double distaa3(double *img, double *gximg, double *gyimg, int w, int c, int xc, int yc, int xi, int yi)
{
double di, df, dx, dy, gx, gy, a;
int closest;
closest = c-xc-yc*w; // Index to the edge pixel pointed to from c
a = img[closest]; // Grayscale value at the edge pixel
gx = gximg[closest]; // X gradient component at the edge pixel
gy = gyimg[closest]; // Y gradient component at the edge pixel
if(a > 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)
}
// Adjust distance values near edges based on the local edge gradient
void postprocess(double *img, double *gximg, double *gyimg, int w, int h, short *distx, short *disty, double *dist)
{
int i, c, n;
double a, gx, gy, dx, dy, df, t, u, v, uvmargin;
for(i = 0; i < w*h; i++) {
dx = distx[i];
dy = disty[i];
if((dx==0) && (dy==0)) continue; // Don't touch edges, they are OK
c = i - disty[i]*w - distx[i]; // Index of closest edge pixel
a = img[c];
gx = gximg[c];
gy = gyimg[c];
if(dist[i] < 3.0) { // We can improve things only near edges (3.0 is ad hoc)
df = edgedf(gx, gy, a);
t = dy*gx - dx*gy; // Offset to orthogonal hit point in edge tangent direction
u = -df*gx + t*gy; // (u,v) pixel-local coordinates of orthogonal hit point
v = -df*gy - t*gx; // (pixel center is at (0,0), pixel is a unit square)
uvmargin = 1.0; // Margin +/- 0.5 is formally correct, but allow some overshoot
if ((fabs(u) <= uvmargin) && (fabs(v) <= uvmargin)) {
// Use estimated orthogonal distance to edge based on gradient
dist[i] = sqrt((dx+u)*(dx+u) + (dy+v)*(dy+v));
}
}
}
}
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<w*h; i++) {
distx[i] = 0; // At first, all pixels point to
disty[i] = 0; // themselves as the closest known.
if(img[i] <= 0.0)
{
dist[i]= 1000000.0; // Big value, means "not set yet"
}
else if (img[i]<1.0) {
dist[i] = edgedf(gx[i], gy[i], img[i]); // Gradient-assisted estimate
}
else {
dist[i]= 0.0; // Inside the object
}
}
/* Perform the transformation */
do
{
changed = 0;
/* Scan rows, except first row */
for(y=1; y<h; y++)
{
/* move index to leftmost pixel of current row */
i = y*w;
/* scan right, propagate distances from above & left */
/* Leftmost pixel is special, has no left neighbors */
olddist = dist[i];
if(olddist > 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<w-1; x++, i++)
{
olddist = dist[i];
if(olddist <= 0) continue; // No need to update further
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;
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;
}
}
/* Rightmost pixel of row is special, has no right neighbors */
olddist = dist[i];
if(olddist > 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<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. */
}