how to visualize a 3D matrix in MATLAB

Question

I am trying to visualize the data contained a 3D array in MATLAB.

The array is has the dimension of 20*20*40 which all except some of the elements being zero.

I am looking for a way to plot these non-zero points in a scatter plot so that the non-zero points are connected to each other.

here is what I've done so far:

b=zeros(6,6,3);
a=[1 1 1;2 2 1;2 1 1;1 2 1;
1 1 2;1 2 2;2 1 2;2 2 2;
6 6 3;6 5 3;5 6 3;5 5 3;
6 6 2;6 5 2;5 6 2;5 5 2];
[r c]=size(a);
for i = 1:r
 b(a(i,c-2),a(i,c-1),a(i,c)) = 1;
end
[m n o]=size(b);
figure (1)
[x,y,z] = meshgrid(1:m,1:n,1:o);
scatter3(x(:),y(:),z(:),90,b(:),'filled')

So, what I am after is being able to connect each of the eight points two form to cubic lattices. Any thoughts is much appreciated.

EDIT: Many thanks to all the experts who helped a lot. Now, I am facing another issue with memory.

The b matrix for my real case would be 1000*1000*2000 and I have the "a" matrix of the size 4,4700,000*3 . All the elements of "a" matrix are integer values. Although I have up to 48GB of memory availabe. However, in the "for loop" above the program bounces back an "out of memory" error.

Any ideas to make this more memory efficient is greatly appreciated.

Answer 1

Consider the following (based on a previous answer):

%# adjacency matrix
adj = false(numel(b));

%# extract first cube, and connect all its points
bb = b;
bb(:,1:3,:) = false;
idx = find(bb);
adj(idx,idx) = true;

%# extract second cube, and connect all its points
bb = b;
bb(:,4:6,:) = false;
idx = find(bb);
adj(idx,idx) = true;

%# points indices
[r c] = find(adj);
p = [r c]';

%# plot
plot3(x(p), y(p), z(p), 'LineWidth',2, 'Color',[.4 .4 1], ...
    'Marker','o', 'MarkerSize',6, ...
    'MarkerFaceColor','g', 'MarkerEdgeColor','g')
axis equal, axis vis3d, grid on, view(3)
xlabel x, ylabel y, zlabel z

---

EDIT:

It would be easier to just manually connect the points:

%# edges: connecting points indices
p = [
    1 2; 2 8; 8 7; 7 1;
    37 38; 38 44; 44 43; 43 37;
    1 37; 2 38; 7 43; 8 44;
    65 66; 66 72; 72 71; 71 65;
    101 102; 102 108; 108 107; 107 101;
    65 101; 66 102; 71 107; 72 108
]';

%# plot
figure
plot3(x(p), y(p), z(p), 'LineWidth',2, 'Color',[.4 .4 1], ...
    'Marker','o', 'MarkerSize',6, ...
    'MarkerFaceColor','g', 'MarkerEdgeColor','g')
axis equal, axis vis3d, grid on, view(3)
xlabel x, ylabel y, zlabel z

%# label points
labels = strtrim(cellstr( num2str((1:numel(b))','%d') ));
idx = find(b);
text(x(idx(:)), y(idx(:)), z(idx(:)), labels(idx(:)), ...
    'Color','m', ...
    'VerticalAlignment','bottom', 'HorizontalAlignment','left')

---

EDIT#2: (credit goes to @tmpearce)

You can semi-automate the process of builing the edges list. Just replace the manually constructed matrx p in the above code with the following:

%# compute edges: pairs of vertex indices 
yIdx = {1:3 4:6};           %# hack to separate each cube points
p = cell(numel(yIdx),1);
for i=1:numel(yIdx)         %# for each cube
    %# find indices of vertices in this cube
    bb = b;
    bb(:,yIdx{i},:) = false;
    idx = find(bb);

    %# compute L1-distance between all pairs of vertices,
    %# and find pairs which are unit length apart
    [r,c] = find(triu(squareform(pdist([x(idx) y(idx) z(idx)],'cityblock'))==1));

    %# store the edges
    p{i} = [idx(r) idx(c)]';
end
p = cat(2,p{:});            %# merge all edges found

The idea is, for each cube, we compute the city-block distance between all vertices. The "side" edges will have a distance of 1, while the diagonals have a distance greater than or equal to 2.

This process still assume that the list of vertices belonging to each cube is provided to us, or easily extracted as we did in the code above...

Answer 2

I thought I'd answer the follow-up to Amro's answer, and show how you can automate the connection of edges along a cubic matrix. This answer is intended to be a supplement to Amro's, and I would recommend incorporating it into that solution so it is easier to read for future viewers.

This starts with idx from Amro's solution, which contains the linear indices of the corners of the cubes. Below I've done it with only one cube so the matrices aren't grossly large and we can see them here.

>> idx' %# transposed to save space in the printed output
ans =
 1     2     7     8    37    38    43    44 '

%# now get the subindex of each point in 3D
>> [sx sy sz] = ind2sub([6 6 3],idx);
%# calculate the "edge distance" between each corner (not euclidean distance)
>> dist = abs(bsxfun(@minus,sx,sx')) +...
          abs(bsxfun(@minus,sy,sy')) +...
          abs(bsxfun(@minus,sz,sz'))
dist =

 0     1     1     2     1     2     2     3
 1     0     2     1     2     1     3     2
 1     2     0     1     2     3     1     2
 2     1     1     0     3     2     2     1
 1     2     2     3     0     1     1     2
 2     1     3     2     1     0     2     1
 2     3     1     2     1     2     0     1
 3     2     2     1     2     1     1     0 '

%# find row and column index of points one edge apart
>> [r c]=find(triu(dist==1)); %# triu means don't duplicate edges

%# create 'p' matrix like in Amro's answer
>> p = [idx(r) idx(c)]'
p =
 1     1     2     7     1     2    37     7    37     8    38    43
 2     7     8     8    37    38    38    43    43    44    44    44

To visualize, you can plot exactly like in Amro's answer.

Answer 3

Is this what you need?

b=logical(b);                                  
scatter3(x(b(:)),y(b(:)),z(b(:)),90,'filled')