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Canny edge detector

Canny edge detector
You are encouraged to solve this task according to the task description, using any language you may know.

Write a program that performs so-called canny edge detection on an image.

A possible algorithm consists of the following steps:

1. Noise reduction.   May be performed by Gaussian filter.

2. Compute intensity gradient   (matrices ${\displaystyle G_{x}}$ and ${\displaystyle G_{y}}$)   and its magnitude   ${\displaystyle G}$:
${\displaystyle G={\sqrt {G_{x}^{2}+G_{y}^{2}}}}$
May be performed by convolution of an image with Sobel operators.

3. Non-maximum suppression.
For each pixel compute the orientation of intensity gradient vector:   ${\displaystyle \theta ={\rm {atan2}}\left(G_{y},\,G_{x}\right)}$.
Transform   angle ${\displaystyle \theta }$   to one of four directions:   0, 45, 90, 135 degrees.
Compute new array   ${\displaystyle N}$:     if         ${\displaystyle G\left(p_{a}\right)
where   ${\displaystyle p}$   is the current pixel,   ${\displaystyle p_{a}}$   and   ${\displaystyle p_{b}}$   are the two neighbour pixels in the direction of gradient,
then     ${\displaystyle N(p)=G(p)}$,       otherwise   ${\displaystyle N(p)=0}$.
Nonzero pixels in resulting array correspond to local maxima of   ${\displaystyle G}$   in direction   ${\displaystyle \theta (p)}$.

4. Tracing edges with hysteresis.
At this stage two thresholds for the values of   ${\displaystyle G}$   are introduced:   ${\displaystyle T_{min}}$   and   ${\displaystyle T_{max}}$.
Starting from pixels with   ${\displaystyle N(p)\geqslant T_{max}}$,
find all paths of pixels with   ${\displaystyle N(p)\geqslant T_{min}}$   and put them to the resulting image.

C

The following program reads an 8 bits per pixel grayscale BMP file and saves the result to out.bmp'. Compile with -lm'.

#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <float.h>
#include <math.h>
#include <string.h>
#include <stdbool.h>
#include <assert.h>

#define MAX_BRIGHTNESS 255

// C99 doesn't define M_PI (GNU-C99 does)
#define M_PI 3.14159265358979323846264338327

/*
* BMP info:
* http://en.wikipedia.org/wiki/BMP_file_format
*
* Note: the magic number has been removed from the bmpfile_header_t
* structure since it causes alignment problems
* bmpfile_magic_t should be written/read first
* followed by the
* [this avoids compiler-specific alignment pragmas etc.]
*/

typedef struct {
uint8_t magic[2];
} bmpfile_magic_t;

typedef struct {
uint32_t filesz;
uint16_t creator1;
uint16_t creator2;
uint32_t bmp_offset;

typedef struct {
int32_t width;
int32_t height;
uint16_t nplanes;
uint16_t bitspp;
uint32_t compress_type;
uint32_t bmp_bytesz;
int32_t hres;
int32_t vres;
uint32_t ncolors;
uint32_t nimpcolors;

typedef struct {
uint8_t r;
uint8_t g;
uint8_t b;
uint8_t nothing;
} rgb_t;

// Use short int instead `unsigned char' so that we can
// store negative values.
typedef short int pixel_t;

pixel_t *load_bmp(const char *filename,
{
FILE *filePtr = fopen(filename, "rb");
if (filePtr == NULL) {
perror("fopen()");
return NULL;
}

bmpfile_magic_t mag;
if (fread(&mag, sizeof(bmpfile_magic_t), 1, filePtr) != 1) {
fclose(filePtr);
return NULL;
}

// verify that this is a bmp file by check bitmap id
// warning: dereferencing type-punned pointer will break
// strict-aliasing rules [-Wstrict-aliasing]
if (*((uint16_t*)mag.magic) != 0x4D42) {
fprintf(stderr, "Not a BMP file: magic=%c%c\n",
mag.magic[0], mag.magic[1]);
fclose(filePtr);
return NULL;
}

1, filePtr) != 1) {
fclose(filePtr);
return NULL;
}

1, filePtr) != 1) {
fclose(filePtr);
return NULL;
}

if (bitmapInfoHeader->compress_type != 0)
fprintf(stderr, "Warning, compression is not supported.\n");

// move file point to the beginning of bitmap data
if (fseek(filePtr, bitmapFileHeader.bmp_offset, SEEK_SET)) {
fclose(filePtr);
return NULL;
}

// allocate enough memory for the bitmap image data
pixel_t *bitmapImage = malloc(bitmapInfoHeader->bmp_bytesz *
sizeof(pixel_t));

// verify memory allocation
if (bitmapImage == NULL) {
fclose(filePtr);
return NULL;
}

// read in the bitmap image data
unsigned char c;
for(size_t i=0; i<bitmapInfoHeader->height; i++){
for(size_t j=0; j<bitmapInfoHeader->width; j++){
if (fread(&c, sizeof(unsigned char), 1, filePtr) != 1) {
fclose(filePtr);
return NULL;
}
bitmapImage[count++] = (pixel_t) c;
}
}

// If we were using unsigned char as pixel_t, then:

// close file and return bitmap image data
fclose(filePtr);
return bitmapImage;
}

// Return: true on error.
bool save_bmp(const char *filename, const bitmap_info_header_t *bmp_ih,
const pixel_t *data)
{
FILE* filePtr = fopen(filename, "wb");
if (filePtr == NULL)
return true;

bmpfile_magic_t mag = {{0x42, 0x4d}};
if (fwrite(&mag, sizeof(bmpfile_magic_t), 1, filePtr) != 1) {
fclose(filePtr);
return true;
}

const uint32_t offset = sizeof(bmpfile_magic_t) +
((1U << bmp_ih->bitspp) * 4);

const bmpfile_header_t bmp_fh = {
.filesz = offset + bmp_ih->bmp_bytesz,
.creator1 = 0,
.creator2 = 0,
.bmp_offset = offset
};

if (fwrite(&bmp_fh, sizeof(bmpfile_header_t), 1, filePtr) != 1) {
fclose(filePtr);
return true;
}
if (fwrite(bmp_ih, sizeof(bitmap_info_header_t), 1, filePtr) != 1) {
fclose(filePtr);
return true;
}

// Palette
for (size_t i = 0; i < (1U << bmp_ih->bitspp); i++) {
const rgb_t color = {(uint8_t)i, (uint8_t)i, (uint8_t)i};
if (fwrite(&color, sizeof(rgb_t), 1, filePtr) != 1) {
fclose(filePtr);
return true;
}
}

// We use int instead of uchar, so we can't write img
// in 1 call any more.
// fwrite(data, 1, bmp_ih->bmp_bytesz, filePtr);

size_t pad = 4*ceil(bmp_ih->bitspp*bmp_ih->width/32.) - bmp_ih->width;
unsigned char c;
for(size_t i=0; i < bmp_ih->height; i++) {
for(size_t j=0; j < bmp_ih->width; j++) {
c = (unsigned char) data[j + bmp_ih->width*i];
if (fwrite(&c, sizeof(char), 1, filePtr) != 1) {
fclose(filePtr);
return true;
}
}
c = 0;
for(size_t j=0; j<pad; j++)
if (fwrite(&c, sizeof(char), 1, filePtr) != 1) {
fclose(filePtr);
return true;
}
}

fclose(filePtr);
return false;
}

// if normalize is true, map pixels to range 0..MAX_BRIGHTNESS
void convolution(const pixel_t *in, pixel_t *out, const float *kernel,
const int nx, const int ny, const int kn,
const bool normalize)
{
assert(kn % 2 == 1);
assert(nx > kn && ny > kn);
const int khalf = kn / 2;
float min = FLT_MAX, max = -FLT_MAX;

if (normalize)
for (int m = khalf; m < nx - khalf; m++)
for (int n = khalf; n < ny - khalf; n++) {
float pixel = 0.0;
size_t c = 0;
for (int j = -khalf; j <= khalf; j++)
for (int i = -khalf; i <= khalf; i++) {
pixel += in[(n - j) * nx + m - i] * kernel[c];
c++;
}
if (pixel < min)
min = pixel;
if (pixel > max)
max = pixel;
}

for (int m = khalf; m < nx - khalf; m++)
for (int n = khalf; n < ny - khalf; n++) {
float pixel = 0.0;
size_t c = 0;
for (int j = -khalf; j <= khalf; j++)
for (int i = -khalf; i <= khalf; i++) {
pixel += in[(n - j) * nx + m - i] * kernel[c];
c++;
}

if (normalize)
pixel = MAX_BRIGHTNESS * (pixel - min) / (max - min);
out[n * nx + m] = (pixel_t)pixel;
}
}

