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564 lines
18 KiB
C++
564 lines
18 KiB
C++
/*
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* edtaa3()
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*
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* Sweep-and-update Euclidean distance transform of an
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* image. Positive pixels are treated as object pixels,
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* zero or negative pixels are treated as background.
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* An attempt is made to treat antialiased edges correctly.
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* The input image must have pixels in the range [0,1],
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* and the antialiased image should be a box-filter
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* sampling of the ideal, crisp edge.
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* If the antialias region is more than 1 pixel wide,
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* the result from this transform will be inaccurate.
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*
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* By Stefan Gustavson (stefan.gustavson@gmail.com).
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*
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* Originally written in 1994, based on a verbal
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* description of the SSED8 algorithm published in the
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* PhD dissertation of Ingemar Ragnemalm. This is his
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* algorithm, I only implemented it in C.
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*
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* Updated in 2004 to treat border pixels correctly,
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* and cleaned up the code to improve readability.
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*
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* Updated in 2009 to handle anti-aliased edges.
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*
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* Updated in 2011 to avoid a corner case infinite loop.
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*
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*/
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/*
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Copyright (C) 2009 Stefan Gustavson (stefan.gustavson@gmail.com)
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This program is free software; you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by the
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Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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This program is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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The GNU General Public License is available on <http://www.gnu.org/licenses/>.
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*/
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#include <math.h>
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/*
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* Compute the local gradient at edge pixels using convolution filters.
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* The gradient is computed only at edge pixels. At other places in the
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* image, it is never used, and it's mostly zero anyway.
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*/
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void computegradient(double *img, int w, int h, double *gx, double *gy)
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{
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int i,j,k;
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double glength;
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#define SQRT2 1.4142136
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for(i = 1; i < h-1; i++) { // Avoid edges where the kernels would spill over
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for(j = 1; j < w-1; j++) {
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k = i*w + j;
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if((img[k]>0.0) && (img[k]<1.0)) { // Compute gradient for edge pixels only
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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];
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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];
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glength = gx[k]*gx[k] + gy[k]*gy[k];
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if(glength > 0.0) { // Avoid division by zero
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glength = sqrt(glength);
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gx[k]=gx[k]/glength;
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gy[k]=gy[k]/glength;
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}
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}
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}
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}
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// TODO: Compute reasonable values for gx, gy also around the image edges.
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// (These are zero now, which reduces the accuracy for a 1-pixel wide region
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// around the image edge.) 2x2 kernels would be suitable for this.
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}
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/*
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* A somewhat tricky function to approximate the distance to an edge in a
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* certain pixel, with consideration to either the local gradient (gx,gy)
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* or the direction to the pixel (dx,dy) and the pixel greyscale value a.
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* The latter alternative, using (dx,dy), is the metric used by edtaa2().
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* Using a local estimate of the edge gradient (gx,gy) yields much better
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* accuracy at and near edges, and reduces the error even at distant pixels
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* provided that the gradient direction is accurately estimated.
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*/
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double edgedf(double gx, double gy, double a)
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{
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double df, glength, temp, a1;
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if ((gx == 0) || (gy == 0)) { // Either A) gu or gv are zero, or B) both
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df = 0.5-a; // Linear approximation is A) correct or B) a fair guess
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} else {
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glength = sqrt(gx*gx + gy*gy);
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if(glength>0) {
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gx = gx/glength;
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gy = gy/glength;
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}
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/* Everything is symmetric wrt sign and transposition,
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* so move to first octant (gx>=0, gy>=0, gx>=gy) to
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* avoid handling all possible edge directions.
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*/
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gx = fabs(gx);
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gy = fabs(gy);
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if(gx<gy) {
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temp = gx;
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gx = gy;
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gy = temp;
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}
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a1 = 0.5*gy/gx;
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if (a < a1) { // 0 <= a < a1
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df = 0.5*(gx + gy) - sqrt(2.0*gx*gy*a);
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} else if (a < (1.0-a1)) { // a1 <= a <= 1-a1
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df = (0.5-a)*gx;
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} else { // 1-a1 < a <= 1
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df = -0.5*(gx + gy) + sqrt(2.0*gx*gy*(1.0-a));
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}
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}
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return df;
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}
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double distaa3(double *img, double *gximg, double *gyimg, int w, int c, int xc, int yc, int xi, int yi)
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{
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double di, df, dx, dy, gx, gy, a;
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int closest;
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closest = c-xc-yc*w; // Index to the edge pixel pointed to from c
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a = img[closest]; // Grayscale value at the edge pixel
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gx = gximg[closest]; // X gradient component at the edge pixel
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gy = gyimg[closest]; // Y gradient component at the edge pixel
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if(a > 1.0) a = 1.0;
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if(a < 0.0) a = 0.0; // Clip grayscale values outside the range [0,1]
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if(a == 0.0) return 1000000.0; // Not an object pixel, return "very far" ("don't know yet")
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dx = (double)xi;
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dy = (double)yi;
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di = sqrt(dx*dx + dy*dy); // Length of integer vector, like a traditional EDT
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if(di==0) { // Use local gradient only at edges
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// Estimate based on local gradient only
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df = edgedf(gx, gy, a);
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} else {
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// Estimate gradient based on direction to edge (accurate for large di)
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df = edgedf(dx, dy, a);
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}
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return di + df; // Same metric as edtaa2, except at edges (where di=0)
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}
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// Shorthand macro: add ubiquitous parameters dist, gx, gy, img and w and call distaa3()
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#define DISTAA(c,xc,yc,xi,yi) (distaa3(img, gx, gy, w, c, xc, yc, xi, yi))
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void edtaa3(double *img, double *gx, double *gy, int w, int h, short *distx, short *disty, double *dist)
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{
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int x, y, i, c;
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int offset_u, offset_ur, offset_r, offset_rd,
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offset_d, offset_dl, offset_l, offset_lu;
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double olddist, newdist;
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int cdistx, cdisty, newdistx, newdisty;
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int changed;
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double epsilon = 1e-3;
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/* Initialize index offsets for the current image width */
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offset_u = -w;
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offset_ur = -w+1;
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offset_r = 1;
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offset_rd = w+1;
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offset_d = w;
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offset_dl = w-1;
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offset_l = -1;
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offset_lu = -w-1;
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/* Initialize the distance images */
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for(i=0; i<w*h; i++) {
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distx[i] = 0; // At first, all pixels point to
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disty[i] = 0; // themselves as the closest known.
