How can I interpolate binary 2D matrices?

I am not sure if this is entirely possible, but I am trying to do this:

For a 3d matrix with some number of layers in the z dimension,

The user should input the location of a region (marked by value of 1) in the first layer, and last layer, and the goal is to have matlab fill in the intermediate regions.

for example

layer1 =      [1 1 1 1 1; ...
               1 1 1 1 1; ...
               1 1 1 1 1; ...
               1 1 1 1 1; ...
               1 1 1 1 1]

layer3 =      [0 0 0 0 0; ...
               0 0 0 0 0; ...
               0 0 1 0 0; ...
               0 0 0 0 0; ...
               0 0 0 0 0]

the layer in between the 2 should be filled by matlab and have the following output

layer2 =      [0 0 0 0 0; ...
               0 1 1 1 0; ...
               0 1 1 1 0; ...
               0 1 1 1 0; ...
               0 0 0 0 0; ...]

This would be a very very simple case. Ideally I am trying to make this work for a 3d matrix with dimensions probably ranging from 500*500*500 to 2000*2000*2000

Is there any function in matlab that would help in this process?

Answer 1

[Matt J]

If the final, filled in region is convex, it can be obtained as follows

layers=false(5,5,3)
layers(:,:,1)=1;
layers(3,3,3)=1;

T=regionprops3(double(layers),'ConvexImage','SubarrayIdx')
layers(T.SubarrayIdx{:})=T.ConvexImage{1}

layers(:,:,1) =

   1   1   1   1   1
   1   1   1   1   1
   1   1   1   1   1
   1   1   1   1   1
   1   1   1   1   1


layers(:,:,2) =

   0   0   0   0   0
   0   1   1   1   0
   0   1   1   1   0
   0   1   1   1   0
   0   0   0   0   0


layers(:,:,3) =

   0   0   0   0   0
   0   0   0   0   0
   0   0   1   0   0
   0   0   0   0   0
   0   0   0   0   0