There's a lot of good science on this exact issue, dating back to the 50s/60s (good entry point: the Nobel Prize-awarded work of Hubel & Wiesel). The brain does indeed perform many, many passes of feature extraction and reduction. Essentially, this process starts at synapse one -- retinal inputs, for instance, are immediately split into multiple channels coding different features of the incredibly rich feature space impinging on your photoreceptors. The higher up you go, the more diverse the features and the higher their level of complexity.
There's no need for guesswork! Just dive into the literature.