any pixel colored black is true. The syntax is usually, cdata < 255. Where the vale 255 represents white and 0 represents black.
 
* see [[Example:Hough transform/MATLAB]]
<lang MATLAB>function [rho,theta,houghSpace] = houghTransform(theImage,thetaSampleFrequency)
 
=={{header|Nim}}==
theImage = flipud(theImage);
{{trans|D}}
[width,height] = size(theImage);
{{libheader|nimPNG}}
We use the modules from tasks “Bitmap” and “Grayscale image”, adding necessary conversions to read and write PNG files.
rhoLimit = norm([width height]);
<syntaxhighlight lang="nim">import lenientops, math
rho = (-rhoLimit:1:rhoLimit);
import grayscale_image
theta = (0:thetaSampleFrequency:pi);
 
const White = 255
numThetas = numel(theta);
 
func houghTransform*(img: GrayImage; hx = 460; hy = 360): GrayImage =
houghSpace = zeros(numel(rho),numThetas);
assert not img.isNil
accumulator = zeros(numel(theImage),numThetas);
assert hx > 0 and hy > 0
assert (hy and 1) == 0, "hy argument must be even"
%Preallocate cosine and sine calculations to increase speed. In
 
%addition to precallculating sine and cosine we are also multiplying
result = newGrayImage(hx, hy)
%them by the proper pixel weights such that the rows will be indexed by
result.fill(White)
%the pixel number and the columns will be indexed by the thetas.
 
%Example: cosine(3,:) is 2*cosine(0 to pi)
let rMax = hypot(img.w.toFloat, img.h.toFloat)
% cosine(:,1) is (0 to width of image)*cosine(0)
let dr = rMax / (hy / 2)
cosine = (0:width-1)'*cos(theta); %Matrix Outerproduct
let dTh = PI / hx
sine = (0:height-1)'*sin(theta); %Matrix Outerproduct
 
for y in 0..<img.h:
%Calculate the hough transform of each "edge" pixel and store that
for x in 0..<img.w:
%curve in the accumulator array. The columns of which are indexed by
%theta and theif rowsimg[x, arey] an== arbitraryWhite: index.continue
for iTh in 0..<hx:
index let th = 1;dTh * iTh
let r = x * cos(th) + y * sin(th)
for x let iry = hy div 2 - (1:widthr / dr).toInt
forif yresult[iTh, =iry] (1> 0:height)
result[iTh, iry] if(theImage(x= result[iTh,y)) iry] - 1
 
accumulator(index,:) = cosine(x,:) + sine(y,:);
 
index = index + 1;
when isMainModule:
end
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)</syntaxhighlight>
 
=={{header|Perl}}==
{{trans|Sidef}}
<syntaxhighlight lang="perl">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');
</syntaxhighlight>
 
=={{header|Phix}}==
{{libheader|Phix/pGUI}}
{{trans|Sidef}}
<!--<syntaxhighlight lang="phix">(notonline)-->
<span style="color: #000080;font-style:italic;">-- demo\rosetta\Hough_transform.exw</span>
<span style="color: #008080;">without</span> <span style="color: #008080;">js</span> <span style="color: #000080;font-style:italic;">-- IupImage, imImage, im_width/height/pixel, allocate,
-- imFileImageLoadBitmap, IupImageFromImImage</span>
<span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">hypot</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span><span style="color: #0000FF;">+</span><span style="color: #000000;">b</span><span style="color: #0000FF;">*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">hough_transform</span><span style="color: #0000FF;">(</span><span style="color: #000000;">imImage</span> <span style="color: #000000;">im</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">width</span><span style="color: #0000FF;">=</span><span style="color: #000000;">460</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">height</span><span style="color: #0000FF;">=</span><span style="color: #000000;">360</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">height</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">height</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">xsize</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">im_width</span><span style="color: #0000FF;">(</span><span style="color: #000000;">im</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">ysize</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">im_height</span><span style="color: #0000FF;">(</span><span style="color: #000000;">im</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">canvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">255</span><span style="color: #0000FF;">,</span><span style="color: #000000;">width</span><span style="color: #0000FF;">),</span><span style="color: #000000;">height</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">rmax</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">hypot</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xsize</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ysize</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">dr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">rmax</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">height</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">dth</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #004600;">PI</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">width</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">ysize</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">xsize</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">g</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">im_pixel</span><span style="color: #0000FF;">(</span><span style="color: #000000;">im</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">255</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">width</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">th</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dth</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">r2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">th</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">th</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">iry</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">height</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span> <span style="color: #0000FF;">+</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r2</span><span style="color: #0000FF;">/</span><span style="color: #000000;">dr</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">0.5</span><span style="color: #0000FF;">))+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">cik</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">canvas</span><span style="color: #0000FF;">[</span><span style="color: #000000;">iry</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">cik</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">canvas</span><span style="color: #0000FF;">[</span><span style="color: #000000;">iry</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cik</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">canvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">flatten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (needed by IupImage)</span>
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">new_img</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupImage</span><span style="color: #0000FF;">(</span><span style="color: #000000;">width</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">height</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">canvas</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">255</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">IupSetStrAttributeId</span><span style="color: #0000FF;">(</span><span style="color: #000000;">new_img</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d %d %d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">new_img</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">pError</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">allocate</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">machine_word</span><span style="color: #0000FF;">())</span>
<span style="color: #000000;">imImage</span> <span style="color: #000000;">im1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">imFileImageLoadBitmap</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"Pentagon320.png"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pError</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">im1</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #008000;">"error opening Pentagon320.png"</span> <span style="color: #7060A8;">abort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">Ihandln</span> <span style="color: #000000;">image1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">IupImageFromImImage</span><span style="color: #0000FF;">(</span><span style="color: #000000;">im1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">image2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">hough_transform</span><span style="color: #0000FF;">(</span><span style="color: #000000;">im1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">label1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupLabel</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">label2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupLabel</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupSetAttributeHandle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">label1</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"IMAGE"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">image1</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetAttributeHandle</span><span style="color: #0000FF;">(</span><span style="color: #000000;">label2</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"IMAGE"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">image2</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">IupHbox</span><span style="color: #0000FF;">({</span><span style="color: #000000;">label1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">label2</span><span style="color: #0000FF;">}))</span>
<span style="color: #7060A8;">IupSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"TITLE"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"Hough transform"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- (no chance...)</span>
<span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<!--</syntaxhighlight>-->
 
