How to generate a zero-thickness surface and output the mesh?

I have a 3D bindary dataset in which the 1s represent thin planes. I wanted to triangulate these plane surfaces to get nodes and connectivity information. I tried delaunayTriangulation but it always gave me 3D mesh (i.e. tetrahedrons) instead of 2D surface mesh (triangles). I also tried using isosurface, which did not allow me to choose an isovalue of 1, as a result, a isosurface was a very thin volume in fact. How could I get a zero-thickness surface by connecting the points and then export the triangles?

[KSSV]

For delaunayTriangulation did you provide (x,y) or (x,y,z) ? Show us your code and attach your data.

[Yulai Zhang]

I used delaunayTriangulation(x,y,z) as the code below, because my data is 3D.

In my data.mat, there are 3 thin planes (the 1s). I wanted my 1s to be connected to form 3 surfaces with no thickness and then get triangle mesh, not tetrahedrons.

Thanks

ind = find(model);

sz = [43 32 50];

[row,col,lay]=ind2sub(sz,ind);

DT = delaunayTriangulation(row,col,lay);