Compute,store, and find min of 3d distances between two different matrices.

Hello, I have trouble using the built in functions of matlab to do this because what I want is different from what I think those functions do. I have two matrices of 3d points, say A and B. They do not have the same number than elements A<<B. I want to compute distances between each point in A and all points in B, and then be able to store it with the distance and index of the point in B. Then repeat for the next point in A until the end. I was thinking to try to use nested loops reiterating through A and the inner one through B, I just am unsure how to finely put the storage of the distance and index of the min into another vector or matrix (size A x 1)

Answer 1

[Matt J]

Here's what I use, but there are better optimized alternatives on the FEX.

 [distances,index]=min(interdists(A,B),[],2);

function Graph=interdists(A,B)
%Finds the graph of distances between point coordinates
%
% (1) Graph=interdists(A,B)
%
% in:
% 
% A:  matrix whose columns are coordinates of points, for example 
%          [[x1;y1;z1], [x2;y2;z2] ,..., [xM;yM;zM]]
%     but the columns may be points in a space of any dimension, not just 3D.
% 
% B:  A second matrix whose columns are coordinates of points in the same
%     Euclidean space. Default B=A.
% 
% 
% out:
% 
% Graph: The MxN  matrix of separation distances in l2 norm between the coordinates. 
%        Namely, Graph(i,j) will be the distance between A(:,i) and B(:,j).
%
%
% (2) interdists(A,'noself') is the same as interdists(A), except the output 
%     diagonals will be NaN instead of zero. Hence, for example, operations
%     like min(interdists(A,'noself')) will ignore self-distances.
%
% See also getgraph

noself=false;
if nargin<2  
    B=A; 
elseif ischar(B)&&strcmpi(B,'noself')
    noself=true;
    B=A;
end

N=size(A,1);
B=reshape(B,N,1,[]);

Graph=l2norm(bsxfun(@minus, A, B),1);

Graph=permute(Graph,[2,3,1]);

if noself
    n=length(Graph);
   Graph(linspace(1,n^2,n))=nan; 

function out=l2norm(X,varargin)
%out=l2norm(X,varargin)
%
%Takes the L2 norm along desired dimensions of the array X.
%
%VARARGIN can be any of the additional arguments of the sum.m function
%and follows the same conventions as this and similar functions. That is, 
%if VARARGIN={}, the function operates along the first non-singleton 
%dimension, etc...
%
%SEE ALSO sumsq

X=X.^2;

out=sum(X,varargin{:});

out=sqrt(out);

[Bernard]

thankyou I will try this!

Answer 2

[Azzi Abdelmalek]

A=randi(100,2,2,3)
B=randi(100,2,2,3)
D=sqrt(sum((A-B).^2,3))

[Bernard]

I said A and B are not the same size