Sandbox/Realazthat/Hough transform
Implement the Hough transform, which is used as part of feature extraction with digital images. It is a tool that makes it far easier to identify straight lines in the source image, whatever their orientation.
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You are encouraged to solve this task according to the task description, using any language you may know.
The transform maps each point in the target image, , to the average color of the pixels on the corresponding line of the source image (in -space, where the line corresponds to points of the form ). The idea is that where there is a straight line in the original image, it corresponds to a bright (or dark, depending on the color of the background field) spot; by applying a suitable filter to the results of the transform, it is possible to extract the locations of the lines in the original image.
![](http://static.miraheze.org/rosettacodewiki/thumb/c/c6/Pentagon.png/300px-Pentagon.png)
The target space actually uses polar coordinates, but is conventionally plotted on rectangular coordinates for display. There's no specification of exactly how to map polar coordinates to a flat surface for display, but a convenient method is to use one axis for and the other for , with the center of the source image being the origin.
There is also a spherical Hough transform, which is more suited to identifying planes in 3D data.
C
This solution has no libraries specified.
Code: #include <stdio.h> #include <stdlib.h> #include <stdint.h> #include <string.h> #include <math.h> #include <cairo.h> #ifndef M_PI #define M_PI 3.1415927 #endif #define GR(X,Y) (d[(*s)*(Y)+bpp*(X)+((2)%bpp)]) #define GG(X,Y) (d[(*s)*(Y)+bpp*(X)+((1)%bpp)]) #define GB(X,Y) (d[(*s)*(Y)+bpp*(X)+((0)%bpp)]) #define SR(X,Y) (ht[4*tw*((Y)%th)+4*((X)%tw)+2]) #define SG(X,Y) (ht[4*tw*((Y)%th)+4*((X)%tw)+1]) #define SB(X,Y) (ht[4*tw*((Y)%th)+4*((X)%tw)+0]) #define RAD(A) (M_PI*((double)(A))/180.0) uint8_t *houghtransform(uint8_t *d, int *w, int *h, int *s, int bpp) { int rho, theta, y, x, W = *w, H = *h; int th = sqrt(W*W + H*H)/2.0; int tw = 360; uint8_t *ht = malloc(th*tw*4); memset(ht, 0, 4*th*tw); // black bg for(rho = 0; rho < th; rho++) { for(theta = 0; theta < tw/*720*/; theta++) { double C = cos(RAD(theta)); double S = sin(RAD(theta)); uint32_t totalred = 0; uint32_t totalgreen = 0; uint32_t totalblue = 0; uint32_t totalpix = 0; if ( theta < 45 || (theta > 135 && theta < 225) || theta > 315) { for(y = 0; y < H; y++) { double dx = W/2.0 + (rho - (H/2.0-y)*S)/C; if ( dx < 0 || dx >= W ) continue; x = floor(dx+.5); if (x == W) continue; totalpix++; totalred += GR(x, y); totalgreen += GG(x, y); totalblue += GB(x, y); } } else { for(x = 0; x < W; x++) { double dy = H/2.0 - (rho - (x - W/2.0)*C)/S; if ( dy < 0 || dy >= H ) continue; y = floor(dy+.5); if (y == H) continue; totalpix++; totalred += GR(x, y); totalgreen += GG(x, y); totalblue += GB(x, y); } } if ( totalpix > 0 ) { double dp = totalpix; SR(theta, rho) = (int)(totalred/dp) &0xff; SG(theta, rho) = (int)(totalgreen/dp) &0xff; SB(theta, rho) = (int)(totalblue/dp) &0xff; } } } *h = th; // sqrt(W*W+H*H)/2 *w = tw; // 360 *s = 4*tw; return ht; } int main(int argc, char **argv) { cairo_surface_t *inputimg = NULL; cairo_surface_t *houghimg = NULL; uint8_t *houghdata = NULL, *inputdata = NULL; int w, h, s, bpp; if ( argc < 3 ) return EXIT_FAILURE; inputimg = cairo_image_surface_create_from_png(argv[1]); w = cairo_image_surface_get_width(inputimg); h = cairo_image_surface_get_height(inputimg); s = cairo_image_surface_get_stride(inputimg); bpp = cairo_image_surface_get_format(inputimg); switch(bpp) { case CAIRO_FORMAT_ARGB32: bpp = 4; break; case CAIRO_FORMAT_RGB24: bpp = 3; break; case CAIRO_FORMAT_A8: bpp = 1; break; default: fprintf(stderr, "unsupported\n"); goto destroy; } inputdata = cairo_image_surface_get_data(inputimg); houghdata = houghtransform(inputdata, &w, &h, &s, bpp); printf("w=%d, h=%d\n", w, h); houghimg = cairo_image_surface_create_for_data(houghdata, CAIRO_FORMAT_RGB24, w, h, s); cairo_surface_write_to_png(houghimg, argv[2]); destroy: if (inputimg != NULL) cairo_surface_destroy(inputimg); if (houghimg != NULL) cairo_surface_destroy(houghimg); return EXIT_SUCCESS; }
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