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@@ -1,570 +0,0 @@
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-/*
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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 ([email protected]).
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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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- * Updated 2012 to change license from LGPL to MIT.
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- */
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-
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-/*
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- Copyright (C) 2009-2012 Stefan Gustavson ([email protected])
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- The code in this file is distributed under the MIT license:
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-
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- Permission is hereby granted, free of charge, to any person obtaining a copy
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- of this software and associated documentation files (the "Software"), to deal
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- in the Software without restriction, including without limitation the rights
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- to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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- copies of the Software, and to permit persons to whom the Software is
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- furnished to do so, subject to the following conditions:
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-
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- The above copyright notice and this permission notice shall be included in
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- all copies or substantial portions of the Software.
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-
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- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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- IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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- FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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- AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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- LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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- OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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- THE SOFTWARE.
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- */
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-
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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,p,q;
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- double glength, phi, phiscaled, ascaled, errsign, pfrac, qfrac, err0, err1, err;
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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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-/*
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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- /* move index to leftmost pixel of current row */
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- i = y*w;
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-
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- /* scan right, propagate distances from above & left */
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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 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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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- {
|
|
|
- /* 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 */
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|
|
- olddist = dist[i];
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|
|
- if(olddist > 0) // If not already zero distance
|
|
|
- {
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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)
|
|
|
- {
|
|
|
- distx[i]=newdistx;
|
|
|
- disty[i]=newdisty;
|
|
|
- dist[i]=newdist;
|
|
|
- olddist=newdist;
|
|
|
- changed = 1;
|
|
|
- }
|
|
|
-
|
|
|
- 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);
|
|
|
- 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<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. */
|
|
|
-
|
|
|
-}
|
Daniele Bartolini