/*
* Copyright 2009 Stefan Gustavson (stefan.gustavson@gmail.com)
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY STEFAN GUSTAVSON ''AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
* EVENT SHALL STEFAN GUSTAVSON OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
* INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* The views and conclusions contained in the software and documentation are
* those of the authors and should not be interpreted as representing official
* policies, either expressed or implied, of Stefan Gustavson.
*
*
* edtaa3()
*
* Sweep-and-update Euclidean distance transform of an
* image. Positive pixels are treated as object pixels,
* zero or negative pixels are treated as background.
* An attempt is made to treat antialiased edges correctly.
* The input image must have pixels in the range [0,1],
* and the antialiased image should be a box-filter
* sampling of the ideal, crisp edge.
* If the antialias region is more than 1 pixel wide,
* the result from this transform will be inaccurate.
*
* By Stefan Gustavson (stefan.gustavson@gmail.com).
*
* Originally written in 1994, based on a verbal
* description of the SSED8 algorithm published in the
* PhD dissertation of Ingemar Ragnemalm. This is his
* algorithm, I only implemented it in C.
*
* Updated in 2004 to treat border pixels correctly,
* and cleaned up the code to improve readability.
*
* Updated in 2009 to handle anti-aliased edges.
*
* Updated in 2011 to avoid a corner case infinite loop.
*
*/
#include
#include "edtaa3func.h"
/*
* Compute the local gradient at edge pixels using convolution filters.
* The gradient is computed only at edge pixels. At other places in the
* image, it is never used, and it's mostly zero anyway.
*/
void computegradient(double *img, int w, int h, double *gx, double *gy)
{
int i,j,k;
double glength;
#define SQRT2 1.4142136
for(i = 1; i < h-1; i++) { // Avoid edges where the kernels would spill over
for(j = 1; j < w-1; j++) {
k = i*w + j;
if((img[k]>0.0) && (img[k]<1.0)) { // Compute gradient for edge pixels only
gx[k] = -img[k-w-1] - SQRT2*img[k-1] - img[k+w-1] + img[k-w+1] + SQRT2*img[k+1] + img[k+w+1];
gy[k] = -img[k-w-1] - SQRT2*img[k-w] - img[k+w-1] + img[k-w+1] + SQRT2*img[k+w] + img[k+w+1];
glength = gx[k]*gx[k] + gy[k]*gy[k];
if(glength > 0.0) { // Avoid division by zero
glength = sqrt(glength);
gx[k]=gx[k]/glength;
gy[k]=gy[k]/glength;
}
}
}
}
// TODO: Compute reasonable values for gx, gy also around the image edges.
// (These are zero now, which reduces the accuracy for a 1-pixel wide region
// around the image edge.) 2x2 kernels would be suitable for this.
}
/*
* A somewhat tricky function to approximate the distance to an edge in a
* certain pixel, with consideration to either the local gradient (gx,gy)
* or the direction to the pixel (dx,dy) and the pixel greyscale value a.
* The latter alternative, using (dx,dy), is the metric used by edtaa2().
* Using a local estimate of the edge gradient (gx,gy) yields much better
* accuracy at and near edges, and reduces the error even at distant pixels
* provided that the gradient direction is accurately estimated.
*/
double edgedf(double gx, double gy, double a)
{
double df, glength, temp, a1;
if ((gx == 0) || (gy == 0)) { // Either A) gu or gv are zero, or B) both
df = 0.5-a; // Linear approximation is A) correct or B) a fair guess
} else {
glength = sqrt(gx*gx + gy*gy);
if(glength>0) {
gx = gx/glength;
gy = gy/glength;
}
/* Everything is symmetric wrt sign and transposition,
* so move to first octant (gx>=0, gy>=0, gx>=gy) to
* avoid handling all possible edge directions.