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if(img[i] <= 0.0)
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{
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dist[i]= 1000000.0; // Big value, means "not set yet"
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}
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else if (img[i]<1.0) {
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dist[i] = edgedf(gx[i], gy[i], img[i]); // Gradient-assisted estimate
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}
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else {
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dist[i]= 0.0; // Inside the object
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}
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}
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/* Perform the transformation */
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do
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{
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changed = 0;
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/* Scan rows, except first row */
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for(y=1; y<h; y++)
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{
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/* move index to leftmost pixel of current row */
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i = y*w;
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/* scan right, propagate distances from above & left */
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/* Leftmost pixel is special, has no left neighbors */
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olddist = dist[i];
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if(olddist > 0) // If non-zero distance or not set yet
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{
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c = i + offset_u; // Index of candidate for testing
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx;
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newdisty = cdisty+1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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olddist=newdist;
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changed = 1;
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}
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c = i+offset_ur;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx-1;
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newdisty = cdisty+1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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changed = 1;
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}
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}
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i++;
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/* Middle pixels have all neighbors */
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for(x=1; x<w-1; x++, i++)
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{
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olddist = dist[i];
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if(olddist <= 0) continue; // No need to update further
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c = i+offset_l;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx+1;
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newdisty = cdisty;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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olddist=newdist;
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changed = 1;
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}
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c = i+offset_lu;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx+1;
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newdisty = cdisty+1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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olddist=newdist;
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changed = 1;
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}
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c = i+offset_u;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx;
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newdisty = cdisty+1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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olddist=newdist;
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changed = 1;
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}
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c = i+offset_ur;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx-1;
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newdisty = cdisty+1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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changed = 1;
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}
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}
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/* Rightmost pixel of row is special, has no right neighbors */
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olddist = dist[i];
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if(olddist > 0) // If not already zero distance
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{
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c = i+offset_l;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx+1;
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newdisty = cdisty;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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olddist=newdist;
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changed = 1;
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}
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c = i+offset_lu;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx+1;
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newdisty = cdisty+1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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olddist=newdist;
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changed = 1;
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}
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c = i+offset_u;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx;
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newdisty = cdisty+1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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changed = 1;
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}
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}
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/* Move index to second rightmost pixel of current row. */
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/* Rightmost pixel is skipped, it has no right neighbor. */
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i = y*w + w-2;
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/* scan left, propagate distance from right */
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for(x=w-2; x>=0; x--, i--)
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{
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olddist = dist[i];
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if(olddist <= 0) continue; // Already zero distance
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c = i+offset_r;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx-1;
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newdisty = cdisty;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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changed = 1;
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}
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}
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}
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/* Scan rows in reverse order, except last row */
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for(y=h-2; y>=0; y--)
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{
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/* move index to rightmost pixel of current row */
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i = y*w + w-1;
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/* Scan left, propagate distances from below & right */
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/* Rightmost pixel is special, has no right neighbors */
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olddist = dist[i];
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if(olddist > 0) // If not already zero distance
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{
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c = i+offset_d;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx;
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newdisty = cdisty-1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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olddist=newdist;
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changed = 1;
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}
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c = i+offset_dl;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx+1;
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newdisty = cdisty-1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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changed = 1;
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}
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}
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i--;
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/* Middle pixels have all neighbors */
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for(x=w-2; x>0; x--, i--)
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{
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olddist = dist[i];
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if(olddist <= 0) continue; // Already zero distance
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c = i+offset_r;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx-1;
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newdisty = cdisty;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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olddist=newdist;
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changed = 1;
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}
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c = i+offset_rd;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx-1;
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newdisty = cdisty-1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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olddist=newdist;
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changed = 1;
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}
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c = i+offset_d;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx;
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newdisty = cdisty-1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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olddist=newdist;
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changed = 1;
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}
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c = i+offset_dl;
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cdistx = distx[c];
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cdisty = disty[c];
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newdistx = cdistx+1;
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newdisty = cdisty-1;
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newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
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if(newdist < olddist-epsilon)
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{
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distx[i]=newdistx;
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disty[i]=newdisty;
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dist[i]=newdist;
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changed = 1;
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}
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}
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/* Leftmost pixel is special, has no left neighbors */
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olddist = dist[i];
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if(olddist > 0) // If not already zero distance
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{
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c = i+offset_r;
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cdistx = distx[c];
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cdisty = disty[c];
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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<w; x++, i++)
|
|
{
|
|
/* scan right, propagate distance from left */
|
|
olddist = dist[i];
|
|
if(olddist <= 0) continue; // 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;
|
|
changed = 1;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
while(changed); // Sweep until no more updates are made
|
|
|
|
/* The transformation is completed. */
|
|
|
|
}
|