Layering multiple images in 3D-space

Question

Suppose we have a matrix I of size 49x49x5, corresponding to 5 images of size 49x49 stacked along the third dimension so we have a total of 5 images. These images should visualize the density of a gas in a 3D space, so we can think of each image as a section cut of the room at different locations.

Is there any way to make a figure in MATLAB where all 5 images are shown as hanging in the 3D space they "came from"?

Here is an image hopefully making it clearer what I am after:

Answer 1

Consider the following example. It uses the low-level SURFACE function to plot stacked images:

%# create stacked images (I am simply repeating the same image 5 times)
img = load('clown');
I = repmat(img.X,[1 1 5]);
cmap = img.map;

%# coordinates
[X,Y] = meshgrid(1:size(I,2), 1:size(I,1));
Z = ones(size(I,1),size(I,2));

%# plot each slice as a texture-mapped surface (stacked along the Z-dimension)
for k=1:size(I,3)
    surface('XData',X-0.5, 'YData',Y-0.5, 'ZData',Z.*k, ...
        'CData',I(:,:,k), 'CDataMapping','direct', ...
        'EdgeColor','none', 'FaceColor','texturemap')
end
colormap(cmap)
view(3), box on, axis tight square
set(gca, 'YDir','reverse', 'ZLim',[0 size(I,3)+1])

I am using indexed color images (with direct color mapping), but it can be easily changed to use grayscale images (with scaled color mapping).

Now if you want to get the 3D space arranged like you have shown in your question, simply interchange the Y and Z dimensions (images stacked along the Y-dimension instead of the Z-dimension).

In general, to have more control on the viewing angle, use the camera manipulation functions.

Answer 2

The function you're looking for is the patch function. By way of example:

x=[1 1 6]; y=[2 7 2]; z=[1 1 -1];

This specifies a triangle (three points), and the coordinates of the vertices are (1,2,1), (1,6,1), and (6,2,-1). If you would add a fourth point to each vector it would be a rectangle, with the new vertex at the new x,y,z coordinate.

To answer your posted question directly, you can plot a number of rectangles for each variable simply by using a multidimensional array for x, y, and z, where each column specifies a different polygon. In practice, this works as follows:

% plot two rectangles
x = [1 1 1 1;
    1 1 1 1;
    4 4 4 4;
    4 4 4 4;];

y = [1 1 1 1;
    2 2 2 2;
    2 2 2 2;
    1 1 1 1;];

z = [1 2 3 4;
    1 2 3 4;
    1 2 3 4;
    1 2 3 4;];

patch(x,y,z,'w');

Which makes:

There are options you can use to add color to the polygons, check the docs.

Answer 3

If I understand you correctly, you can use the slice() or contourslice() functions to do this.

Check out this example: http://www.mathworks.com/help/matlab/visualize/techniques-for-visualizing-scalar-volume-data.html