通过在2D曲面中投影来分析3D点云 [英] Analysis of a 3D point cloud by projection in a 2D surface

问题描述

我有一个3D点云(XYZ)，其中Z可以是位置或能量.我想将它们投影在 n -by- m 网格(在我的问题n = m中)的2D曲面上，方式是每个网格单元的值为在Z是位置的情况下，Z的最大差，在Z是能量的情况下，Z的总和值.

I have a 3D point cloud (XYZ) where the Z can be position or energy. I want to project them on a 2D surface in a n-by-m grid (in my problem n = m) in a manner that each grid cell has a value of the maximum difference of Z, in case of Z being position, or a value of summation over Z, in case of Z being energy.

例如，在0 <= (x,y) <= 20范围内，有500点.假设xy平面具有 n -by- m 个分区，例如 4 -by- 4 ;我的意思是，在x和y方向上，我们有4个分区，每个分区的间隔为5(以使其最大为20.现在，这些单元格中的每一个都应具有求和的值，或者在定义的xy平面的相应列中的那些点的Z值的最大差.

For example, in a range of 0 <= (x,y) <= 20, there are 500 points. Let's say the xy-plane has n-by-m partitions, e.g. 4-by-4; by which I mean in both x and y directions we have 4 partitions with an interval of 5 (to make it 20 at maximum. Now, each of these cells should have a value of the summation, or maximum difference, of the Z value of those points which are in the corresponding column in the defined xy-plane.

为进行如下测试，我制作了一个简单的XYZ数组，在这种情况下，Z表示每个点的能量.

I made a simple array of XYZ just for a test as follows, where in this case, Z denotes the energy of the each point.

n=1;
for i=1:2*round(random('Uniform',1,5))
    for j=1:2*round(random('Uniform',1,5))
        table(n,:)=[i,j,random('normal',1,1)];
        n=n+1;
    end
end

如何做到没有循环?

推荐答案

备注:

1. 通过python熊猫和切割方法，所有这些几乎都是一线的.
2. 我已经重写了您的随机云初始化

---

您可以做的是

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What you can do is

1. 通过meshgrid
布局xy网格
2. 将云投影在xy上(简单边缘化)
3. 通过kd-tree搜索找到最近的网格点，即 label 将您的数据与每个云点相关联的网格节点
4. 按标签分组数据并评估您的本地统计信息(通过accumarray).

1. layout an xy grid via meshgrid,
2. project the cloud on xy (simple marginalization)
3. find the nearest grid point via a kd-tree search, i.e. label your data associating to each cloud point a grid node
4. group data by label and evaluate your local statistic (via accumarray).

这是一个可行的示例:

 samples = 500;
 %data extrema
 xl = 0; xr = 1; yl = 0; yr = 1;

 % # grid points
 sz = 20;
 % # new random cloud    
 table = [random('Uniform',xl,xr,[samples,1]) , random('Uniform',yr,yl,[samples,1]), random('normal',1,1,[samples,1])];

 figure; scatter3(table(:,1),table(:,2),table(:,3));

 % # grid construction
 xx = linspace(xl,xr,sz); yy = linspace(yl,yr,sz);
 [X,Y] = meshgrid(xx,yy);
 grid_centers = [X(:),Y(:)];

 x = table(:,1); y = table(:,2); 

 % # kd-tree
 kdtreeobj = KDTreeSearcher(grid_centers);
 clss = kdtreeobj.knnsearch([x,y]); % # classification

 % # defintion of local statistic
 local_stat = @(x)sum(x) % # for total energy
 % local_stat = @(x)max(x)-min(x) % # for position off-set

 % # data_grouping
 class_stat = accumarray(clss,table(:,3),[],local_stat );       
 class_stat_M  = reshape(class_stat , size(X)); % # 2D reshaping

 figure; contourf(xx,yy,class_stat_M,20); 

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