/*
* gaussianFilter:
* http://www.songho.ca/dsp/cannyedge/cannyedge.html
* determine size of kernel (odd #)
* 0.0 <= sigma < 0.5 : 3
* 0.5 <= sigma < 1.0 : 5
* 1.0 <= sigma < 1.5 : 7
* 1.5 <= sigma < 2.0 : 9
* 2.0 <= sigma < 2.5 : 11
* 2.5 <= sigma < 3.0 : 13 ...
* kernelSize = 2 * int(2*sigma) + 3;
*/

void gaussian_filter(const pixel_t *in, pixel_t *out,
const int nx, const int ny, const float sigma)
{
const int n = 2 * (int)(2 * sigma) + 3;
const float mean = (float)floor(n / 2.0);
float kernel[n * n]; // variable length array

fprintf(stderr, "gaussian_filter: kernel size %d, sigma=%g\n",
n, sigma);
size_t c = 0;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
kernel[c] = exp(-0.5 * (pow((i - mean) / sigma, 2.0) +
pow((j - mean) / sigma, 2.0)))
/ (2 * M_PI * sigma * sigma);
c++;
}

convolution(in, out, kernel, nx, ny, n, true);
}

/*
* http://en.wikipedia.org/wiki/Canny_edge_detector
* http://www.tomgibara.com/computer-vision/CannyEdgeDetector.java
* http://fourier.eng.hmc.edu/e161/lectures/canny/node1.html
* http://www.songho.ca/dsp/cannyedge/cannyedge.html
*
* Note: T1 and T2 are lower and upper thresholds.
*/

pixel_t *canny_edge_detection(const pixel_t *in,
const int tmin, const int tmax,
const float sigma)
{
const int nx = bmp_ih->width;
const int ny = bmp_ih->height;

pixel_t *G = calloc(nx * ny * sizeof(pixel_t), 1);
pixel_t *after_Gx = calloc(nx * ny * sizeof(pixel_t), 1);
pixel_t *after_Gy = calloc(nx * ny * sizeof(pixel_t), 1);
pixel_t *nms = calloc(nx * ny * sizeof(pixel_t), 1);
pixel_t *out = malloc(bmp_ih->bmp_bytesz * sizeof(pixel_t));

if (G == NULL || after_Gx == NULL || after_Gy == NULL ||
nms == NULL || out == NULL) {
fprintf(stderr, "canny_edge_detection:"
" Failed memory allocation(s).\n");
exit(1);
}

gaussian_filter(in, out, nx, ny, sigma);

const float Gx[] = {-1, 0, 1,
-2, 0, 2,
-1, 0, 1};

convolution(out, after_Gx, Gx, nx, ny, 3, false);

const float Gy[] = { 1, 2, 1,
0, 0, 0,
-1,-2,-1};

convolution(out, after_Gy, Gy, nx, ny, 3, false);

for (int i = 1; i < nx - 1; i++)
for (int j = 1; j < ny - 1; j++) {
const int c = i + nx * j;
// G[c] = abs(after_Gx[c]) + abs(after_Gy[c]);
G[c] = (pixel_t)hypot(after_Gx[c], after_Gy[c]);
}

// Non-maximum suppression, straightforward implementation.
for (int i = 1; i < nx - 1; i++)
for (int j = 1; j < ny - 1; j++) {
const int c = i + nx * j;
const int nn = c - nx;
const int ss = c + nx;
const int ww = c + 1;
const int ee = c - 1;
const int nw = nn + 1;
const int ne = nn - 1;
const int sw = ss + 1;
const int se = ss - 1;

const float dir = (float)(fmod(atan2(after_Gy[c],
after_Gx[c]) + M_PI,
M_PI) / M_PI) * 8;

if (((dir <= 1 || dir > 7) && G[c] > G[ee] &&
G[c] > G[ww]) || // 0 deg
((dir > 1 && dir <= 3) && G[c] > G[nw] &&
G[c] > G[se]) || // 45 deg
((dir > 3 && dir <= 5) && G[c] > G[nn] &&
G[c] > G[ss]) || // 90 deg
((dir > 5 && dir <= 7) && G[c] > G[ne] &&
G[c] > G[sw])) // 135 deg
nms[c] = G[c];
else
nms[c] = 0;
}

// Reuse array
// used as a stack. nx*ny/2 elements should be enough.
int *edges = (int*) after_Gy;
memset(out, 0, sizeof(pixel_t) * nx * ny);
memset(edges, 0, sizeof(pixel_t) * nx * ny);

// Tracing edges with hysteresis . Non-recursive implementation.
size_t c = 1;
for (int j = 1; j < ny - 1; j++)
for (int i = 1; i < nx - 1; i++) {
if (nms[c] >= tmax && out[c] == 0) { // trace edges
out[c] = MAX_BRIGHTNESS;
int nedges = 1;
edges[0] = c;

do {
nedges--;
const int t = edges[nedges];

int nbs[8]; // neighbours
nbs[0] = t - nx; // nn
nbs[1] = t + nx; // ss
nbs[2] = t + 1; // ww
nbs[3] = t - 1; // ee
nbs[4] = nbs[0] + 1; // nw
nbs[5] = nbs[0] - 1; // ne
nbs[6] = nbs[1] + 1; // sw
nbs[7] = nbs[1] - 1; // se

for (int k = 0; k < 8; k++)
if (nms[nbs[k]] >= tmin && out[nbs[k]] == 0) {
out[nbs[k]] = MAX_BRIGHTNESS;
edges[nedges] = nbs[k];
nedges++;
}
} while (nedges > 0);
}
c++;
}

free(after_Gx);
free(after_Gy);
free(G);
free(nms);

return out;
}

int main(const int argc, const char ** const argv)
{
if (argc < 2) {
printf("Usage: %s image.bmp\n", argv[0]);
return 1;
}

const pixel_t *in_bitmap_data = load_bmp(argv[1], &ih);
if (in_bitmap_data == NULL) {
fprintf(stderr, "main: BMP image not loaded.\n");
return 1;
}

printf("Info: %d x %d x %d\n", ih.width, ih.height, ih.bitspp);

const pixel_t *out_bitmap_data =
canny_edge_detection(in_bitmap_data, &ih, 45, 50, 1.0f);
if (out_bitmap_data == NULL) {
fprintf(stderr, "main: failed canny_edge_detection.\n");
return 1;
}

if (save_bmp("out.bmp", &ih, out_bitmap_data)) {
fprintf(stderr, "main: BMP image not saved.\n");
return 1;
}

free((pixel_t*)in_bitmap_data);
free((pixel_t*)out_bitmap_data);
return 0;
}

D

Translation of: C

This version retains some of the style of the original C version. This code is faster than the C version, even with the DMD compiler. This version loads and saves PGM images, using the module of the Grayscale image Task.

import core.stdc.stdio, std.math, std.typecons, std.string, std.conv,
std.algorithm, std.ascii, std.array, bitmap, grayscale_image;

enum maxBrightness = 255;

alias Pixel = short;
alias IntT = typeof(size_t.init.signed);

