寻找 3d 矩阵的局部最大值

Question

我正在尝试在 Matlab 中实现霍夫变换以在 picture 中找到圆圈。

在累加器矩阵中，全局最大值在A(32,31,24)处105。所以我能够得到这个：max circle

问题是，我怎样才能找到局部最大值来找到其余的圆？

我写这个是为了找到比 26 个相邻点（26 连接的体素邻域）大的 A(i,j,k)：

[i j k]=find(A~=0) ;
f=0;
for s=1:size(i)
    if(i(s)~=100&&j(s)~=100&&k(s)~=141&&i(s)~=1&&j(s)~=1&&k(s)~=1)
    if     (A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s)-1))
        f=f+1
        i(s)
        j(s)
        k(s)
    end
    end
end

为什么我从来没有得到正确的 i、j、k 而 f 总是 0？我想我至少应该找到 (32,31,24) 和 f=1?

谁能帮帮我？非常感谢！

完整代码在这里：

im=imread('C:\Users\dell\Desktop\tp-complet\Hough\four.png');

sigma = 0.3;
gausFilter = fspecial('gaussian',[5 5],sigma);
sobelFilter=fspecial('sobel');
img=imfilter(im,gausFilter,'replicate');

ims=edge(img,'sobel');

rmax=size(im,1);
cmax=size(im,2);
radmax=round(sqrt(rmax^2+cmax^2));

for i=1:rmax
   for j=1:cmax
      for k=1:radmax
          A(i,j,k)=0;
      end
  end
end

[r c]=find(ims==1);
length=size(r);

for k=1:length
    for l=1:rmax
    for m=1:cmax
        if((l~=r(k))&&(m~=c(k)))
            x=sqrt((l-r(k))^2+(m-c(k))^2);
            x=round(x);
            A(l,m,x)=A(l,m,x)+1;
        end
   end
   end
end

[i j k]=find(A~=0) ;
f=0;
for s=1:size(i)
    if(i(s)~=100&&j(s)~=100&&k(s)~=141&&i(s)~=1&&j(s)~=1&&k(s)~=1)
    if     (A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s))&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s))&&A(i(s),j(s),k(s))>A(i(s),j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s)+1)&&A(i(s),j(s),k(s))>A(i(s),j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s),k(s)-1)&&A(i(s),j(s),k(s))>A(i(s),j(s)-1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s),j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)-1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)-1,j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)+1,k(s)-1)&&A(i(s),j(s),k(s))>A(i(s)+1,j(s)-1,k(s)-1))
        f=f+1
        i(s)
        j(s)
        k(s)
    end
    end
end

Answer 1

我没有图像处理工具箱，所以不能轻易运行你的代码。但是，快速查看后我发现您错误地使用了 find 函数。当提供 3 个输出（正如您所拥有的那样）时，find 不会 return 3D 索引，而是行、列和值的向量。这意味着 k 只是一个由 1 组成的巨大向量，因此您的 for 循环的 if k(s)~=1 语句永远不会满足。如果您想要 3D 索引，则应该执行类似 [i,j,k]=ind2sub(size(A),find(A~=0)) 的操作。

另外，仅供参考，这个：

for i=1:rmax
   for j=1:cmax
      for k=1:radmax
          A(i,j,k)=0;
      end
  end
end

可以替换为A=zeros(rmax,cmax,radmax);。

寻找 3d 矩阵的局部最大值

Finding local maxima for 3d matrix

matlab

geometry

hough-transform