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Envoyé par pseudocode
Voici une implémentation Java de l'algorithme "Snake" (contour actif).
L'algorithme Snake permet de tracer le contour d'une zone irrégulière en déformant progressivement une courbe de départ. Pour plus d'informations, je vous conseille l' article de khayyam90.
La classe Snake (attributs+constructeur)
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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"
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/**
* 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:
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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:
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// 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--;
}
}
} |
Utilisation:
Le constructeur de la classe Snake a besoin des paramètres suivants:
- int width,height: la taille de l'image (et des deux tableaux suivants)
- int[][] gradient: un tableau contenant la norme du gradient pour chaque pixel [x][y]
- int[][] flow: un tableau contenant la norme du vecteur de flux pour chaque pixel [x][y].
En pratique, on peut utiliser la carte des distances jusqu'au pic de gradient le plus proche
- Point... points: la liste des points constituant le snake initial
La méthode publique "loop()" fait évoluer le snake jusqu'a convergence et retourne la liste des points du snake final. |
Salut, si tu peut mieux m'expliquer Les méthodes du mécanisme d'auto-adaptation, j'aimerai bien savoir quelle sont ces méthodes est ce que ce sont des méthode d'interpolation comme B-Spline puis ce que dans le code source je voit l'utilisation des coeffissions, merci de plus de détail.
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27/07/2012, 16h27
Xavier Philippeau
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