// If normalize is true, map pixels to range 0...maxBrightness.
void convolution(bool normalize)(in Pixel[] inp, Pixel[] outp,
in float[] kernel,
in IntT nx, in IntT ny, in IntT kn)
pure nothrow @nogc in {
assert(kernel.length == kn ^^ 2);
assert(kn % 2 == 1);
assert(nx > kn && ny > kn);
assert(inp.length == outp.length);
} body {
//immutable IntT kn = sqrti(kernel.length);
immutable IntT khalf = kn / 2;

static if (normalize) {
float pMin = float.max, pMax = -float.max;

foreach (immutable m; khalf .. nx - khalf) {
foreach (immutable n; khalf .. ny - khalf) {
float pixel = 0.0;
size_t c;
foreach (immutable j; -khalf .. khalf + 1) {
foreach (immutable i; -khalf .. khalf + 1) {
pixel += inp[(n - j) * nx + m - i] * kernel[c];
c++;
}
}

if (pixel < pMin) pMin = pixel;
if (pixel > pMax) pMax = pixel;
}
}
}

foreach (immutable m; khalf .. nx - khalf) {
foreach (immutable n; khalf .. ny - khalf) {
float pixel = 0.0;
size_t c;
foreach (immutable j; -khalf .. khalf + 1) {
foreach (immutable i; -khalf .. khalf + 1) {
pixel += inp[(n - j) * nx + m - i] * kernel[c];
c++;
}
}

static if (normalize)
pixel = maxBrightness * (pixel - pMin) / (pMax - pMin);
outp[n * nx + m] = cast(Pixel)pixel;
}
}
}

void gaussianFilter(in Pixel[] inp, Pixel[] outp,
in IntT nx, in IntT ny, in float sigma)
pure nothrow in {
assert(inp.length == outp.length);
} body {
immutable IntT n = 2 * cast(IntT)(2 * sigma) + 3;
immutable float mean = floor(n / 2.0);
auto kernel = new float[n * n];

debug fprintf(stderr,
"gaussianFilter: kernel size %d, sigma=%g\n",
n, sigma);

size_t c;
foreach (immutable i; 0 .. n) {
foreach (immutable j; 0 .. n) {
kernel[c] = exp(-0.5 * (((i - mean) / sigma) ^^ 2 +
((j - mean) / sigma) ^^ 2))
/ (2 * PI * sigma * sigma);
c++;
}
}

convolution!true(inp, outp, kernel, nx, ny, n);
}

Image!Pixel cannyEdgeDetection(in Image!Pixel inp,
in IntT tMin, in IntT tMax,
in float sigma)
pure nothrow in {
assert(inp !is null);
} body {
immutable IntT nx = inp.nx.signed;
immutable IntT ny = inp.ny.signed;
auto outp = new Pixel[nx * ny];

gaussianFilter(inp.image, outp, nx, ny, sigma);

static immutable float[] Gx = [-1, 0, 1,
-2, 0, 2,
-1, 0, 1];
auto after_Gx = new Pixel[nx * ny];
convolution!false(outp, after_Gx, Gx, nx, ny, 3);

static immutable float[] Gy = [ 1, 2, 1,
0, 0, 0,
-1,-2,-1];
auto after_Gy = new Pixel[nx * ny];
convolution!false(outp, after_Gy, Gy, nx, ny, 3);

auto G = new Pixel[nx * ny];
foreach (i; 1 .. nx - 1)
foreach (j; 1 .. ny - 1) {
immutable size_t c = i + nx * j;
G[c] = cast(Pixel)hypot(after_Gx[c], after_Gy[c]);
}

// Non-maximum suppression, straightforward implementation.
auto nms = new Pixel[nx * ny];
foreach (immutable i; 1 .. nx - 1)
foreach (immutable j; 1 .. ny - 1) {
immutable IntT c = i + nx * j,
nn = c - nx,
ss = c + nx,
ww = c + 1,
ee = c - 1,
nw = nn + 1,
ne = nn - 1,
sw = ss + 1,
se = ss - 1;

immutable aux = atan2(double(after_Gy[c]),
double(after_Gx[c])) + PI;
immutable float dir = float((aux % PI) / PI) * 8;

if (((dir <= 1 || dir > 7) && G[c] > G[ee] &&
G[c] > G[ww]) || // 0 deg.
((dir > 1 && dir <= 3) && G[c] > G[nw] &&
G[c] > G[se]) || // 45 deg.
((dir > 3 && dir <= 5) && G[c] > G[nn] &&
G[c] > G[ss]) || // 90 deg.
((dir > 5 && dir <= 7) && G[c] > G[ne] &&
G[c] > G[sw])) // 135 deg.
nms[c] = G[c];
else
nms[c] = 0;
}

// Reuse array used as a stack. nx*ny/2 elements should be enough.
IntT[] edges = (cast(IntT*)after_Gy.ptr)[0 .. after_Gy.length / 2];
outp[] = Pixel.init;
edges[] = 0;

// Tracing edges with hysteresis. Non-recursive implementation.
size_t c = 1;
foreach (immutable j; 1 .. ny - 1) {
foreach (immutable i; 1 .. nx - 1) {
if (nms[c] >= tMax && outp[c] == 0) { // Trace edges.
outp[c] = maxBrightness;
IntT nedges = 1;
edges[0] = c;

do {
nedges--;
immutable IntT t = edges[nedges];

immutable IntT[8] neighbours = [
t - nx, // nn
t + nx, // ss
t + 1, // ww
t - 1, // ee
t - nx + 1, // nw
t - nx - 1, // ne
t + nx + 1, // sw
t + nx - 1]; // se

foreach (immutable n; neighbours)
if (nms[n] >= tMin && outp[n] == 0) {
outp[n] = maxBrightness;
edges[nedges] = n;
nedges++;
}
} while (nedges > 0);
}
c++;
}
}

return Image!Pixel.fromData(outp, nx, ny);
}

void main(in string[] args) {
immutable fileName = (args.length == 2) ? args[1] : "lena.pgm";
Image!Pixel imIn;
printf("Image size: %d x %d\n", imIn.nx, imIn.ny);
imIn.cannyEdgeDetection(45, 50, 1.0f).savePGM("lena_canny.pgm");
}

Go

Library: Imger

The example image for this program is the color photograph of a steam engine taken from the Wikipedia article linked to in the task description.

After applying the Canny edge detector, the resulting image is similar to but not quite the same as the Wikipedia image, probably due to differences in the parameters used though a 5×5 Gaussian filter is used in both cases.

Note that on Linux the extension of the example image file name needs to be changed from .PNG to .png in order for the library used to recognize it.

package main

import (
ed "github.com/Ernyoke/Imger/edgedetection"
"github.com/Ernyoke/Imger/imgio"
"log"
)

func main() {
img, err := imgio.ImreadRGBA("Valve_original_(1).png")
if err != nil {
log.Fatal("Could not read image", err)
}

cny, err := ed.CannyRGBA(img, 15, 45, 5)
if err != nil {
log.Fatal("Could not perform Canny Edge detection")
}

err = imgio.Imwrite(cny, "Valve_canny_(1).png")
if err != nil {
log.Fatal("Could not write Canny image to disk")
}
}

J

In this solution images are represented as 2D arrays of pixels, with first and second axes representing down and right respectively. Each processing step has a specific pixel representation. In the original and Gaussian-filtered images, array elements represent monochromatic intensity values as numbers ranging from 0 (black) to 255 (white). In the intensity gradient image, gradient values are vectors, and are represented as complex numbers, with real and imaginary components representing down and right respectively.

Detected edge and non-edge points are represented as ones and zeros respectively. An edge is a set of connected edge points (points adjacent horizontally, vertically, or diagonally are considered to be connected). In the final image, each edge is represented by assigning its set of points a common unique value.

