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