611 lines
21 KiB
C
611 lines
21 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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* Updated 2012 to change license from LGPL to MIT.
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*
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* Updated 2014 to fix a bug with the 'gy' gradient computation.
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*
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*/
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/*
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Copyright (C) 2009-2012 Stefan Gustavson (stefan.gustavson@gmail.com)
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The code in this file is distributed under the MIT license:
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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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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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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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#include <math.h>
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#include "edtaa3func.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, p, q;
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double glength, phi, phiscaled, ascaled, errsign, pfrac, qfrac, err0, err1,
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err;
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#define SQRT2 1.4142136
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for (i = 1; i < h - 1; i++)
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{ // Avoid edges where the kernels would spill over
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for (j = 1; j < w - 1; j++)
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{
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k = i * w + j;
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if ((img[k] > 0.0) && (img[k] < 1.0))
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{ // Compute gradient for edge pixels only
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gx[k] = -img[k - w - 1] - SQRT2 * img[k - 1] - img[k + w - 1] +
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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] +
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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)
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{ // 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))
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{ // 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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}
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else
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{
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glength = sqrt(gx * gx + gy * gy);
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if (glength > 0)
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{
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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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{
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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)
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{ // 0 <= a < a1
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df = 0.5 * (gx + gy) - sqrt(2.0 * gx * gy * a);
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}
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else if (a < (1.0 - a1))
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{ // a1 <= a <= 1-a1
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df = (0.5 - a) * gx;
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}
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else
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{ // 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,
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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)
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a = 1.0;
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if (a < 0.0)
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a = 0.0; // Clip grayscale values outside the range [0,1]
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if (a == 0.0)
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return 1000000.0; // Not an object pixel, return "very far" ("don't know
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// yet")
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dx = (double) xi;
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dy = (double) yi;
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di = sqrt(dx * dx +
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dy * dy); // Length of integer vector, like a traditional EDT
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if (di == 0)
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{ // 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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}
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else
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{
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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
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// 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,
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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, offset_d, offset_dl, offset_l,
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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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{
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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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{
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dist[i] =
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edgedf(gx[i], gy[i], img[i]); // Gradient-assisted estimate
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}
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else
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{
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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)
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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)
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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)
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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;
|
|
}
|
|
|
|
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. */
|
|
}
|