NB. 2D convolution, filtering, ...

convolve =: 4 : 'x apply (($x) partition y)' partition=: 2 1 3 0 |: {:@[ ]\ 2 1 0 |: {[email protected][ ]\ ] apply=: [: +/ [: +/ * max3x3 =: 3 : '(0<1{1{y) * (>./>./y)' addborder =: (0&,@|:@|.)^:4 normalize =: ]%+/@, attach =: 3 : 'max3x3 (3 3 partition (addborder y))' unique =: 3 : 'y*i.$y'
connect =: 3 : 'attach^:_ unique y'

NB. on low memory devices, cropping or resampling of high-resolution images may be required
crop =: 4 : 0
'h w h0 w0' =: x
|: w{. w0}. |: h{. h0}. y
)
resample =: 4 : '|: (1{-x)(+/%#)\ |: (0{-x)(+/%#)\ y'
NB. on e. g. smartphones, image may need to be expanded for viewing
inflate1 =: 4 : 0
'h w' =: $y r =: ,y c =: #r rr =: (c$x) # r
(h,x*w)$rr ) inflate =: 4 : '|: x inflate1 (|: x inflate1 y)' NB. Step 1 - gaussian smoothing step1 =: 3 : 0 NB. Gaussian kernel (from Wikipedia article) <] gaussianKernel =: 5 5$2 4 5 4 2 4 9 12 9 4 5 12 15 12 5 4 9 12 9 4 2 4 5 4 2
gaussianKernel =: gaussianKernel % 159
gaussianKernel convolve y
)

NB. Step 2 - gradient
step2 =: 3 : 0
<] gradientKernel =: 3 3$0 _1 0 0j_1 0 0j1 0 1 0 gradientKernel convolve y ) NB. Step 3 - edge detection step3 =: 3 : 0 NB. find the octant (eighth of circle) in which the gradient lies octant =: 3 : '4|(>.(_0.5+((4%(o. 1))*(12&o. y))))' <(i:6)(4 : 'octant (x j. y)')"0/(i:6) NB. is this gradient greater than [the projection of] a neighbor? greaterThan =: 4 : ' (9 o.((x|.y)%y))<1' NB. is this gradient the greatest of immmediate colinear neighbore? greatestOf =: 4 : '(x greaterThan y) *. ((-x) greaterThan y)' NB. relative address of neighbor relevant to grad direction krnl0 =. _1 0 krnl1 =. _1 _1 krnl2 =. 0 _1 krnl3 =. 1 _1 image =. y og =. octant image NB. mask for maximum gradient colinear with gradient ok0 =. (0=og) *. krnl0 greatestOf image ok1 =. (1=og) *. krnl1 greatestOf image ok2 =. (2=og) *. krnl2 greatestOf image ok3 =. (3=og) *. krnl3 greatestOf image image *. (ok0 +. ok1 +. ok2 +. ok3) ) NB. Step 4 - Weak edge suppression step4 =: 3 : 0 magnitude =. 10&o. y NB. weak, strong threshholds NB. TODO: parameter picker algorithm or helper threshholds =. 1e14 1e15 nearbyKernel =. 3 3$ 4 1 4 # 1 0 1
weak =. magnitude > 0{threshholds
strong =. magnitude > 1{threshholds
strongs =. addborder (nearbyKernel convolve strong) > 0
strong +. (weak *. strongs)
)

NB. given the edge points, find the edges
step5 =: connect

canny =: step5 @ step4 @ step3 @ step2 @ step1

The above implementation solves the 'inner problem' of Canny Edge Detection in the J language, with no external dependencies. J's Qt IDE provides additional support including interfaces to image file formats, graphic displays, and the user. The following code exercises these features

The file 'valve.png' referenced in this code is from one of several Wikipedia articles on edge detection. It can be viewed at [https://upload.wikimedia.org/wikipedia/commons/2/2e/Valve_gaussian_%282%29.PNG]

require 'gl2'
coclass 'edge'
coinsert'jgl2'

PJ=: jpath '~Projects/edges/' NB. optionally install and run as project under IDE

run=: 3 : 0
wd 'pc form;pn canny'
wd 'cc txt static;cn "Canny in J";'
wd 'cc png isidraw'
wd 'cc inc button;cn "Next";'
wd 'pshow'
glclear''
image =: readimg_jqtide_ PJ,'valve.png'
image =: 240 360 120 150 crop image
edges =: canny 256 | image
ids =: }. ~.,edges
nids =: # ids
case =: 0
)

