/* * edtaa3() * * Sweep-and-update Euclidean distance transform of an * image. Positive pixels are treated as object pixels, * zero or negative pixels are treated as background. * An attempt is made to treat antialiased edges correctly. * The input image must have pixels in the range [0,1], * and the antialiased image should be a box-filter * sampling of the ideal, crisp edge. * If the antialias region is more than 1 pixel wide, * the result from this transform will be inaccurate. * * By Stefan Gustavson (stefan.gustavson@gmail.com). * * Originally written in 1994, based on a verbal * description of Per-Erik Danielsson's SSED8 algorithm * as presented in the PhD dissertation of Ingemar * Ragnemalm. This is Per-Erik Danielsson's scanline * scheme from 1979 - I only implemented it in C. * * Updated in 2004 to treat border pixels correctly, * and cleaned up the code to improve readability. * * Updated in 2009 to handle anti-aliased edges, * as published in the article "Anti-aliased Euclidean * distance transform" by Stefan Gustavson and Robin Strand, * Pattern Recognition Letters 32 (2011) 252–257. * * Updated in 2011 to avoid a corner case causing an * infinite loop for some input data. * */ /* Copyright (C) 2011 by Stefan Gustavson (stefan.gustavson@liu.se) This code is distributed under the permissive "MIT license": Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ #include /* * Compute the local gradient at edge pixels using convolution filters. * The gradient is computed only at edge pixels. At other places in the * image, it is never used, and it's mostly zero anyway. */ void computegradient(double *img, int w, int h, double *gx, double *gy) { int i,j,k; double glength; #define SQRT2 1.4142136 for(i = 1; i < h-1; i++) { // Avoid edges where the kernels would spill over for(j = 1; j < w-1; j++) { k = i*w + j; if((img[k]>0.0) && (img[k]<1.0)) { // Compute gradient for edge pixels only gx[k] = -img[k-w-1] - SQRT2*img[k-1] - img[k+w-1] + img[k-w+1] + SQRT2*img[k+1] + img[k+w+1]; gy[k] = -img[k-w-1] - SQRT2*img[k-w] - img[k-w+1] + img[k+w-1] + SQRT2*img[k+w] + img[k+w+1]; glength = gx[k]*gx[k] + gy[k]*gy[k]; if(glength > 0.0) { // Avoid division by zero glength = sqrt(glength); gx[k]=gx[k]/glength; gy[k]=gy[k]/glength; } } } } // TODO: Compute reasonable values for gx, gy also around the image edges. // (These are zero now, which reduces the accuracy for a 1-pixel wide region // around the image edge.) 2x2 kernels would be suitable for this. } /* * A somewhat tricky function to approximate the distance to an edge in a * certain pixel, with consideration to either the local gradient (gx,gy) * or the direction to the pixel (dx,dy) and the pixel greyscale value a. * The latter alternative, using (dx,dy), is the metric used by edtaa2(). * Using a local estimate of the edge gradient (gx,gy) yields much better * accuracy at and near edges, and reduces the error even at distant pixels * provided that the gradient direction is accurately estimated. */ double edgedf(double gx, double gy, double a) { double df, glength, temp, a1; if ((gx == 0) || (gy == 0)) { // Either A) gu or gv are zero, or B) both df = 0.5-a; // Linear approximation is A) correct or B) a fair guess } else { glength = sqrt(gx*gx + gy*gy); if(glength>0) { gx = gx/glength; gy = gy/glength; } /* Everything is symmetric wrt sign and transposition, * so move to first octant (gx>=0, gy>=0, gx>=gy) to * avoid handling all possible edge directions. */ gx = fabs(gx); gy = fabs(gy); if(gx 1.0) a = 1.0; if(a < 0.0) a = 0.0; // Clip grayscale values outside the range [0,1] if(a == 0.0) return 1000000.0; // Not an object pixel, return "very far" ("don't know yet") dx = (double)xi; dy = (double)yi; di = sqrt(dx*dx + dy*dy); // Length of integer vector, like a traditional EDT if(di==0) { // Use local gradient only at edges // Estimate based on local gradient only df = edgedf(gx, gy, a); } else { // Estimate gradient based on direction to edge (accurate for large di) df = edgedf(dx, dy, a); } return di + df; // Same metric as edtaa2, except at edges (where di=0) } // Shorthand macro: add ubiquitous parameters img, gx, gy and w and call distaa3() #define DISTAA(c,xc,yc,xi,yi) (distaa3(img, gx, gy, w, c, xc, yc, xi, yi)) void edtaa3(double *img, double *gx, double *gy, int w, int h, short *distx, short *disty, double *dist) { int