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| public class Snake {
// Points of the snake
private List<Point> snake;
// Length of the snake (euclidean distance)
private double snakelength=0;
// size of the image (and of the 2 arrays below)
private int width=0,height=0;
// gradient value (modulus)
private int[][] gradient;
// gradient flow (modulus)
private int[][] flow;
// 3x3 neighborhood used to compute energies
private double[][] e_uniformity = new double[3][3];
private double[][] e_curvature = new double[3][3];
private double[][] e_flow = new double[3][3];
private double[][] e_inertia = new double[3][3];
// auto add/remove points to the snake
// according to distance between points
private boolean AUTOADAPT=true;
private static int AUTOADAPT_LOOP=10;
private static int AUTOADAPT_MINLEN=8;
private static int AUTOADAPT_MAXLEN=16;
// maximum number of iterations (if no convergence)
private static int MAXITERATION = 1000;
// coefficients for the 4 energy functions
public double alpha=1.1, beta=1.2, gamma=1.5, delta=3.0;
// alpha = coefficient for uniformity (high => force equals distance between points)
// beta = coefficient for curvature (high => force smooth curvature)
// gamma = coefficient for flow (high => force gradient attraction)
// delta = coefficient for intertia (high => get stuck to gradient)
/**
* Constructor
*
* @param width,height size of the image and of the 2 following arrays
* @param gradient gradient (modulus)
* @param flow gradient flow (modulus)
* @param points inital points of the snake
*/
public Snake(int width, int height, int[][] gradient, int[][] flow, Point... points) {
this.snake = new ArrayList<Point>(Arrays.asList(points));
this.gradient = gradient;
this.flow = flow;
this.width = width;
this.height = height;
}
// add here the other methods.
}
Les méthodes de l'algorithme "snake"
Code java :
/**
* main loop
*
* @return the final snake
*/
public List<Point> loop() {
int loop=0;
while(step() && loop<MAXITERATION) {
// auto adapt the number of points in the snake
if (AUTOADAPT && (loop%AUTOADAPT_LOOP)==0) {
removeOverlappingPoints(AUTOADAPT_MINLEN);
addMissingPoints(AUTOADAPT_MAXLEN);
}
loop++;
}
// rebuild using spline interpolation
if (AUTOADAPT) rebuild(AUTOADAPT_MAXLEN);
return this.snake;
}
/**
* update the position of each point of the snake
*
* @return true if the snake has changed, otherwise false.
*/
private boolean step() {
boolean changed=false;
Point p = new Point(0,0);
// compute length of original snake (used by method: f_uniformity)
this.snakelength = getsnakelength();
// compute the new snake
List<Point> newsnake = new ArrayList<Point>(snake.size());
// for each point of the previous snake
for(int i=0;i<snake.size();i++) {
Point prev = snake.get((i+snake.size()-1)%snake.size());
Point cur = snake.get(i);
Point next = snake.get((i+1)%snake.size());
// compute all energies
for(int dy=-1;dy<=1;dy++) {
for(int dx=-1;dx<=1;dx++) {
p.setLocation(cur.x+dx, cur.y+dy);
e_uniformity[1+dx][1+dy] = f_uniformity(prev,next,p);
e_curvature[1+dx][1+dy] = f_curvature(prev,p,next);
e_flow[1+dx][1+dy] = f_gflow(cur,p);
e_inertia[1+dx][1+dy] = f_inertia(cur,p);
}
}
// normalize energies
normalize(e_uniformity);
normalize(e_curvature);
normalize(e_flow);
normalize(e_inertia);
// find the point with the minimum sum of energies
double emin = Double.MAX_VALUE, e=0;
int x=0,y=0;
for(int dy=-1;dy<=1;dy++) {
for(int dx=-1;dx<=1;dx++) {
e = 0;
e+= alpha * e_uniformity[1+dx][1+dy]; // internal energy
e+= beta * e_curvature[1+dx][1+dy]; // internal energy
e+= gamma * e_flow[1+dx][1+dy]; // external energy
e+= delta * e_inertia[1+dx][1+dy]; // external energy
if (e<emin) { emin=e; x=cur.x+dx; y=cur.y+dy; }
}
}
// boundary check
if (x<1) x=1;
if (x>=(this.width-1)) x=this.width-2;
if (y<1) y=1;
if (y>=(this.height-1)) y=this.height-2;
// compute the returned value
if (x!=cur.x || y!=cur.y) changed=true;
// create the point in the new snake
newsnake.add(new Point(x,y));
}
// new snake becomes current
this.snake=newsnake;
return changed;
}
// normalize energy matrix
private void normalize(double[][] array3x3) {
double sum=0;
for(int i=0;i<3;i++)
for(int j=0;j<3;j++)
sum+=Math.abs(array3x3[i][j]);
if (sum==0) return;