form_inc_button =: 3 : 0
select. case
case. 0 do.
wd 'set txt text "original image";'
img =: 255 setalpha image
case. 1 do.
wd 'set txt text "points on edges";'
img =: edges>0
img =: 1-img
img =: img * (+/ 256^i.3) * 255
img =: 255 setalpha img
ix =: 0
case. 2 do.
wd 'set txt text "... iterating over edges with >75 points ...";'
img =: edges=ix{ids
whilst. (num<75) *. (ix<nids) do.
img =: edges=ix{ids
num =: +/,img
ix=:>:ix
if. ix=#ids do. case=:_1 end.
end.
img =: 1-img
img =: img * (+/ 256^i.3) * 255
img =: 255 setalpha img
ix =: (#ids)|(>:ix)
end.
if. case<2 do. case =: >: case end.
NB. img =: 5 inflate img NB. might need this for high-res cellphone display
glfill 255 128 255
glpixels 0 0,(|.$img), ,img glpaint'' ) form_close=: exit bind 0 run'' Java El código es de Tom Gibara (http://www.tomgibara.com/) Se implementa utilizando una sola clase Java. import java.awt.image.BufferedImage; import java.util.Arrays; /** * <p><em>This software has been released into the public domain. * <strong>Please read the notes in this source file for additional information. * </strong></em></p> * * <p>This class provides a configurable implementation of the Canny edge * detection algorithm. This classic algorithm has a number of shortcomings, * but remains an effective tool in many scenarios. <em>This class is designed * for single threaded use only.</em></p> * * <p>Sample usage:</p> * * <pre><code> * //create the detector * CannyEdgeDetector detector = new CannyEdgeDetector(); * //adjust its parameters as desired * detector.setLowThreshold(0.5f); * detector.setHighThreshold(1f); * //apply it to an image * detector.setSourceImage(frame); * detector.process(); * BufferedImage edges = detector.getEdgesImage(); * </code></pre> * * <p>For a more complete understanding of this edge detector's parameters * consult an explanation of the algorithm.</p> * * @author Tom Gibara * */ public class CannyEdgeDetector { // statics private final static float GAUSSIAN_CUT_OFF = 0.005f; private final static float MAGNITUDE_SCALE = 100F; private final static float MAGNITUDE_LIMIT = 1000F; private final static int MAGNITUDE_MAX = (int) (MAGNITUDE_SCALE * MAGNITUDE_LIMIT); // fields private int height; private int width; private int picsize; private int[] data; private int[] magnitude; private BufferedImage sourceImage; private BufferedImage edgesImage; private float gaussianKernelRadius; private float lowThreshold; private float highThreshold; private int gaussianKernelWidth; private boolean contrastNormalized; private float[] xConv; private float[] yConv; private float[] xGradient; private float[] yGradient; // constructors /** * Constructs a new detector with default parameters. */ public CannyEdgeDetector() { lowThreshold = 2.5f; highThreshold = 7.5f; gaussianKernelRadius = 2f; gaussianKernelWidth = 16; contrastNormalized = false; } // accessors /** * The image that provides the luminance data used by this detector to * generate edges. * * @return the source image, or null */ public BufferedImage getSourceImage() { return sourceImage; } /** * Specifies the image that will provide the luminance data in which edges * will be detected. A source image must be set before the process method * is called. * * @param image a source of luminance data */ public void setSourceImage(BufferedImage image) { sourceImage = image; } /** * Obtains an image containing the edges detected during the last call to * the process method. The buffered image is an opaque image of type * BufferedImage.TYPE_INT_ARGB in which edge pixels are white and all other * pixels are black. * * @return an image containing the detected edges, or null if the process * method has not yet been called. */ public BufferedImage getEdgesImage() { return edgesImage; } /** * Sets the edges image. Calling this method will not change the operation * of the edge detector in any way. It is intended to provide a means by * which the memory referenced by the detector object may be reduced. * * @param edgesImage expected (though not required) to be null */ public void setEdgesImage(BufferedImage edgesImage) { this.edgesImage = edgesImage; } /** * The low threshold for hysteresis. The default value is 2.5. * * @return the low hysteresis threshold */ public float getLowThreshold() { return lowThreshold; } /** * Sets the low threshold for hysteresis. Suitable values for this parameter * must be determined experimentally for each application. It is nonsensical * (though not prohibited) for this value to exceed the high threshold value. * * @param threshold a low hysteresis threshold */ public void setLowThreshold(float threshold) { if (threshold < 0) throw new IllegalArgumentException(); lowThreshold = threshold; } /** * The high threshold for hysteresis. The default value is 7.5. * * @return the high hysteresis threshold */ public float getHighThreshold() { return highThreshold; } /** * Sets the high threshold for hysteresis. Suitable values for this * parameter must be determined experimentally for each application. It is * nonsensical (though not prohibited) for this value to be less than the * low threshold value. * * @param threshold a high hysteresis threshold */ public void setHighThreshold(float threshold) { if (threshold < 0) throw new IllegalArgumentException(); highThreshold = threshold; } /** * The number of pixels across which the Gaussian kernel is applied. * The default value is 16. * * @return the radius of the convolution operation in pixels */ public int getGaussianKernelWidth() { return gaussianKernelWidth; } /** * The number of pixels across which the Gaussian kernel is applied. * This implementation will reduce the radius if the contribution of pixel * values is deemed negligable, so this is actually a maximum radius. * * @param gaussianKernelWidth a radius for the convolution operation in * pixels, at least 2. */ public void setGaussianKernelWidth(int gaussianKernelWidth) { if (gaussianKernelWidth < 2) throw new IllegalArgumentException(); this.gaussianKernelWidth = gaussianKernelWidth; } /** * The radius of the Gaussian convolution kernel used to smooth the source * image prior to gradient calculation. The default value is 16. * * @return the Gaussian kernel radius in pixels */ public float getGaussianKernelRadius() { return gaussianKernelRadius; } /** * Sets the radius of the Gaussian convolution kernel used to smooth the * source image prior to gradient calculation. * * @return a Gaussian kernel radius in pixels, must exceed 0.1f. */ public void setGaussianKernelRadius(float gaussianKernelRadius) { if (gaussianKernelRadius < 0.1f) throw new IllegalArgumentException(); this.gaussianKernelRadius = gaussianKernelRadius; } /** * Whether the luminance data extracted from the source image is normalized * by linearizing its histogram prior to edge extraction. The default value * is false. * * @return whether the contrast is normalized */ public boolean isContrastNormalized() { return contrastNormalized; } /** * Sets whether the contrast is normalized * @param contrastNormalized true if the contrast should be normalized, * false otherwise */ public void setContrastNormalized(boolean contrastNormalized) { this.contrastNormalized = contrastNormalized; } // methods public void process() { width = sourceImage.getWidth(); height = sourceImage.getHeight(); picsize = width * height; initArrays(); readLuminance(); if (contrastNormalized) normalizeContrast(); computeGradients(gaussianKernelRadius, gaussianKernelWidth); int low = Math.round(lowThreshold * MAGNITUDE_SCALE); int high = Math.round( highThreshold * MAGNITUDE_SCALE); performHysteresis(low, high); thresholdEdges(); writeEdges(data); } // private utility methods private void initArrays() { if (data == null || picsize != data.length) { data = new int[picsize]; magnitude = new int[picsize]; xConv = new float[picsize]; yConv = new float[picsize]; xGradient = new float[picsize]; yGradient = new float[picsize]; } } //NOTE: The elements of the method below (specifically the technique for //non-maximal suppression and the technique for gradient computation) //are derived from an implementation posted in the following forum (with the //clear intent of others using the code): // http://forum.java.sun.com/thread.jspa?threadID=546211&start=45&tstart=0 //My code effectively mimics the algorithm exhibited above. //Since I don't know the providence of the code that was posted it is a //possibility (though I think a very remote one) that this code violates //someone's intellectual property rights. If this concerns you feel free to //contact me for an alternative, though less efficient, implementation. private void computeGradients(float kernelRadius, int kernelWidth) { //generate the gaussian convolution masks float kernel[] = new float[kernelWidth]; float diffKernel[] = new float[kernelWidth]; int kwidth; for (kwidth = 0; kwidth < kernelWidth; kwidth++) { float g1 = gaussian(kwidth, kernelRadius); if (g1 <= GAUSSIAN_CUT_OFF && kwidth >= 2) break; float g2 = gaussian(kwidth - 0.5f, kernelRadius); float g3 = gaussian(kwidth + 0.5f, kernelRadius); kernel[kwidth] = (g1 + g2 + g3) / 3f / (2f * (float) Math.PI * kernelRadius * kernelRadius); diffKernel[kwidth] = g3 - g2; } int initX = kwidth - 1; int maxX = width - (kwidth - 1); int initY = width * (kwidth - 1); int maxY = width * (height - (kwidth - 1)); //perform convolution in x and y directions for (int x = initX; x < maxX; x++) { for (int y = initY; y < maxY; y += width) { int index = x + y; float sumX = data[index] * kernel[0]; float sumY = sumX; int xOffset = 1; int yOffset = width; for(; xOffset < kwidth ;) { sumY += kernel[xOffset] * (data[index - yOffset] + data[index + yOffset]); sumX += kernel[xOffset] * (data[index - xOffset] + data[index + xOffset]); yOffset += width; xOffset++; } yConv[index] = sumY; xConv[index] = sumX; } } for (int x = initX; x < maxX; x++) { for (int y = initY; y < maxY; y += width) { float sum = 0f; int index = x + y; for (int i = 1; i < kwidth; i++) sum += diffKernel[i] * (yConv[index - i] - yConv[index + i]); xGradient[index] = sum; } } for (int x = kwidth; x < width - kwidth; x++) { for (int y = initY; y < maxY; y += width) { float sum = 0.0f; int index = x + y; int yOffset = width; for (int i = 1; i < kwidth; i++) { sum += diffKernel[i] * (xConv[index - yOffset] - xConv[index + yOffset]); yOffset += width; } yGradient[index] = sum; } } initX = kwidth; maxX = width - kwidth; initY = width * kwidth; maxY = width * (height - kwidth); for (int x = initX; x < maxX; x++) { for (int y = initY; y < maxY; y += width) { int index = x + y; int indexN = index - width; int indexS = index + width; int indexW = index - 1; int indexE = index + 1; int indexNW = indexN - 1; int indexNE = indexN + 1; int indexSW = indexS - 1; int indexSE = indexS + 1; float xGrad = xGradient[index]; float yGrad = yGradient[index]; float gradMag = hypot(xGrad, yGrad); //perform non-maximal supression float nMag = hypot(xGradient[indexN], yGradient[indexN]); float sMag = hypot(xGradient[indexS], yGradient[indexS]); float wMag = hypot(xGradient[indexW], yGradient[indexW]); float eMag = hypot(xGradient[indexE], yGradient[indexE]); float neMag = hypot(xGradient[indexNE], yGradient[indexNE]); float seMag = hypot(xGradient[indexSE], yGradient[indexSE]); float swMag = hypot(xGradient[indexSW], yGradient[indexSW]); float nwMag = hypot(xGradient[indexNW], yGradient[indexNW]); float tmp; /* * An explanation of what's happening here, for those who want * to understand the source: This performs the "non-maximal * supression" phase of the Canny edge detection in which we * need to compare the gradient magnitude to that in the * direction of the gradient; only if the value is a local * maximum do we consider the point as an edge candidate. * * We need to break the