=={{header|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.
<syntaxhighlight lang="python">
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()
 
</syntaxhighlight>
 
{{omit from|PARI/GP}}
 
=={{header|Racket}}==
* see [[Hough transform/Racket]]
 
=={{header|Raku}}==
(formerly Perl 6)
The <code>GD</code> module the output palette to 255 colors, so only transform darker pixels in the image.
{{trans|Perl}}
<syntaxhighlight lang="raku" line>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;</syntaxhighlight>
See [https://github.com/thundergnat/rc/blob/master/img/hough-transform.png Hough Transform] (offsite .png image)
 
=={{header|Ruby}}==
 
<syntaxhighlight lang="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</syntaxhighlight>
 
=={{header|Rust}}==
<syntaxhighlight lang="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(())
}
 
</syntaxhighlight>
 
 
=={{header|Scala}}==
{{trans|Kotlin}}
<syntaxhighlight lang="scala">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)
}</syntaxhighlight>
 
=={{header|SequenceL}}==
{{trans|Java}}
'''Tail-Recursive SequenceL Code:'''<br>
<syntaxhighlight lang="sequencel">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));</syntaxhighlight>
 
'''C++ Driver Code:'''<br>
{{libheader|CImg}}
<syntaxhighlight lang="c">#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());
%%During the accumulator preallocation there is enough memory allocated
for(int y = 0; y < result.size(); y++)
%%should every single pixel happen to be an "edge" pixel. This little
for(int x = 0; x < result[y+1].size(); x++)
%%line deallocates the unused memory.
resultImage(x,result.size() - 1 - y) = result[y+1][x+1];
if index < numel(theImage)
accumulator(index:end,:) = [];
end
sprintf(titleBuffer, "SequenceL Hough Transformation: %d X %d Image to %d X %d Result | %d Cores | Processed in %f sec\0",
for i = (1:numThetas)
image.width(), image.height(), resultImage.width(), resultImage.height(), threads, t.getTime());
houghSpace(:,i) = hist(accumulator(:,i),rho);
resultImage.display(titleBuffer);
end
 
pcolorsl_done(theta,rho,houghSpace);
shadingreturn flat0;
}</syntaxhighlight>
title('Hough Transform');
xlabel('Theta (radians)');
ylabel('Rho (pixels)');
colormap('gray');
 
{{out}}
end</lang>
[http://i.imgur.com/McCuZP3.png Output Screenshot]
 
=={{header|Sidef}}==
{{trans|Python}}
<syntaxhighlight lang="ruby">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')</syntaxhighlight>
 
Sample Usage:
<lang MATLAB>>> uiopen('C:\Documents and Settings\owner\Desktop\Chris\MATLAB\RosettaCode\180px-Pentagon.png',1)
>> houghTransform(cdata(:,:,1)<255,1/200); %The image from uiopen is stored in cdata. The reason why the image is cdata<255 is because the "edge" pixels are black.</lang>
[[Image:HoughTransformHex.png|thumb|left|360x200px|Image produced by MATLAB implementation of the Hough transform when applied to the sample pentagon image.]]
<br style="clear:both" />
=={{header|Tcl}}==
{{libheader|Tk}}
 
