Hello community!

I have recently read some papers and found that **Euler number** is often used to express connectivity. The formula I see in this highly cited article（ *Vogel, H., & Roth, K. 2001. Quantitative morphology and network representation of soil pore structure. Advances in Water Resources, 24, 233–242* .）

is similar to one answers in a post said that：

If there are any similarities between the two? Euler number in this paper is equal to Euler characteristic in BoneJ? Can I think that **C** in the paper is equal to **b1** in the answer, and **H** is equal to **b2**? Does b1 represent the connection（sorry, I don’t quite understand “handles” meaning）？

Because there is a *Purify* image process before *BoneJ/Connectivity*, should **b0** be 1 in this case？

If Euler number is Euler characteristic, what is **connectivity β1 = 1 - Δχ**? According to the above answer formula, it is 1-(b0-b1+b2)? If b0 is 1, then it is b1-b2? If Euler characteristic can be used to express connectivity of objects, Why set this **connectivity**？

This is very important for my work, hope to get your reply and check!

Thanks in advance

Mengying