comparison into a number of different * cases depending on the gradient direction so that the * appropriate values can be used. To avoid computing the * gradient direction, we use two simple comparisons: first we * check that the partial derivatives have the same sign (1) * and then we check which is larger (2). As a consequence, we * have reduced the problem to one of four identical cases that * each test the central gradient magnitude against the values at * two points with 'identical support'; what this means is that * the geometry required to accurately interpolate the magnitude * of gradient function at those points has an identical * geometry (upto right-angled-rotation/reflection). * * When comparing the central gradient to the two interpolated * values, we avoid performing any divisions by multiplying both * sides of each inequality by the greater of the two partial * derivatives. The common comparand is stored in a temporary * variable (3) and reused in the mirror case (4). * */ if (xGrad * yGrad <= (float) 0 /*(1)*/ ? Math.abs(xGrad) >= Math.abs(yGrad) /*(2)*/ ? (tmp = Math.abs(xGrad * gradMag)) >= Math.abs(yGrad * neMag - (xGrad + yGrad) * eMag) /*(3)*/ && tmp > Math.abs(yGrad * swMag - (xGrad + yGrad) * wMag) /*(4)*/ : (tmp = Math.abs(yGrad * gradMag)) >= Math.abs(xGrad * neMag - (yGrad + xGrad) * nMag) /*(3)*/ && tmp > Math.abs(xGrad * swMag - (yGrad + xGrad) * sMag) /*(4)*/ : Math.abs(xGrad) >= Math.abs(yGrad) /*(2)*/ ? (tmp = Math.abs(xGrad * gradMag)) >= Math.abs(yGrad * seMag + (xGrad - yGrad) * eMag) /*(3)*/ && tmp > Math.abs(yGrad * nwMag + (xGrad - yGrad) * wMag) /*(4)*/ : (tmp = Math.abs(yGrad * gradMag)) >= Math.abs(xGrad * seMag + (yGrad - xGrad) * sMag) /*(3)*/ && tmp > Math.abs(xGrad * nwMag + (yGrad - xGrad) * nMag) /*(4)*/ ) { magnitude[index] = gradMag >= MAGNITUDE_LIMIT ? MAGNITUDE_MAX : (int) (MAGNITUDE_SCALE * gradMag); //NOTE: The orientation of the edge is not employed by this //implementation. It is a simple matter to compute it at //this point as: Math.atan2(yGrad, xGrad); } else { magnitude[index] = 0; } } } } //NOTE: It is quite feasible to replace the implementation of this method //with one which only loosely approximates the hypot function. I've tested //simple approximations such as Math.abs(x) + Math.abs(y) and they work fine. private float hypot(float x, float y) { return (float) Math.hypot(x, y); } private float gaussian(float x, float sigma) { return (float) Math.exp(-(x * x) / (2f * sigma * sigma)); } private void performHysteresis(int low, int high) { //NOTE: this implementation reuses the data array to store both //luminance data from the image, and edge intensity from the processing. //This is done for memory efficiency, other implementations may wish //to separate these functions. Arrays.fill(data, 0); int offset = 0; for (int y = 0; y < height; y++) { for (int x = 0; x < width; x++) { if (data[offset] == 0 && magnitude[offset] >= high) { follow(x, y, offset, low); } offset++; } } } private void follow(int x1, int y1, int i1, int threshold) { int x0 = x1 == 0 ? x1 : x1 - 1; int x2 = x1 == width - 1 ? x1 : x1 + 1; int y0 = y1 == 0 ? y1 : y1 - 1; int y2 = y1 == height -1 ? y1 : y1 + 1; data[i1] = magnitude[i1]; for (int x = x0; x <= x2; x++) { for (int y = y0; y <= y2; y++) { int i2 = x + y * width; if ((y != y1 || x != x1) && data[i2] == 0 && magnitude[i2] >= threshold) { follow(x, y, i2, threshold); return; } } } } private void thresholdEdges() { for (int i = 0; i < picsize; i++) { data[i] = data[i] > 0 ? -1 : 0xff000000; } } private int luminance(float r, float g, float b) { return Math.round(0.299f * r + 0.587f * g + 0.114f * b); } private void readLuminance() { int type = sourceImage.getType(); if (type == BufferedImage.TYPE_INT_RGB || type == BufferedImage.TYPE_INT_ARGB) { int[] pixels = (int[]) sourceImage.getData().getDataElements(0, 0, width, height, null); for (int i = 0; i < picsize; i++) { int p = pixels[i]; int r = (p & 0xff0000) >> 16; int g = (p & 0xff00) >> 8; int b = p & 0xff; data[i] = luminance(r, g, b); } } else if (type == BufferedImage.TYPE_BYTE_GRAY) { byte[] pixels = (byte[]) sourceImage.getData().getDataElements(0, 0, width, height, null); for (int i = 0; i < picsize; i++) { data[i] = (pixels[i] & 0xff); } } else if (type == BufferedImage.TYPE_USHORT_GRAY) { short[] pixels = (short[]) sourceImage.getData().getDataElements(0, 0, width, height, null); for (int i = 0; i < picsize; i++) { data[i] = (pixels[i] & 0xffff) / 256; } } else if (type == BufferedImage.TYPE_3BYTE_BGR) { byte[] pixels = (byte[]) sourceImage.getData().getDataElements(0, 0, width, height, null); int offset = 0; for (int i = 0; i < picsize; i++) { int b = pixels[offset++] & 0xff; int g = pixels[offset++] & 0xff; int r = pixels[offset++] & 0xff; data[i] = luminance(r, g, b); } } else { throw new IllegalArgumentException("Unsupported image type: " + type); } } private void normalizeContrast() { int[] histogram = new int[256]; for (int i = 0; i < data.length; i++) { histogram[data[i]]++; } int[] remap = new int[256]; int sum = 0; int j = 0; for (int i = 0; i < histogram.length; i++) { sum += histogram[i]; int target = sum*255/picsize; for (int k = j+1; k <=target; k++) { remap[k] = i; } j = target; } for (int i = 0; i < data.length; i++) { data[i] = remap[data[i]]; } } private void writeEdges(int pixels[]) { //NOTE: There is currently no mechanism for obtaining the edge data //in any other format other than an INT_ARGB type BufferedImage. //This may be easily remedied by providing alternative accessors. if (edgesImage == null) { edgesImage = new BufferedImage(width, height, BufferedImage.TYPE_INT_ARGB); } edgesImage.getWritableTile(0, 0).setDataElements(0, 0, width, height, pixels); } } Julia Works with: Julia version 0.6 using Images canny_edges = canny(img, sigma = 1.4, upperThreshold = 0.80, lowerThreshold = 0.20) Mathematica/Wolfram Language Export["out.bmp", EdgeDetect[Import[InputString[]]]]; Mathematica uses canny edge detection by default. This seems so cheaty next to all of these giant answers... MATLAB / Octave There is a function in the image processing toolbox edge, that has Canny Edge Detection as one of its options. BWImage = edge(GrayscaleImage,'canny'); Nim Translation of: D Library: nimPNG We use the PNG image present on Wikipedia article as input and produce a PNG grayscale image as result. import lenientops import math import nimPNG const MaxBrightness = 255 type Pixel = int16 # Used instead of byte to be able to store negative values. #--------------------------------------------------------------------------------------------------- func convolution*[normalize: static bool](input: seq[Pixel]; output: var seq[Pixel]; kernel: seq[float]; nx, ny, kn: int) = ## Do a convolution. ## If normalize is true, map pixels to range 0...maxBrightness. doAssert kernel.len == kn * kn doAssert (kn and 1) == 1 doAssert nx > kn and ny > kn doAssert input.len == output.len let khalf = kn div 2 when normalize: var pMin = float.high var pMax = -float.high for m in khalf..<(nx - khalf): for n in khalf..<(ny - khalf): var pixel = 0.0 var c = 0 for j in -khalf..khalf: for i in -khalf..khalf: pixel += input[(n - j) * nx + m - i] * kernel[c] inc c if pixel < pMin: pMin = pixel if pixel > pMax: pMax = pixel for m in khalf..<(nx - khalf): for n in khalf..<(ny - khalf): var pixel = 0.0 var c = 0 for j in -khalf..khalf: for i in -khalf..khalf: pixel += input[(n - j) * nx + m - i] * kernel[c] inc c when normalize: pixel = MaxBrightness * (pixel - pMin) / (pMax - pMin) output[n * nx + m] = Pixel(pixel) #--------------------------------------------------------------------------------------------------- func gaussianFilter(input: seq[Pixel]; output: var seq[Pixel]; nx, ny: int; sigma: float) = ## Apply a gaussian filter. doAssert input.len == output.len let n = 2 * (2 * sigma).toInt + 3 let mean = floor(n / 2) var kernel = newSeq[float](n * n) var c = 0 for i in 0..<n: for j in 0..<n: kernel[c] = exp(-0.5 * (((i - mean) / sigma) ^ 2 + ((j - mean) / sigma) ^ 2)) / (2 * PI * sigma * sigma) inc c convolution[true](input, output, kernel, nx, ny, n) #--------------------------------------------------------------------------------------------------- proc cannyEdgeDetection(input: seq[Pixel]; nx, ny: int; tmin, tmax: int; sigma: float): seq[byte] = ## Detect edges. var output = newSeq[Pixel](input.len) gaussianFilter(input, output, nx, ny, sigma) const Gx = @[float -1, 0, 1, -2, 0, 2, -1, 0, 1] var afterGx = newSeq[Pixel](input.len) convolution[false](input, afterGx, Gx, nx, ny, 3) const Gy = @[float 1, 2, 1, 0, 0, 0, -1, -2, -1] var afterGy = newSeq[Pixel](input.len) convolution[false](input, afterGy, Gy, nx, ny, 3) var g = newSeq[Pixel](input.len) for i in 1..(nx - 2): for j in 1..(ny - 2): let c = i + nx * j g[c] = hypot(afterGx[c].toFloat, afterGy[c].toFloat).Pixel # Non-maximum suppression: straightforward implementation. var nms = newSeq[Pixel](input.len) for i in 1..(nx - 2): for j in 1..(ny - 2): let c = i + nx * j nn = c - nx ss = c + nx ww = c + 1 ee = c - 1 nw = nn + 1 ne = nn - 1 sw = ss + 1 se = ss - 1 let aux = arctan2(afterGy[c].toFloat, afterGx[c].toFloat) + PI let dir = aux mod PI / PI * 8 if (((dir <= 1 or dir > 7) and g[c] > g[ee] and g[c] > g[ww]) or # O°. ((dir > 1 and dir <= 3) and g[c] > g[nw] and g[c] > g[se]) or # 45°. ((dir > 3 and dir <= 5) and g[c] > g[nn] and g[c] > g[ss]) or # 90°. ((dir > 5 and dir <= 7) and g[c] > g[ne] and g[c] > g[sw])): # 135°. nms[c] = g[c] else: nms[c] = 0 # Tracing edges with hysteresis. Non-recursive implementation. var edges = newSeq[int](input.len div 2) for item in output.mitems: item = 0 var c = 0 for j in 1..(ny - 2): for i in 1..(nx - 2): inc c if nms[c] >= tMax and output[c] == 0: # Trace edges. output[c] = MaxBrightness var nedges = 1 edges[0] = c while nedges > 0: dec nedges let t = edges[nedges] let neighbors = [t - nx, # nn. t + nx, # ss. t + 1, # ww. t - 1, # ee. t - nx + 1, # nw. t - nx - 1, # ne. t + nx + 1, # sw. t + nx - 1] # se. for n in neighbors: if nms[n] >= tMin and output[n] == 0: output[n] = MaxBrightness edges[nedges] = n inc nedges # Store the result as a sequence of bytes. result = newSeqOfCap[byte](output.len) for val in output: result.add(byte(val)) #——————————————————————————————————————————————————————————————————————————————————————————————————— when isMainModule: const Input = "Valve.png" Output = "Valve_edges.png" let pngImage = loadPNG24(seq[byte], Input).get() # Convert to grayscale and store luminances as 16 bits signed integers. var pixels = newSeq[Pixel](pngImage.width * pngImage.height) for i in 0..pixels.high: pixels[i] = Pixel(0.2126 * pngImage.data[3 * i] + 0.7152 * pngImage.data[3 * i + 1] + 0.0722 * pngImage.data[3 * i + 2] + 0.5) # Find edges. let data = cannyEdgeDetection(pixels, pngImage.width, pngImage.height, 45, 50, 1.0) # Save result as a PNG image. let status = savePNG(Output, data, LCT_GREY, 8, pngImage.width, pngImage.height) if status.isOk: echo "File ", Input, " processed. Result is available in file ", Output else: echo "Error: ", status.error PHP PHP implementation // input: r,g,b in range 0..255 function RGBtoHSV($r, $g,$b) {
$r =$r/255.; // convert to range 0..1
$g =$g/255.;
$b =$b/255.;
$cols = array("r" =>$r, "g" => $g, "b" =>$b);
asort($cols, SORT_NUMERIC);$min = key(array_slice($cols, 1)); // "r", "g" or "b"$max = key(array_slice($cols, -1)); // "r", "g" or "b" // hue if($cols[$min] ==$cols[$max]) {$h = 0;
} else {
if($max == "r") {$h = 60. * ( 0 + ( ($cols["g"]-$cols["b"]) / ($cols[$max]-$cols[$min]) ) );
} elseif ($max == "g") {$h = 60. * ( 2 + ( ($cols["b"]-$cols["r"]) / ($cols[$max]-$cols[$min]) ) );
} elseif ($max == "b") {$h = 60. * ( 4 + ( ($cols["r"]-$cols["g"]) / ($cols[$max]-$cols[$min]) ) );
}
if($h < 0) {$h += 360;
}
}

