Ti is an abstract deductive reasoning process. Would it be correct to say that Ti focuses on stripping away at the superficial side of any given object/situation to find the inner and pure objective information? Ti then goes to define and ultimately fit the piece of information into an internal model of all objective information collected thus far. All done unconsciously for the most part until a particularly complex bit of information cannot fit in which case both the information and the internal construct are called into question until all inconsistencies are worked out and the puzzle is solved. The larger problems require varying amounts of time, energy, and logical processing until everything fits once again. This is how Ti can pinpoint inconsistencies from miles away, the information they received is not the proper shape or not even from the same puzzle as they understand the world to function.
Fi would then be an abstract integration process taking into account pure subjective information or 'feelings'. The internal world model is constructed less of logical systems as Ti. Fi focuses less on defining new information and more on simply understanding and then integrating it to the basic framework already in place. Like conducting and building a song one instrumental piece at a time. Fi is focused on how things work together, and dissonance is readily apparent. A distinction from the inconsistency targeting of Ti where things must fit, Fi can work with small inconsistencies as long as the bigger picture can still function as whole.
Objectivity and subjectivity are a large separation in the functions. Fi types are very close to their inner feelings, understand them, yet the objectivity of language prevents them from expressing this portion of their being. Fi then needs to take subjective viewpoints into account in their internal world model because that is the part world they best understand and they see it to affect their worldview greatly. This is not to say they ignore objectivity, yet a danger zone for Fi (DomFi especially) is to ignore objective truth that doesn't harmonize with their subjective truth resulting in either an overly-emotional or a self-centered person (or both, depending on your perspective). Ti, on the other hand, is either does not understand it like Fi can (much like Fi has a harder time with deductive reasoning of objective qualities), or deems it irrelevant. An unbalanced Ti would be entirely disconnected with the human element leaving their world model incomplete and too rigid for that sort of information. (ironically becoming too subjective in their objectivity)
I view the two functions as then starting from the same point when given piece of information and going opposite directions (not necessarily to opposing conclusions, however). Fi preferring to work outward only going inward when harmony is not achieved, and Ti working inward venturing outward when the pieces do not fit. Thus, they are almost mirror processes, neither being more or less rational than the other; only as rational as the information going in.