* See [[Example:Hough transform/Tcl]]
<lang tcl>package require Tk
 
=={{header|Wren}}==
set PI 3.1415927
{{trans|Kotlin}}
proc HoughTransform {src trg {fieldColor "#000000"}} {
{{libheader|DOME}}
global PI
<syntaxhighlight lang="wren">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 }
set w [image width $src]
set h [image height $src]
set targetH [expr {int(hypot($w, $h)/2)}]
 
class ArrayData {
# Configure the target buffer
$trgconstruct configure -new(width, 360 -height) $targetH{
_width = width
$trg put $fieldColor -to 0 0 359 [expr {$targetH-1}]
_height = height
_dataArray = List.filled(width * height, 0)
}
 
width { _width }
# Iterate over the target's space of pixels.
height { _height }
for {set rho 0} {$rho < $targetH} {incr rho} {
set row {}
for {set theta 0} {$theta < 720} {incr theta} {
set cos [expr {cos($theta/180.0*$PI)}]
set sin [expr {sin($theta/180.0*$PI)}]
set totalRed 0
set totalGreen 0
set totalBlue 0
set totalPix 0
 
[x, y] { _dataArray[y * _width + x] }
# Sum the colors of the line with equation x*cos(θ) + y*sin(θ) = ρ
if {$theta<45 || ($theta>135 && $theta<225) || $theta>315} {
# For these half-quadrants, it's better to iterate by 'y'
for {set y 0} {$y<$h} {incr y} {
set x [expr {
$w/2 + ($rho - ($h/2-$y)*$sin)/$cos
}]
if {$x < 0 || $x >= $w} continue
set x [expr {round($x)}]
if {$x == $w} continue
incr totalPix
lassign [$src get $x $y] r g b
incr totalRed $r
incr totalGreen $g
incr totalBlue $b
}
} else {
# For the other half-quadrants, it's better to iterate by 'x'
for {set x 0} {$x<$w} {incr x} {
set y [expr {
$h/2 - ($rho - ($x-$w/2)*$cos)/$sin
}]
if {$y < 0 || $y >= $h} continue
set y [expr {round($y)}]
if {$y == $h} continue
incr totalPix
lassign [$src get $x $y] r g b
incr totalRed $r
incr totalGreen $g
incr totalBlue $b
}
}
 
[x, y]=(v) { _dataArray[y * _width + x] = v }
# Convert the summed colors back into a pixel for insertion into
 
# the target buffer.
transform(thetaAxisSize, rAxisSize, minContrast) {
if {$totalPix > 0} {
var maxRadius = Math.ceil(Hypot.call(_width, _height))
set totalPix [expr {double($totalPix)}]
var halfRAxisSize = rAxisSize >> 1
set col [format "#%02x%02x%02x" \
var outputData = ArrayData.new(thetaAxisSize, rAxisSize)
[expr {round($totalRed/$totalPix)}] \
// x output ranges from 0 to pi
[expr {round($totalGreen/$totalPix)}] \
// y output ranges from -maxRadius to maxRadius
[expr {round($totalBlue/$totalPix)}]]
var sinTable = List.filled(thetaAxisSize, 0)
} else {
var cosTable = List.filled(thetaAxisSize, 0)
set col $fieldColor
for (theta in thetaAxisSize - 1..0) {
}
var thetaRadians = theta * Num.pi / thetaAxisSize
lappend row $col
sinTable[theta] = Math.sin(thetaRadians)
}
cosTable[theta] = Math.cos(thetaRadians)
$trg put [list $row] -to 0 $rho
}
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
}
}</lang>
 
accumulate(x, y, delta) { this[x, y] = this[x, y] + delta }
===Demonstration Code===
 
Takes the name of the image to apply the transform to as an argument. If using PNG images,
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)</syntaxhighlight>
 
{{out}}
<pre>
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.
</pre>
 
=={{header|zkl}}==
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
{{trans|D}}
<syntaxhighlight lang="zkl">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
}</syntaxhighlight>
 
<syntaxhighlight lang="zkl">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"));</syntaxhighlight>
{{out}}
The output image looks the same as in the Go solution.
 
http://www.zenkinetic.com/Images/RosettaCode/pentagon_hough.jpg
{{works with|Tk|8.6}} or {{libheader|TkImg}}
<lang tcl># Demonstration code
if {[catch {
package require Tk 8.6; # Just for PNG format handler
}] == 1} then {catch {
package require Img
}}
# If neither Tk8.6 nor Img, then only GIF and PPM images can be loaded
 
{{omit from|PARI/GP}}
set f [lindex $argv 0]
image create photo srcImg -file $f
image create photo targetImg
pack [labelframe .l1 -text Source] [labelframe .l2 -text Target]
pack [label .l1.i -image srcImg]
pack [label .l2.i -image targetImg]
# Postpone until after we've drawn ourselves
after idle HoughTransform srcImg targetImg [lrange $argv 1 end]</lang>
 
[[Category:Geometry]]
[[Image:Hough-Pentagon-Tcl-Results.gif|thumb|left|360x200px|Image produced by Tcl implementation of the Hough transform when applied to the sample pentagon image.]]
PureFox
9,485

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/136333...349998"