x, y, i, c; int offset_u, offset_ur, offset_r, offset_rd, offset_d, offset_dl, offset_l, offset_lu; double olddist, newdist; int cdistx, cdisty, newdistx, newdisty; int changed; double epsilon = 1e-3; // Safeguard against errors due to limited precision /* Initialize index offsets for the current image width */ offset_u = -w; offset_ur = -w+1; offset_r = 1; offset_rd = w+1; offset_d = w; offset_dl = w-1; offset_l = -1; offset_lu = -w-1; /* Initialize the distance images */ for(i=0; i 0) // If non-zero distance or not set yet { c = i + offset_u; // Index of candidate for testing cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx; newdisty = cdisty+1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; olddist=newdist; changed = 1; } c = i+offset_ur; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx-1; newdisty = cdisty+1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; changed = 1; } } i++; /* Middle pixels have all neighbors */ for(x=1; x 0) // If not already zero distance { c = i+offset_l; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx+1; newdisty = cdisty; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; olddist=newdist; changed = 1; } c = i+offset_lu; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx+1; newdisty = cdisty+1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; olddist=newdist; changed = 1; } c = i+offset_u; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx; newdisty = cdisty+1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; changed = 1; } } /* Move index to second rightmost pixel of current row. */ /* Rightmost pixel is skipped, it has no right neighbor. */ i = y*w + w-2; /* scan left, propagate distance from right */ for(x=w-2; x>=0; x--, i--) { olddist = dist[i]; if(olddist <= 0) continue; // Already zero distance c = i+offset_r; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx-1; newdisty = cdisty; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; changed = 1; } } } /* Scan rows in reverse order, except last row */ for(y=h-2; y>=0; y--) { /* move index to rightmost pixel of current row */ i = y*w + w-1; /* Scan left, propagate distances from below & right */ /* Rightmost pixel is special, has no right neighbors */ olddist = dist[i]; if(olddist > 0) // If not already zero distance { c = i+offset_d; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx; newdisty = cdisty-1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; olddist=newdist; changed = 1; } c = i+offset_dl; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx+1; newdisty = cdisty-1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; changed = 1; } } i--; /* Middle pixels have all neighbors */ for(x=w-2; x>0; x--, i--) { olddist = dist[i]; if(olddist <= 0) continue; // Already zero distance c = i+offset_r; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx-1; newdisty = cdisty; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; olddist=newdist; changed = 1; } c = i+offset_rd; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx-1; newdisty = cdisty-1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; olddist=newdist; changed = 1; } c = i+offset_d; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx; newdisty = cdisty-1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; olddist=newdist; changed = 1; } c = i+offset_dl; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx+1; newdisty = cdisty-1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; changed = 1; } } /* Leftmost pixel is special, has no left neighbors */ olddist = dist[i]; if(olddist > 0) // If not already zero distance { c = i+offset_r; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx-1; newdisty = cdisty; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; olddist=newdist; changed = 1; } c = i+offset_rd; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx-1; newdisty = cdisty-1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; olddist=newdist; changed = 1; } c = i+offset_d; cdistx = distx[c]; cdisty = disty[c]; newdistx = cdistx; newdisty = cdisty-1; newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty); if(newdist < olddist-epsilon) { distx[i]=newdistx; disty[i]=newdisty; dist[i]=newdist; changed = 1; } } /* Move index to second leftmost pixel of current row. */ /* Leftmost pixel is skipped, it has no left neighbor. */ i = y*w + 1; for(x=1; x