膨胀 dilation

考虑两幅二值图像A,B。它们的前景用黑色，背景用白色。另f_A和f_B表示各自前景点的集合。定义膨胀运算为：dilation(A,B) = {a+b| a∈A,b∈B}。比如：

A = {(2,8),(3,6),(4,4),(5,6),(6,4),(7,6),(8,8)}

B = {(0,0),(0,1)}

dilation(A,B) = {(2,8),(2,9),(3,6),(3,7),(4,4),(4,5),(5,6),(5,7),(6,4),(6,5),(7,6),(7,7),(8,8),(8,9)}

腐蚀 erosion

同样考虑两幅图像A,B。定义腐蚀运算为: erosion(A,B) = {a|(a+b)∈A, a∈A,b∈B}

膨胀腐蚀运算的性质

• 交换律 dilation(A,B) = dilation(B,A)
• 结合律 dilation(dilation(A,B),C) = dilation(A,dilation(B,C))
• 并集     dilation(A,B∪C) = dilation(A,B)∪dilation(A,C)
• 增长性 if A blongs to B then dilation(A,K) blongs to dilation(B,K)

C++ 实现

这里 buf 相当于 A，model相当于B 计算dilation(buf,model)

void ShapeOper::dilation(unsigned char* buf, int width, int height, vector<point> model)
{
int i,j,k;
point P;
unsigned char* temp = new unsigned char[width*height];
memcpy(temp,buf,width*height);
for(i=0;i<height;i++){
   for(j=0;j<width;j++){
    if(temp[(i*width+j)] < 10){
     for(k=0;k<model.size();k++){
      P.x = i + model[k].x;       //Dilation Operation 求取并集
      P.y = j + model[k].y;
      if(P.x>=0 && P.x<width && P.y>=0 && P.y<height){
       buf[(P.x*width+P.y)] = 0;
      }
     }
    }
   }
}
if(temp!=NULL){
   delete[] temp;
}
}

计算erosion(buf,model)

void ShapeOper::erosion(unsigned char* buf, int width, int height, vector<point> model)
{
int i,j,k;
point P;
unsigned char* temp = new unsigned char[width*height];
memcpy(temp,buf,width*height);
bool is_point = true;
for(i=0;i<height;i++){
   for(j=0;j<width;j++){
    if(temp[(i*width+j)] < 10){
     is_point = true;
     for(k=0;k<model.size();k++){
      P.x = i + model[k].x;
      P.y = j + model[k].y;
      if(P.x>=0 && P.x<width && P.y>=0 && P.y<height){
       if(temp[(P.x*width+P.y)] > 10){
        is_point = false;
        //cout<<"other"<<endl;
        break;
       }
      }
     }
     if(is_point){
      buf[(i*width+j)] = 0;
     }
    }
   }
}
if(temp!=NULL){
   delete[] temp;
}
}