Closest coordinate points between two data sets

I have two data sets of different sizes, one of which is a 15x3 matrix of latitude, longitude, and concentration data and the other of which is a 2550x3 matrix, also composed of latitude, longitude, and concentration data. I want to find the coordinates in the first data set that are closest to those in the second, larger set. Then based on the index locations of those coordinates in the larger matrix, extract out the concentration values from that correspond to those coordinates so that I can plot the two sets of concentrations against one another. The difficult part of this is that the coordinate locations in the smaller matrix do not align perfectly with those in the larger matrix, so I would like to be able to find the closest possible coordinate locations between the two matrices.

For example:

Matrix 1

A = [
 -62.232  47.993  6.3
 -63.321  49.888  5.4
 -63.442  50.201  2.1
 -63.845  51.268  9.7]

Matrix 2

   B = [
   -62.859  48.918  4.9
   -63.987  49.971  3.0
   -62.234  47.990  4.6
   -62.909  48.236  5.7
   -63.325  49.885  7.1
   -64.897  48.032  6.3
   -63.440  50.200  5.9
   -62.921  51.679  3.2
   -63.849  51.270  4.5
   -64.018  50.327  2.6]

The intersect function does not produce any intersection points because of the mismatch in the coordinates, so I have attempted to use the pdist2 function and dsearchn, but to no avail.

I would like to produce a matrix of indices of the matrix B where the longitude and latitude values are closest to those in matrix A.

For example:

Result (from Matrix B)=

   -62.234  47.990  4.6
   -63.325  49.885  7.1
   -63.440  50.200  5.9
   -63.849  51.270  4.5

Indices=

   3   3   3
   5   5   5
   7   7   7
   9   9   9

With the end goal being B(indices), allowing me to plot B(:,3) against A(:,3).

Please let me know if you need any more information regarding my issue- thank you!

[Walter Roberson]

Please leave A and B in the form of assignment statements so that people can copy and paste them to test and develop their own ideas.

Answer 1

[Walter Roberson]

One way to do it would be to use interp2() in which your X and Y values were your lat and long, and your Z value is corresponding matrix linear indices (integers), and you set the interpolation method to 'nearest'. Then interpolate the other coordinates in order to get out the indices into the first matrix.

[Walter Roberson]

I see that your coordinates are not arranged in a grid. In a case like this you would substitute scatteredInterpolant or equivalent for interp2() in what I wrote above.

[Amy Eisenstadt]

I've tried the below code and receive the following error message:

F=scatteredInterpolant(T1',T2','nearest');
Error using scatteredInterpolant
The input points must be 2D or 3D coordinates in numpoints-by-ndim format.

My data are arranged in a double array with three columns each. Do you know how I might be able to adjust to format the data into something that scatteredInterpolant can handle?

[Walter Roberson]

F = scatteredInterpolant(B(:,1), B(:,2), (1:size(B,1)).', 'nearest');

A_is_nearest_idx = F( A(:,1:2) )

B_closest_to_A = B(A_is_nearest_idx, :)

Answer 2

[Image Analyst]

To find the distance of every point in A to every point in B, use pdist2() if you have the stats toolbox:

distances = pdist2(A(:, 1:2), B(:, 1:2))

You get

distances =
       1.1175       2.6443    0.0036056      0.71929        2.185       2.6653        2.516       3.7498       3.6542       2.9389
       1.0744      0.67115       2.1872       1.7026        0.005       2.4349      0.33392       1.8351       1.4794      0.82373
       1.4092      0.59154       2.5195        2.036      0.33696       2.6118    0.0022361       1.5671       1.1439      0.58962
       2.5485       1.3048       3.6525       3.1732       1.4775       3.4027       1.1422       1.0113    0.0044721      0.95677

If you want the single closest pair of points, you can do this:

minDistance = min(distances(:))
[rowOfA, rowOfB] = find(distances == minDistance)

There are alternative definitions of closeness for sets of points. Perhaps you'd like to learn about the Hausdorff distance: http://cgm.cs.mcgill.ca/~godfried/teaching/cg-projects/98/normand/main.html