如何在2D图像堆栈上可视化3D结构张量？

Question

我正在模拟我读过的一篇论文。他们已经可视化3D结构膝关节MRI的张量，如下图所示： Visualization of structure tensor

我上网很多，但我找不到适当的回答。我已经计算了3D结构Tensor的特征值和特征向量如下：

function [mu3,mu2,mu1,v3x,v3y,v3z,v2x,v2y,v2z,v1x,v1y,v1z]=EigenVectors3DTensor(G1x.^2, G1x.*G1y, G1x.*G1z, G1y.^2, G1y.*G1z, G1z.^2)

% first derivative of each voxel in three directions (x,y,z) have been saved and vectorized in G1x, G1y and G1z, respectively.  

 Dxx=G1x.^2    
v1x=zeros(size(Dxx),'single');
v1y=zeros(size(Dxx),'single');
v1z=zeros(size(Dxx),'single');
v2x=zeros(size(Dxx),'single');
v2y=zeros(size(Dxx),'single');
v2z=zeros(size(Dxx),'single');
v3x=zeros(size(Dxx),'single');
v3y=zeros(size(Dxx),'single');
v3z=zeros(size(Dxx),'single');
mu1=zeros(size(Dxx),'single');
mu2=zeros(size(Dxx),'single');
mu3=zeros(size(Dxx),'single');

rho=1.1; %sigma out

for i=1:numel(Dxx)
    Jxx = imgaussian(Dxx(i),rho,4*rho);
    Jxy = imgaussian(Dxy(i),rho,4*rho);
    Jxz = imgaussian(Dxz(i),rho,4*rho);
    Jyy = imgaussian(Dyy(i),rho,4*rho);
    Jyz = imgaussian(Dyz(i),rho,4*rho);
    Jzz = imgaussian(Dzz(i),rho,4*rho);
    M=[Jxx Jxy Jxz; Jxy Jyy Jyz; Jxz Jyz Jzz];

    [v,d]=eig(M);
    v=v';
    ev1=d(1,1); ev2=d(2,2); ev3=d(3,3);
    ev1a=abs(ev1); ev2a=abs(ev2); ev3a=abs(ev3);

    if((ev1a>=ev2a)&&(ev1a>ev3a))
        d=ev3; dt=ev3a;  dat=v(3,:);
        ev3=ev1; v(3,:)=v(1,:);
        ev1=d; ev1a=dt; v(1,:)=dat;
    elseif((ev2a>=ev1a)&&(ev2a>ev3a))
        d=ev3; dt=ev3a;  dat=v(3,:);
        ev3=ev1; v(3,:)=v(2,:);
        ev2=d; ev2a=dt; v(2,:)=dat;
    end
    if(ev1a>ev2a)
        d=ev2; dat=v(2,:);
        ev2=ev1; v(2,:)=v(1,:);
        ev1=d; v(1,:)=dat;
    end

    mu1(i)=ev1; mu2(i)=ev2; mu3(i)=ev3;
    v1x(i)=v(1,1); v1y(i)=v(1,2); v1z(i)=v(1,3);
    v2x(i)=v(2,1); v2y(i)=v(2,2); v2z(i)=v(2,3);
    v3x(i)=v(3,1); v3y(i)=v(3,2); v3z(i)=v(3,3);
end

我有两个主要问题：

1）结构张量的特征值和特征向量的计算是否正确？

2）如何可视化扫描结构张量（2D图像堆栈）？

如果有人帮助我，我将非常感激。