Hi, I`m Jeon from South Korea.
I used BoneJ plugin for analyzing connectivity.
Actually, I couldnt fully understand about calculation algorithm.
According to user guide of BoneJ,
 Calculation of Euler characteristic for each voxel.  (1)
 Summing (1) for entire structure (is it right?)  (2)
 Calculation of the Euler characteristic of the entire sample  (3)
 Calculation of Δ(χ)
here is my questions,

Calculation method of Euler characteristic
χ = v  e + f  n, (v,e,f,n is vertices, edges, faces, voxels, respectively) right ?
Then, at (1), what is the number of n ? is it just 1? because this calculation is for each voxel 
Actually, what is the difference between (2) and (3) ?
In detail, (2) means summing to give an Euler characteristic for bone (χ)
and (3) means the Euler characteristic of the bone sample as though it is floating in space (χ = ∑δχ)maybe,… (2) was considered the addition theorem (χ (A∪B) = χ (A) + χ (B)  χ (A∩B))
or… (3) was calculation for entire structure ( only one calculation)I couldnt understand difference of theirs… and very confused.

and, what is Δ(χ) ?
It means the bone sample’s contribution to the Euler characteristic of the bone to which it was connected.It didnt mean enough to me.
Can you explain more about it ?
Thanks,