Analysis of a 3D point cloud by projection in a 2D surface

Question

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

Answer 1

The accumarray function is quite suited for this kind of task. First I define example data:

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

• The three columns of table represent x, y, z respectively
• No point has x lower than that of first edge of your grid or greater than last edge, and the same for y. That is, the grid covers all points.
• If a bin contains no values the result should be NaN (if you want some other fill value, just change last argument of accumarray).

Then:

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:

• The key is obtaining ii and jj, which give the indices of the x and y bins in which each point lies. I use repmat to do that. It would have been better to usebsxfun, but it doesn't support the multiple-output version of @max.
• The result has size (M-1) x (N-1) (numbers of bins in each dimension)