Because your data is two logical arrays, you can easily test if the smaller is inside the larger. Finding out if the smaller object is touching the edge is slightly more tricky: we reduce the big object to only its shell, and then we do the same thing again.
%2D test cases
%case 1: completely inside
SmallObj=[0 0 0;0 1 0;0 0 0];
BigObj=true(3,3);
%case 2: edge
SmallObj=[0 0 0;0 1 0;0 1 0];
BigObj=true(3,3);
%case 3: outside
SmallObj=[0 0 0;0 1 0;0 1 0];
BigObj=[0 0 0;0 1 0;0 0 0];
%convert to logical
BigObj=logical(BigObj);
SmallObj=logical(SmallObj);
clc
s=load('data.mat');SmallObj=s.SmallObj;BigObj=s.BigObj;
temp_small=SmallObj;
temp_small=temp_small(~BigObj);
if any(temp_small(:))
disp('some part of SmallObj is outside BigObj')
else
temp_big = bwperim(BigObj);%get the shell voxels
temp_small=SmallObj;
temp_small=temp_small(temp_big);
if any(temp_small(:))
disp('some part of SmallObj along the edge of BigObj')
else
disp('SmallObj is completely inside BigObj')
end
end
