Canny edge detector

Canny edge detector is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task: Write a program that performs so-called canny edge detection on an image. The algorithm consists of the following steps:

1. Noise reduction. May be performed by Gaussian filter.
2. Compute intensity gradient (matrices $G_{x}$ and $G_{y}$) and its magnitude $G$.
      $G={\sqrt {G_{x}^{2}+G_{y}^{2}}}$
   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: $\theta ={\rm {atan2}}\left(G_{y},\,G_{x}\right)$. Transform angle $\theta$ to one of four directions: 0, 45, 90, 135 degrees. Compute new array $N$: if
      $G\left(p_{a}\right)<G\left(p\right)<G\left(p_{b}\right)$
   where $p$ is the current pixel, $p_{a}$ and $p_{b}$ are the two neighbour pixels in the direction of gradient, then $N(p)=G(p)$, otherwise $N(p)=0$. Nonzero pixels in resulting array correspond to local maxima of $G$ in direction $\theta (p)$.
4. Tracing edges with hysteresis. At this stage two thresholds for the values of $G$ are introduced: $T_{min}$ and $T_{max}$. Starting from pixels with $N(p)\geqslant T_{max}$ find all paths of pixels with $N(p)\geqslant T_{min}$ 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'. <lang c>#include <stdint.h>

1. include <stdio.h>
2. include <stdlib.h>
3. include <float.h>
4. include <math.h>
5. include <string.h>

1. define MAX_BRIGHTNESS 255

/*

* 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 structure
* since it causes alignment problems
*     struct bmpfile_magic should be written/read first
* followed by the
*     struct bmpfile_header
* [this avoids compiler-specific alignment pragmas etc.]
*/

struct bmpfile_magic {

   unsigned char magic[2];

};

struct bmpfile_header {

   uint32_t filesz;
   uint16_t creator1;
   uint16_t creator2;
   uint32_t bmp_offset;

};

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;

} BITMAPINFOHEADER;

typedef struct {

   uint8_t r;
   uint8_t g;
   uint8_t b;
   uint8_t null;

} rgb_t;

BITMAPINFOHEADER ih;

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

pixel_t *load_bmp(char *filename, BITMAPINFOHEADER *bitmapInfoHeader) {

   FILE *filePtr; // our file pointer
   struct bmpfile_magic  mag;
   struct bmpfile_header bitmapFileHeader; // our bitmap file header
   pixel_t *bitmapImage;  // store image data
   size_t i;
   unsigned char c;

   filePtr = fopen(filename,"r");
   if (filePtr == NULL) {
       perror("fopen()");
       exit(1);
   }

   fread(&mag, sizeof(struct bmpfile_magic), 1, filePtr);
   // 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;
   }

   // read the bitmap file header
   fread(&bitmapFileHeader, sizeof(struct bmpfile_header), 1, filePtr);

   // read the bitmap info header
   fread(bitmapInfoHeader, sizeof(BITMAPINFOHEADER), 1, filePtr);

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

   // move file point to the beginning of bitmap data
   fseek(filePtr, bitmapFileHeader.bmp_offset, SEEK_SET);

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

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

   // read in the bitmap image data
   for (i = 0; i < bitmapInfoHeader->bmp_bytesz; i++) {
       fread(&c, sizeof(unsigned char), 1, filePtr);
       bitmapImage[i] = (int) c;
   }

   // 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: nonzero on error. int save_bmp(char *filename, BITMAPINFOHEADER *bmp_ih, pixel_t *data) {

   unsigned int offset =
       sizeof(struct bmpfile_magic)
       + sizeof(struct bmpfile_header)
       + sizeof(BITMAPINFOHEADER)
       + (1 << bmp_ih->bitspp) * 4;
   struct bmpfile_header bmp_fh = {
       .filesz = offset + bmp_ih->bmp_bytesz,
       .creator1 = 0,
       .creator2 = 0,
       .bmp_offset = offset
   };
   struct bmpfile_magic mag = Template:0x42, 0x4d;
   rgb_t color = {0, 0, 0, 0};
   int i;
   size_t j;
   FILE* fp = fopen(filename, "w");

   if (fp == NULL)
       return 1;

   fwrite(&mag, 1, sizeof(struct bmpfile_magic), fp);
   fwrite(&bmp_fh, 1, sizeof(struct bmpfile_header), fp);
   fwrite(bmp_ih, 1, sizeof(BITMAPINFOHEADER), fp);

   // Palette
   for (i = 0; i < (1 << bmp_ih->bitspp); i++) {
       color.r = i;
       color.g = i;
       color.b = i;
       fwrite(&color, 1, sizeof(rgb_t), fp);
   }

   // We use int instead of uchar, so we can't write img in 1 call any more.
   // fwrite(data, 1, bmp_ih->bmp_bytesz, fp);
   for (j = 0; j < bmp_ih->bmp_bytesz; j++) {
       unsigned char c = (unsigned char) data[j];

       fwrite(&c, sizeof(unsigned char), 1, fp);
   }

   fclose(fp);
   return 0;

}

// if norm==1, map pixels to range 0..MAX_BRIGHTNESS void convolution(pixel_t *in, pixel_t *out, float *kernel, int nx, int ny, int kn, int norm) {

   int i, j, m, n, c;
   int khalf = floor(kn / 2.0);
   float pixel, min = DBL_MAX, max = DBL_MIN;

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

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

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

}

// 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(pixel_t *in, pixel_t *out, int nx, int ny, float sigma) {

   int i, j, c = 0;
   const int n = 2 * (int)(2 * sigma) + 3;
   float mean = floor(n / 2.0);
   float kernel[n * n];

   fprintf(stderr, "gaussian_filter: kernel size %d, sigma=%g\n", n, sigma);
   for (i = 0; i < n; i++)
       for (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);
   convolution(in, out, kernel, nx, ny, n, 1);

}

/*

* 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.
*/

void canny_edge_detection(pixel_t *in, pixel_t *out, int nx, int ny, int tmin, int tmax, float sigma) {

   int i, j, c, Gmax;
   float Gx[] = {
       -1, 0, 1,
       -2, 0, 2,
       -1, 0, 1};
   float Gy[] = {
        1, 2, 1,
        0, 0, 0,
       -1,-2,-1};
   pixel_t *G    = calloc(nx * ny * sizeof(pixel_t), 1),
       *after_Gx = calloc(nx * ny * sizeof(pixel_t), 1),
       *after_Gy = calloc(nx * ny * sizeof(pixel_t), 1),
       *nms      = calloc(nx * ny * sizeof(pixel_t), 1);
   pixel_t *edges;
   int nedges, k, t;
   int nbs[8]; // neighbours

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

   convolution(out, after_Gx, Gx, nx, ny, 3, 0);
   convolution(out, after_Gy, Gy, nx, ny, 3, 0);

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

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

           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;

           dir = 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
   edges = after_Gy; // used as a stack
   memset(out, 0, sizeof(pixel_t) * nx * ny);
   memset(edges, 0, sizeof(pixel_t) * nx * ny);

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

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

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

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

}

int main(int argc, char **argv) {

   pixel_t *bitmap_data, *temp_image;

   if (argc < 2) {
       printf("Usage: %s image.bmp\n", argv[0]);
       exit(1);
   }

   bitmap_data = load_bmp(argv[1], &ih);
   temp_image = (pixel_t*) malloc(ih.bmp_bytesz * sizeof(pixel_t));

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

   canny_edge_detection(bitmap_data, temp_image, ih.width, ih.height, 45, 50, 1);

   save_bmp("out.bmp", &ih, temp_image);
   free(bitmap_data);
   free(temp_image);

   return 0;

}</lang>