Since we are talking about understanding thought, it should be first noted that this is a philosophically challenging topic in it's own right. And a good path would be to study Cartesian duality, Gilbert Ryle's work, as well as the work of Jaegwon Kim. You'd also have to study what we know about the anatomy and physiology of perception.
Now, to respond to your question from the philosophical angle, yes, human's are capable of logic, but a lot of thought is (EDIT) alogical. Human beings are not logic engines, but rely heavily on their emotions to draw even logical conclusions. (See Thinking, Fast and Slow by Nobel-prize winner Daniel Kahneman for the relatively current state of science on logic and decision making).
But, I'm going to dip your toes in the waters that I prefer which is artificial intelligence, in which there are two camps of thinking historically that are recently trying to reconcile their differences, connectionism and computationalism. A connectionists tries to simulate thoughts from the neuron up, and the computationalist attacks the problems by using the logics humans use, such as Boolean logic or Aristotelian syllogism, etc. Ultimately, what the camps have discovered over the last 70 years is that central to the question of what characterizes human thought, it is the creation and use of meaning.
Wittegenstein comes in two flavors, Tractatus and Philosophical Investigations, and the early Wittegenstein who was a close intellectual ally of Bertrand Russell, diverged largely on the question of meaning after exploring logical thoroughly. In his later work, he is famous for his declaration that logic and words are essentially games played by agents, and that human thought is much more than traditional logic whose rules fall short of the rules used by people. He went on to recognize "family resemblances" in meanings, and other manners of thinking that anticipated cognitive semantics and other findings in cognitive science.
Your question shows your attempts to develop your own ontology, invoking words like input, structure, and computed. The best way to answer your question is to get a good book on the psychology of perception, so you don't have to reinvent the wheel. On my shelf is Perception by Julian E. Hochberg, but it's dated. He seems to have another book copyrighted in 2007. But I'm no expert in the field.
Ultimately, you have to find what in these works appeals to your metaphysics. For me, currently I'm working works by the linguist George Lakoff who along with several allies expresses a theory regarding meaning based on conceptual metaphors and ends with a metaphysics that rejects traditional views on concepts, categories, and computation of the mind based on his views on embodied cognition.
EDIT: To answer your question, which seems to me, does the mind compute, then the answer is yes metaphorically. How does it compute? I would argue that the four important ways the mind functions is intuitively, deductively, inductively, and abductively. Intuition is showcased in Blink by Malcom Gladwell, and the latter three topics are handled in the study of logic increasing in terms of complexity and sophistication. It should be noted that computers excel at deduction, but tend to struggle with induction and abduction, as both types of logic require a better handle on the meaning of the topics reasoned. Computer science has the field of expert systems to implement more heuristic forms of computation and mimic to a better degree how humans 'compute'.
If you want to understand reasoning beyond formal logic, a good introduction would be Stephen Toulmin's Uses of Argument where he floats some ideas about how jurisprudential reckoning, and hence generalized inference functions.