Canny edge detector

Canny edge detector
You are encouraged to solve this task according to the task description, using any language you may know.
Task: 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 /* * Loading part taken from * http://www.vbforums.com/showthread.php?t=261522 * 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 *     bmpfile_header_t * [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;} bmpfile_header_t; typedef struct {    uint32_t header_sz;    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;} bitmap_info_header_t; 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,                  bitmap_info_header_t *bitmapInfoHeader){    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;    }     bmpfile_header_t bitmapFileHeader; // our bitmap file header    // read the bitmap file header    if (fread(&bitmapFileHeader, sizeof(bmpfile_header_t),              1, filePtr) != 1) {        fclose(filePtr);        return NULL;    }     // read the bitmap info header    if (fread(bitmapInfoHeader, sizeof(bitmap_info_header_t),              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    size_t pad, count=0;    unsigned char c;    pad = 4*ceil(bitmapInfoHeader->bitspp*bitmapInfoHeader->width/32.) - bitmapInfoHeader->width;    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;	    }	    fseek(filePtr, pad, SEEK_CUR);    }     // If we were using unsigned char as pixel_t, then:    // fread(bitmapImage, 1, bitmapInfoHeader->bmp_bytesz, filePtr);     // 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) +                            sizeof(bmpfile_header_t) +                            sizeof(bitmap_info_header_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);     // Padding: http://en.wikipedia.org/wiki/BMP_file_format#Pixel_storage    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_BRIGHTNESSvoid 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);} /* * Links: * 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 bitmap_info_header_t *bmp_ih,                              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;    }     static bitmap_info_header_t ih;    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;    imIn = imIn.loadPGM(fileName);    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 (($x) partition y)'partition=: 2 1 3 0 |: {:@[ ]\ 2 1 0 |: {[email protected][ ]\ ]apply=: [: +/ [: +/ *max3x3 =: 3 : '(0<1{1{y) * (>./>./y)'addborder =: (0&,@|:@|.)^:4normalize =: ]%+/@,attach =: 3 : 'max3x3 (3 3 partition (addborder y))'unique =: 3 : 'y*i.$y'connect =: 3 : 'attach^:_ unique y' NB. on low memory devices, cropping or resampling of high-resolution images may be requiredcrop      =: 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 viewinginflate1 =: 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 smoothingstep1 =: 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 - gradientstep2 =: 3 : 0   <] gradientKernel =: 3 3$0 _1 0 0j_1 0 0j1 0 1 0 gradientKernel convolve y) NB. Step 3 - edge detectionstep3 =: 3 : 0 NB. find the octant (eighth of circle) in which the gradient lies octant =: 3 : '4|(>.(_0.5+((4%(o. 1))*(12&o. y))))' <(i:6)(4 : 'octant (x j. y)')"0/(i:6) NB. is this gradient greater than [the projection of] a neighbor? greaterThan =: 4 : ' (9 o.((x|.y)%y))<1' NB. is this gradient the greatest of immmediate colinear neighbore? greatestOf =: 4 : '(x greaterThan y) *. ((-x) greaterThan y)' NB. relative address of neighbor relevant to grad direction krnl0 =. _1 0 krnl1 =. _1 _1 krnl2 =. 0 _1 krnl3 =. 1 _1 image =. y og =. octant image NB. mask for maximum gradient colinear with gradient ok0 =. (0=og) *. krnl0 greatestOf image ok1 =. (1=og) *. krnl1 greatestOf image ok2 =. (2=og) *. krnl2 greatestOf image ok3 =. (3=og) *. krnl3 greatestOf image image *. (ok0 +. ok1 +. ok2 +. ok3)) NB. Step 4 - Weak edge suppressionstep4 =: 3 : 0 magnitude =. 10&o. y NB. weak, strong threshholds NB. TODO: parameter picker algorithm or helper threshholds =. 1e14 1e15 nearbyKernel =. 3 3$ 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]