// saturation
if($cols[$max] == 0) {
$s = 0; } else {$s = ( ($cols[$max]-$cols[$min])/$cols[$max] );
$s =$s * 255;
}

// lightness
$v =$cols[$max];$v = $v * 255; return(array($h, $s,$v));
}

$filename = "image.png";$dimensions = getimagesize($filename);$w = $dimensions[0]; // width$h = $dimensions[1]; // height$im = imagecreatefrompng($filename); for($hi=0; $hi <$h; $hi++) { for($wi=0; $wi <$w; $wi++) {$rgb = imagecolorat($im,$wi, $hi);$r = ($rgb >> 16) & 0xFF;$g = ($rgb >> 8) & 0xFF;$b = $rgb & 0xFF;$hsv = RGBtoHSV($r,$g, $b); // compare pixel below with current pixel$brgb = imagecolorat($im,$wi, $hi+1);$br = ($brgb >> 16) & 0xFF;$bg = ($brgb >> 8) & 0xFF;$bb = $brgb & 0xFF;$bhsv = RGBtoHSV($br,$bg, $bb); // if difference in hue > 20, edge is detected if($hsv[2]-$bhsv[2] > 20) { imagesetpixel($im, $wi,$hi, imagecolorallocate($im, 255, 0, 0)); } else { imagesetpixel($im, $wi,$hi, imagecolorallocate($im, 0, 0, 0)); } } } header('Content-Type: image/jpeg'); imagepng($im);
imagedestroy($im); Phix  This example is in need of improvement: Port to pGUI for linux and 64 bit compatibility. The file demo\Arwen32dibdemo\manip.exw in the standard distribution contains a menu entry for this, Manipulate/Filter/Detect Edges, along with 15 or so other effects. It is however windows-32-bit only, and could do with being ported to pGUI. Python In Python, Canny edge detection would normally be done using scikit-image or OpenCV-Python. Here is an approach using numpy/scipy: #!/bin/python import numpy as np from scipy.ndimage.filters import convolve, gaussian_filter from scipy.misc import imread, imshow def CannyEdgeDetector(im, blur = 1, highThreshold = 91, lowThreshold = 31): im = np.array(im, dtype=float) #Convert to float to prevent clipping values #Gaussian blur to reduce noise im2 = gaussian_filter(im, blur) #Use sobel filters to get horizontal and vertical gradients im3h = convolve(im2,[[-1,0,1],[-2,0,2],[-1,0,1]]) im3v = convolve(im2,[[1,2,1],[0,0,0],[-1,-2,-1]]) #Get gradient and direction grad = np.power(np.power(im3h, 2.0) + np.power(im3v, 2.0), 0.5) theta = np.arctan2(im3v, im3h) thetaQ = (np.round(theta * (5.0 / np.pi)) + 5) % 5 #Quantize direction #Non-maximum suppression gradSup = grad.copy() for r in range(im.shape[0]): for c in range(im.shape[1]): #Suppress pixels at the image edge if r == 0 or r == im.shape[0]-1 or c == 0 or c == im.shape[1] - 1: gradSup[r, c] = 0 continue tq = thetaQ[r, c] % 4 if tq == 0: #0 is E-W (horizontal) if grad[r, c] <= grad[r, c-1] or grad[r, c] <= grad[r, c+1]: gradSup[r, c] = 0 if tq == 1: #1 is NE-SW if grad[r, c] <= grad[r-1, c+1] or grad[r, c] <= grad[r+1, c-1]: gradSup[r, c] = 0 if tq == 2: #2 is N-S (vertical) if grad[r, c] <= grad[r-1, c] or grad[r, c] <= grad[r+1, c]: gradSup[r, c] = 0 if tq == 3: #3 is NW-SE if grad[r, c] <= grad[r-1, c-1] or grad[r, c] <= grad[r+1, c+1]: gradSup[r, c] = 0 #Double threshold strongEdges = (gradSup > highThreshold) #Strong has value 2, weak has value 1 thresholdedEdges = np.array(strongEdges, dtype=np.uint8) + (gradSup > lowThreshold) #Tracing edges with hysteresis #Find weak edge pixels near strong edge pixels finalEdges = strongEdges.copy() currentPixels = [] for r in range(1, im.shape[0]-1): for c in range(1, im.shape[1]-1): if thresholdedEdges[r, c] != 1: continue #Not a weak pixel #Get 3x3 patch localPatch = thresholdedEdges[r-1:r+2,c-1:c+2] patchMax = localPatch.max() if patchMax == 2: currentPixels.append((r, c)) finalEdges[r, c] = 1 #Extend strong edges based on current pixels while len(currentPixels) > 0: newPix = [] for r, c in currentPixels: for dr in range(-1, 2): for dc in range(-1, 2): if dr == 0 and dc == 0: continue r2 = r+dr c2 = c+dc if thresholdedEdges[r2, c2] == 1 and finalEdges[r2, c2] == 0: #Copy this weak pixel to final result newPix.append((r2, c2)) finalEdges[r2, c2] = 1 currentPixels = newPix return finalEdges if __name__=="__main__": im = imread("test.jpg", mode="L") #Open image, convert to greyscale finalEdges = CannyEdgeDetector(im) imshow(finalEdges) Tcl Library: crimp package require crimp package require crimp::pgm proc readPGM {filename} { set f [open$filename rb]
set data [read $f] close$f
return [crimp read pgm $data] } proc writePGM {filename image} { crimp write 2file pgm-raw$filename $image } proc cannyFilterFile {{inputFile "lena.pgm"} {outputFile "lena_canny.pgm"}} { writePGM$outputFile [crimp filter canny sobel [readPGM $inputFile]] } cannyFilterFile {*}$argv