for(int i=0;i<3;i++)
for(int j=0;j<3;j++)
array3x3[i][j]/=sum;
}
private double getsnakelength() {
// total length of snake
double length=0;
for(int i=0;i<snake.size();i++) {
Point cur = snake.get(i);
Point next = snake.get((i+1)%snake.size());
length+=distance2D(cur, next);
}
return length;
}
private double distance2D(Point A, Point B) {
int ux = A.x-B.x;
int uy = A.y-B.y;
double un = ux*ux+uy*uy;
return Math.sqrt(un);
}
Les méthodes des fonctions d'energie:
Code java :
private double f_uniformity(Point prev, Point next, Point p) {
// length of previous segment
double un = distance2D(prev, p);
// mesure of uniformity
double avg = snakelength/snake.size();
double dun = Math.abs(un-avg);
// elasticity energy
return dun*dun;
}
private double f_curvature(Point prev, Point p, Point next) {
int ux = p.x-prev.x;
int uy = p.y-prev.y;
double un = Math.sqrt(ux*ux+uy*uy);
int vx = p.x-next.x;
int vy = p.y-next.y;
double vn = Math.sqrt(vx*vx+vy*vy);
if (un==0 || vn==0) return 0;
double cx = (vx+ux)/(un*vn);
double cy = (vy+uy)/(un*vn);
// curvature energy
double cn = cx*cx+cy*cy;
return cn;
}
private double f_gflow(Point cur, Point p) {
// gradient flow
int dcur = this.flow[cur.x][cur.y];
int dp = this.flow[p.x][p.y];
double d = dp-dcur;
return d;
}
private double f_inertia(Point cur, Point p) {
double d = distance2D(cur, p);
double g = this.gradient[cur.x][cur.y];
double e = g*d;
return e;
}
Les méthodes du mécanisme d'auto-adaptation:
Code java :
// rebuild the snake using cubic spline interpolation
private void rebuild(int space) {
// precompute length(i) = length of the snake from start to point #i
double[] clength = new double[snake.size()+1];
clength[0]=0;
for(int i=0;i<snake.size();i++) {
Point cur = snake.get(i);
Point next = snake.get((i+1)%snake.size());
clength[i+1]=clength[i]+distance2D(cur, next);
}
// compute number of points in the new snake
double total = clength[snake.size()];
int nmb = (int)(0.5+total/space);
// build a new snake
List<Point> newsnake = new ArrayList<Point>(snake.size());
for(int i=0,j=0;j<nmb;j++) {
// current length in the new snake
double dist = (j*total)/nmb;
// find corresponding interval of points in the original snake
while(! (clength[i]<=dist && dist<clength[i+1])) i++;
// get points (P-1,P,P+1,P+2) in the original snake
Point prev = snake.get((i+snake.size()-1)%snake.size());
Point cur = snake.get(i);
Point next = snake.get((i+1)%snake.size());
Point next2 = snake.get((i+2)%snake.size());
// do cubic spline interpolation
double t = (dist-clength[i])/(clength[i+1]-clength[i]);
double t2 = t*t, t3=t2*t;
double c0 = 1*t3;
double c1 = -3*t3 +3*t2 +3*t + 1;
double c2 = 3*t3 -6*t2 + 4;
double c3 = -1*t3 +3*t2 -3*t + 1;
double x = prev.x*c3 + cur.x*c2 + next.x* c1 + next2.x*c0;
double y = prev.y*c3 + cur.y*c2 + next.y* c1 + next2.y*c0;
Point newpoint = new Point( (int)(0.5+x/6), (int)(0.5+y/6) );
// add computed point to the new snake
newsnake.add(newpoint);
}
this.snake = newsnake;
}
private void removeOverlappingPoints(int minlen) {
// for each point of the snake
for(int i=0;i<snake.size();i++) {
Point cur = snake.get(i);
// check the other points (right half)
for(int di=1+snake.size()/2;di>0;di--) {
Point end = snake.get((i+di)%snake.size());
double dist = distance2D(cur,end);
// if the two points are to close...
if ( dist>minlen ) continue;
// ... cut the "loop" part og the snake
for(int k=0;k<di;k++) snake.remove( (i+1) %snake.size() );
break;
}
}
}
private void addMissingPoints(int maxlen) {
// for each point of the snake
for(int i=0;i<snake.size();i++) {
Point prev = snake.get((i+snake.size()-1)%snake.size());
Point cur = snake.get(i);
Point next = snake.get((i+1)%snake.size());
Point next2 = snake.get((i+2)%snake.size());
// if the next point is to far then add a new point
if ( distance2D(cur,next)>maxlen ) {
// precomputed Uniform cubic B-spline for t=0.5
double c0=0.125/6.0, c1=2.875/6.0, c2=2.875/6.0, c3=0.125/6.0;
double x = prev.x*c3 + cur.x*c2 + next.x* c1 + next2.x*c0;
double y = prev.y*c3 + cur.y*c2 + next.y* c1 + next2.y*c0;
Point newpoint = new Point( (int)(0.5+x), (int)(0.5+y) );
snake.add( i+1 , newpoint ); i--;
}
}
} |
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