[英]Analysis of a 3D point cloud by projection in a 2D surface
I have a 3D point cloud (XYZ) where the Z
can be position or energy. 我有一个3D点云(XYZ),其中Z
可以是位置或能量。 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. 我希望将它们投影在n- by- m网格中的2D表面上(在我的问题n = m
),其方式是每个网格单元具有Z
的最大差值,如果Z
是位置,或者求和的超过一个值Z
,在的情况下, Z
是能量。
For example, in a range of 0 <= (x,y) <= 20
, there are 500 points. 例如,在0 <= (x,y) <= 20
,有500个点。 Let's say the xy-plane has n -by- m partitions, eg 4 -by- 4 ; 假设xy平面具有n -by- m分区,例如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. 我的意思是在x
和y
方向上,我们有4个间隔为5
分区(使其最大为20
现在,这些单元格中的每一个都应该具有Z
值的总和或最大差值的值。那些位于定义的xy平面中相应列中的点。
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. 我制作了一个简单的XYZ阵列,仅用于测试,如下所示,在这种情况下, Z
表示每个点的能量。
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
How can this be done without loops? 如何在没有循环的情况下完成?
The accumarray
function is quite suited for this kind of task. accumarray
功能非常适合这种任务。 First I define example data: 首先我定义示例数据:
table = [ 20*rand(1000,1) 30*rand(1000,1) 40*rand(1000,1)]; % random data
x_partition = 0:2:20; % partition of x axis
y_partition = 0:5:30; % partition of y axis
I'm assuming that 我在假设
table
represent x, y, z respectively table
的三列分别代表x,y,z NaN
(if you want some other fill value, just change last argument of accumarray
). 如果bin不包含值,则结果应为NaN
(如果您想要其他填充值,只需更改accumarray
最后一个参数)。 Then: 然后:
L = size(table,1);
M = length(x_partition);
N = length(y_partition);
[~, ii] = max(repmat(table(:,1),1,M) <= repmat(x_partition,L,1),[],2);
[~, jj] = max(repmat(table(:,2),1,N) <= repmat(y_partition,L,1),[],2);
ii = ii-1; % by assumption, all values in ii will be at least 2, so we subtract 1
jj = jj-1; % same for jj
result_maxdif = accumarray([ii jj], table(:,3), [M-1 N-1], @(v) max(v)-min(v), NaN);
result_sum = accumarray([ii jj], table(:,3), [M-1 N-1], @sum, NaN);
Notes to the code: 代码注释:
ii
and jj
, which give the indices of the x and y bins in which each point lies. 关键是获得ii
和jj
,它们给出每个点所在的x和y区的索引。 I use repmat
to do that. 我使用repmat
来做到这一点。 It would have been better to use bsxfun
, but it doesn't support the multiple-output version of @max
. 最好使用bsxfun
,但它不支持@max
的多输出版本。 Remarks: 备注:
What you can do is 你能做的是
meshgrid
, 通过meshgrid
布局xy网格, kd-tree
search, ie label your data associating to each cloud point a grid node 通过kd-tree
搜索找到最近的网格点,即将与每个云点相关联的数据标记为网格节点 accumarray
). 按标签分组数据并评估您当地的统计数据(通过accumarray
)。 Here's a working example: 这是一个有效的例子:
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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