How do I create a structuring element of my own?

I want to create a structuring element with the center '0' (eg. [1 0 1])and I want to see the effect of erosion and dilation of it on a 3x3 binary matrix. How do I go about it? please explain. My code is giving me same answers for erosion and dilation.

aa=[1 1 1; 1 0 1; 1 1 1]
s=[1 1 1];
ero=imerode(aa,s)
dil=imdilate(aa,s)

pp=[1 0 1];
ero1=imerode(aa,pp)
dil1=imdilate(aa,pp)

[Matt J]

My code is giving me same answers for erosion and dilation.

As it should, for that choice of aa. What do you expect the result to be?

[oshawcole]

Mathematically, the result for aa eroded with s=[1 1 1] should be [0 1 0; 0 0 0; 0 1 0]. For s=[1 0 1]; I was curious as to what happens when I take the center of the structuring element to be 0; so I don't know the answer.

Answer 1

[Matt J]

Elements outside the boundary of the matrix do not participate in the erosion/dilation. If you pad aa to a larger size, you will see different effects.

>> aaa=zeros(5); aaa(2:4,2:4)=aa

aaa =

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

>> ero=imerode(aaa,[1,1,1])

ero =

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

>> ero=imerode(aaa,[1,0,1])

ero =

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

>> ero=imdilate(aaa,[1,0,1])

ero =

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

[oshawcole]

Awesome! Can you please explain why is this padding needed? Thank you so much. I really appreciate your help.

[Matt J]

It is needed so that the code can know that you are assuming zeros lie beyond the boundary of the original 3x3 matrix. Otherwise, it doesn't know what you are assuming.