*/
gx = fabs(gx);
gy = fabs(gy);
if(gx 1.0) a = 1.0;
if(a < 0.0) a = 0.0; // Clip grayscale values outside the range [0,1]
if(a == 0.0) return 1000000.0; // Not an object pixel, return "very far" ("don't know yet")
dx = (double)xi;
dy = (double)yi;
di = sqrt(dx*dx + dy*dy); // Length of integer vector, like a traditional EDT
if(di==0) { // Use local gradient only at edges
// Estimate based on local gradient only
df = edgedf(gx, gy, a);
} else {
// Estimate gradient based on direction to edge (accurate for large di)
df = edgedf(dx, dy, a);
}
return di + df; // Same metric as edtaa2, except at edges (where di=0)
}
// Shorthand macro: add ubiquitous parameters dist, gx, gy, img and w and call distaa3()
#define DISTAA(c,xc,yc,xi,yi) (distaa3(img, gx, gy, w, c, xc, yc, xi, yi))
void edtaa3(double *img, double *gx, double *gy, int w, int h, short *distx, short *disty, double *dist)
{
int x, y, i, c;
int offset_u, offset_ur, offset_r, offset_rd,
offset_d, offset_dl, offset_l, offset_lu;
double olddist, newdist;
int cdistx, cdisty, newdistx, newdisty;
int changed;
double epsilon = 1e-3;
/* Initialize index offsets for the current image width */
offset_u = -w;
offset_ur = -w+1;
offset_r = 1;
offset_rd = w+1;
offset_d = w;
offset_dl = w-1;
offset_l = -1;
offset_lu = -w-1;
/* Initialize the distance images */
for(i=0; i 0) // If non-zero distance or not set yet
{
c = i + offset_u; // Index of candidate for testing
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx;
newdisty = cdisty+1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
olddist=newdist;
changed = 1;
}
c = i+offset_ur;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx-1;
newdisty = cdisty+1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
changed = 1;
}
}
i++;
/* Middle pixels have all neighbors */
for(x=1; x 0) // If not already zero distance
{
c = i+offset_l;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx+1;
newdisty = cdisty;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
olddist=newdist;
changed = 1;
}
c = i+offset_lu;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx+1;
newdisty = cdisty+1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
olddist=newdist;
changed = 1;
}
c = i+offset_u;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx;
newdisty = cdisty+1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
changed = 1;
}
}
/* Move index to second rightmost pixel of current row. */
/* Rightmost pixel is skipped, it has no right neighbor. */
i = y*w + w-2;
/* scan left, propagate distance from right */
for(x=w-2; x>=0; x--, i--)
{
olddist = dist[i];
if(olddist <= 0) continue; // Already zero distance
c = i+offset_r;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx-1;
newdisty = cdisty;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
changed = 1;
}
}
}
/* Scan rows in reverse order, except last row */
for(y=h-2; y>=0; y--)
{
/* move index to rightmost pixel of current row */
i = y*w + w-1;
/* Scan left, propagate distances from below & right */
/* Rightmost pixel is special, has no right neighbors */
olddist = dist[i];
if(olddist > 0) // If not already zero distance
{
c = i+offset_d;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx;
newdisty = cdisty-1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
olddist=newdist;
changed = 1;
}
c = i+offset_dl;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx+1;
newdisty = cdisty-1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
changed = 1;
}
}
i--;
/* Middle pixels have all neighbors */
for(x=w-2; x>0; x--, i--)
{
olddist = dist[i];
if(olddist <= 0) continue; // Already zero distance
c = i+offset_r;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx-1;
newdisty = cdisty;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
olddist=newdist;
changed = 1;
}
c = i+offset_rd;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx-1;
newdisty = cdisty-1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
olddist=newdist;
changed = 1;
}
c = i+offset_d;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx;
newdisty = cdisty-1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
olddist=newdist;
changed = 1;
}
c = i+offset_dl;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx+1;
newdisty = cdisty-1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
changed = 1;
}
}
/* Leftmost pixel is special, has no left neighbors */
olddist = dist[i];
if(olddist > 0) // If not already zero distance
{
c = i+offset_r;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx-1;
newdisty = cdisty;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
olddist=newdist;
changed = 1;
}
c = i+offset_rd;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx-1;
newdisty = cdisty-1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
olddist=newdist;
changed = 1;
}
c = i+offset_d;
cdistx = distx[c];
cdisty = disty[c];
newdistx = cdistx;
newdisty = cdisty-1;
newdist = DISTAA(c, cdistx, cdisty, newdistx, newdisty);
if(newdist < olddist-epsilon)
{
distx[i]=newdistx;
disty[i]=newdisty;
dist[i]=newdist;
changed = 1;
}
}
/* Move index to second leftmost pixel of current row. */
/* Leftmost pixel is skipped, it has no left neighbor. */
i = y*w + 1;
for(x=1; x