Wren

Translation of: C
Library: DOME
Library: Wren-check
import "dome" for Window
import "graphics" for Canvas, Color, ImageData
import "math" for Math
import "./check" for Check

var MaxBrightness = 255

class Canny {
construct new(inFile, outFile) {
Window.title = "Canny edge detection"
var image1 = ImageData.loadFromFile(inFile)
var w = image1.width
var h = image1.height
Window.resize(w * 2 + 20, h)
Canvas.resize(w * 2 + 20, h)
var image2 = ImageData.create(outFile, w, h)
var pixels = List.filled(w * h, 0)
var ix = 0
// convert image1 to gray scale as a list of pixels
for (y in 0...h) {
for (x in 0...w) {
var c1 = image1.pget(x, y)
var lumin = (0.2126 * c1.r + 0.7152 * c1.g + 0.0722 * c1.b).floor
pixels[ix] = lumin
ix = ix + 1
}
}

// find edges
var data = cannyEdgeDetection(pixels, w, h, 45, 50, 1)

// write to image2
ix = 0
for (y in 0...h) {
for (x in 0...w) {
var d = data[ix]
var c = Color.rgb(d, d, d)
image2.pset(x, y, c)
ix = ix + 1
}
}

// display the two images side by side
image1.draw(0, 0)
image2.draw(w + 20, 0)

// save image2 to outFile
image2.saveToFile(outFile)
}

init() {}

// If normalize is true, map pixels to range 0..MaxBrightness
convolution(input, output, kernel, nx, ny, kn, normalize) {
Check.ok((kn % 2) == 1)
Check.ok(nx > kn && ny > kn)
var khalf = (kn / 2).floor
var min = Num.largest
var max = -min
if (normalize) {
for (m in khalf...nx-khalf) {
for (n in khalf...ny-khalf) {
var pixel = 0
var c = 0
for (j in -khalf..khalf) {
for (i in -khalf..khalf) {
pixel = pixel + input[(n-j)*nx + m - i] * kernel[c]
c = c + 1
}
}
if (pixel < min) min = pixel
if (pixel > max) max = pixel
}
}
}

for (m in khalf...nx-khalf) {
for (n in khalf...ny-khalf) {
var pixel = 0
var c = 0
for (j in -khalf..khalf) {
for (i in -khalf..khalf) {
pixel = pixel + input[(n-j)*nx + m - i] * kernel[c]
c = c + 1
}
}
if (normalize) pixel = MaxBrightness * (pixel - min) / (max - min)
output[n * nx + m] = pixel.truncate
}
}
}

gaussianFilter(input, output, nx, ny, sigma) {
var n = 2 * (2 * sigma).truncate + 3
var mean = (n / 2).floor
var kernel = List.filled(n * n, 0)
System.print("Gaussian filter: kernel size = %(n), sigma = %(sigma)")
var c = 0
for (i in 0...n) {
for (j in 0...n) {
var t = (-0.5 * (((i - mean) / sigma).pow(2) + ((j - mean) / sigma).pow(2))).exp
kernel[c] = t / (2 * Num.pi * sigma * sigma)
c = c + 1
}
}
convolution(input, output, kernel, nx, ny, n, true)
}

// Returns the square root of 'x' squared + 'y' squared.
hypot(x, y) { (x*x + y*y).sqrt }

cannyEdgeDetection(input, nx, ny, tmin, tmax, sigma) {
var output = List.filled(input.count, 0)
gaussianFilter(input, output, nx, ny, sigma)
var Gx = [-1, 0, 1, -2, 0, 2, -1, 0, 1]
var afterGx = List.filled(input.count, 0)
convolution(output, afterGx, Gx, nx, ny, 3, false)
var Gy = [1, 2, 1, 0, 0, 0, -1, -2, -1]
var afterGy = List.filled(input.count, 0)
convolution(output, afterGy, Gy, nx, ny, 3, false)
var G = List.filled(input.count, 0)
for (i in 1..nx-2) {
for (j in 1..ny-2) {
var c = i + nx * j
G[c] = hypot(afterGx[c], afterGy[c]).floor
}
}

// non-maximum suppression: straightforward implementation
var nms = List.filled(input.count, 0)
for (i in 1..nx-2) {
for (j in 1..ny-2) {
var c = i + nx * j
var nn = c - nx
var ss = c + nx
var ww = c + 1
var ee = c - 1
var nw = nn + 1
var ne = nn - 1
var sw = ss + 1
var se = ss - 1
var temp = Math.atan(afterGy[c], afterGx[c]) + Num.pi
var dir = (temp % Num.pi) / Num.pi * 8
if (((dir <= 1 || dir > 7) && G[c] > G[ee] && G[c] > G[ww]) || // O°
((dir > 1 && dir <= 3) && G[c] > G[nw] && G[c] > G[se]) || // 45°
((dir > 3 && dir <= 5) && G[c] > G[nn] && G[c] > G[ss]) || // 90°
((dir > 5 && dir <= 7) && G[c] > G[ne] && G[c] > G[sw])) { // 135°
nms[c] = G[c]
} else {
nms[c] = 0
}
}
}

// tracing edges with hysteresis: non-recursive implementation
var edges = List.filled((input.count/2).floor, 0)
for (i in 0...output.count) output[i] = 0
var c = 1
for (j in 1..ny-2) {
for (i in 1..nx-2) {
if (nms[c] >= tmax && output[c] == 0) {
// trace edges
output[c] = MaxBrightness
var nedges = 1
edges[0] = c
while (true) {
nedges = nedges - 1
var t = edges[nedges]
var nbs = [ // neighbors
t - nx, // nn
t + nx, // ss
t + 1, // ww
t - 1, // ee
t - nx + 1, // nw
t - nx - 1, // ne
t + nx + 1, // sw
t + nx - 1 // se
]
for (n in nbs) {
if (nms[n] >= tmin && output[n] == 0) {
output[n] = MaxBrightness
edges[nedges] = n
nedges = nedges + 1
}
}
if (nedges == 0) break
}
}
c = c + 1
}
}
return output
}

update() {}

draw(alpha) {}
}
var Game = Canny.new("Valve_original.png", "Valve_monchrome_canny.png")