How can I find distances to the chosen point from all the other points ( Euclidean distance ) ?

Hi all, Let's assume that I have a huge matrix and say that I pick a point from that matrix. Is there a way of calculating euclidean distance from all the other points of that matrix and store them separately in the matrix of the same dimension where the number in each entry of a matrix is a number that represents the Euclidean distance to the pre-chosen point ?? Thank you

Answer 1

[Image Analyst]

Assuming you mean in spatial space (which ignores the actual matrix values and just looks at their location), and not in intensity or value space (which compares differences in intensity or value of the matrix to some other intensity or value), then you can do:

% Setup
rows = 4;  % For example
columns = 5;
% x and y can be column and row indexes, respectively, but they don't have to be.
x = 1;  % For example
y = 1;
% Now compute the distances from every element to (x, y).
[XGrid, YGrid] = meshgrid(1:columns, 1:rows)
distances = sqrt((x - XGrid) .^ 2 + (y - YGrid) .^ 2)

[Damian Wierzbicki]

Yes, it is in spatial space. Your answer works perfectly, thank you so much for your help !

[Damian Wierzbicki]

Let's assume that I'm now in the intensity space and for every entry of the matrix that equals to 0 I would want to get 0 back in my corresponding 'distance matrix' but then for every non-zero value of my reference matrix I would want to calculate the euclidean distance from the selected point and store those values in my 'distance matrix'. Is that possible ? Thank you.

[Damian Wierzbicki]

Actually, it'd be the value space that I'm more interested in.

[Damian Wierzbicki]

I did this, but it doesn't work: B = zeros (rows , columns ); for c = 1:columns for r = 1:rows if ref_matrix ( r , c ) == 0 B = 0; elseif ref_matrix ( r , c ) ~= 0 B = ( r , c ) = distances ( r , c ); end end end

[Damian Wierzbicki]

    B = zeros (rows , columns ); 
for c = 1:columns 
   for r = 1:rows 
    if ref_matrix ( r , c ) == 0 
     B = 0; 
       elseif ref_matrix ( r , c ) ~= 0 
        B = ( r , c ) = distances ( r , c ); 
  end 
 end 
end

[Image Analyst]

It looks like that's what Jan's code does. You can have his X be any number of rows and columns. And Point would be X(someRowIndex, someColumnIndex).

[Damian Wierzbicki]

    B = zeros (rows , columns ); 
for c = 1:columns 
   for r = 1:rows 
    if ref_matrix ( r , c ) == 0 
     B = 0; 
       elseif ref_matrix ( r , c ) ~= 0 
        B = ( r , c ) = distances ( r , c ); 
  end 
 end 
end
% found a mistake, this a working version.

Answer 2

[Jan]

Hm, yes. Why not?

X     = rand(1000, 3);
Pick  = 17;
Point = X(Pick, :);
Dist  = sqrt(sum((X - Point) .^ 2, 2));  % >= R2016b
% Dist  = sqrt(sum(bsxfun(@minus, X, Point) .^ 2, 2));  % < R2016b

If this is time critical: FEX: DNorm2