http://blog.csdn.net/byxdaz/archive/2006/04/18/667432.aspx

Snake 算法或Active Contour Models。這類算法需要給出初始的輪廓，然后進(jìn)行迭代，使輪廓沿能量降低的方向靠近，最后得到一個優(yōu)化的邊界。能量函數(shù)包括內(nèi)外力兩方面，如邊界曲率 和梯度。由于用戶無法估計迭代的最后結(jié)果，應(yīng)用Snake 算法往往需要進(jìn)行多次的交互工作。特別當(dāng)目標(biāo)比較復(fù)雜時，或與其它物體靠得較近時，初始的輪廓不易確定，而迭代的結(jié)果往往不能達(dá)到要求。

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bool termination_point
bool neighbor3by3; /* true means 3x3 neighborhood, false means 5x5 neighborhood */
int grad_mag[500][500]; /* Magnitude of Gradient */
int m_Cols; /* Number of Columns */
int m_Rows; /* Number of Rows */
int no_of_snake_points;
CPoint Snake_points[200]; /* Snake Points */
double *alpha,*beta, *gamma; /* Weights for energies */
double threshold_curvature;?
int threshold_movement;

void Snake_algorithm()?
{
bool flag_change;
int movement,i,j,iteration=0;
double avg_distance=0.0, max_curvature;
CPoint temp;
double *curvature;
alpha=new double[no_of_snake_points];
beta=new double[no_of_snake_points];
gamma=new double[no_of_snake_points];
curvature=new double[no_of_snake_points];
termination_point=false;

for(i=0;i<no_of_snake_points;i++)
{
*(alpha+i)=1.0;
*(beta+i)=1.0;
*(gamma+i)=1.2;
avg_distance+=find_distance(i, Snake_points[i]);
}
j=no_of_snake_points;
pdc=GetDC();
while(!termination_point)
{
movement=0;
avg_distance=avg_distance/(double)no_of_snake_points;
max_curvature=-1000000000.0;
for(i=0;i<no_of_snake_points;i++)
{
temp=find_min_energy(i, Snake_points[i],avg_distance);
flag_change=false;
if(temp!=Snake_points[i]&&temp!=Snake_points[(i-1+j)%j]&&temp!=Snake_points[(i+1)%j])
{
Snake_points[i]=temp;
movement++;
}
curvature[i]=find_curvature(i, Snake_points[i]);
if(max_curvature<curvature[i])
max_curvature=curvature[i];
}
avg_distance=0.0;
for(i=0;i<no_of_snake_points;i++)
curvature[i]=curvature[i]/max_curvature;
for(i=0;i<no_of_snake_points;i++)
{
avg_distance+=find_distance(i, Snake_points[i]);
if(curvature[i]>threshold_curvature&&curvature[i]>curvature[(i+1)%no_of_snake_points]&&curvature[i]>curvature[(i-1+no_of_snake_points)%no_of_snake_points])
*(beta+i)=0;
}
if(movement<threshold_movement)
termination_point=true;
iteration++;
if(iteration>Max_Iterations)
termination_point=true;
}
delete alpha;
delete beta;
delete gamma;
delete curvature;
}


double find_distance(int no, CPoint point)
{
int x=no_of_snake_points;
point-=Snake_points[(no-1+x)%x];
return(sqrt(point.x*point.x+point.y*point.y));
}

double find_curvature(int no, CPoint point)
{
int x=no_of_snake_points;
point=Snake_points[(no-1+x)%x]-point-point+Snake_points[(no+1)%x];
return(point.x*point.x+point.y*point.y);
}

double find_continuity(int no, CPoint point, double avg_distance)
{
return(pow(avg_distance-find_distance(no,point),2));
}


CPoint find_min_energy(int no, CPoint point, double avg_distance)
{
CPoint p, min_point;
double max_curvature, max_continuity, max_internal, min_internal, min_energy, energy;
double curvatures[5][5];
double continuities[5][5];
double internal_energies[5][5];
int i,j, limit=1;
max_curvature=max_continuity=max_internal=-1000000000000.0;
min_internal=1000000000000.0;
if(!neighbor3by3)
limit++;
for(i=-limit;i<=limit;i++)
{
p.y=point.y+i;
if(p.y<0)
p.y=0;
if(p.y>=m_Rows)
p.y=m_Rows-1;
for(j=-limit;j<=limit;j++)
{
p.x=point.x+j;
if(p.x<0)
p.x=0;
if(p.x>=m_Cols)
p.x=m_Cols-1;
curvatures[i+limit][j+limit]=find_curvature(no, p); //This code can cause problem near
continuities[i+limit][j+limit]=find_continuity(no,p,avg_distance); //border of image
internal_energies[i+limit][j+limit]=(double)grad_mag[p.y][p.x];
if(curvatures[i+limit][j+limit]>max_curvature)
max_curvature=curvatures[i+limit][j+limit];
if(continuities[i+limit][j+limit]>max_continuity)
max_continuity=continuities[i+limit][j+limit];
if(internal_energies[i+limit][j+limit]>max_internal)
max_internal=internal_energies[i+limit][j+limit];
if(internal_energies[i+limit][j+limit]<min_internal)
min_internal=internal_energies[i+limit][j+limit];
}
}
for(i=0;i<=2*limit;i++)
{
for(j=0;j<=2*limit;j++)
{
curvatures[i][j]=curvatures[i][j]/max_curvature;
continuities[i][j]=continuities[i][j]/max_continuity;
internal_energies[i][j]=(internal_energies[i][j]-min_internal)/(max_internal-min_internal);
}
}
min_point.x=-limit;
min_point.y=-limit;
min_energy=1000000000000.0;
for(i=-limit;i<=limit;i++)
{
for(j=-limit;j<=limit;j++)
{
energy=*(alpha+no)*continuities[i+limit][j+limit]+*(beta+no)*curvatures[i+limit][j+limit]-*(gamma+no)*internal_energies[i+limit][j+limit];
if(energy<min_energy||(energy==min_energy&&i==0&&j==0))
{
min_energy=energy;
min_point.x=j;
min_point.y=i;
}
}
}
min_point.x=min_point.x+point.x;
min_point.y=min_point.y+point.y;
return(min_point);
}


/

參考資料：[1] Williams. Donna and Shah. Mubarak. "A Fast Algorithm for Active Contours and Curvature Estimation", CVGIP: Image Understanding. Vol. 55, No. 1, January 1992. pp. 14-26.?
[2] M. Kass, A. Witkin, D. Terzopoulos. Snake: Active Contour Models. International Journal of Computer Vision. Vol.1, No.4, pp.321-331, 1988.

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