Vital point method with one point eyes
Here is an attempt for a systematic approach for finding the vital point, if your eye isn't trained to see it on the spot.
This position is taken from Gokyo Shumyo, Section 1, Problem 25. White to live. Let's try to make a one-point eye with as few moves as possible.
Looking back at the reference diagram, points a and b occur in three of the four diagrams. Both are vital points, but a is more valuable than b, because a occurs in both diagrams with two stones. This reasoning can easily be quantified.
Conclusion: a is the vital point.
Is it a correct reasoning that the vital point can be seen as the connection between shared liberties of different groups (marked by )?