The Elementary Operations of Human Vision Are Not Reducible to Template-Matching
Fig 9
The sense in which vision is linear, and the sense in which it is not.
Our results can be intuitively summarized with relation to the simple notion of piecewise linear approximation to a nonlinear function, although this parallel should not be taken literally: the sensory process is far more complex than can be represented here using a single trajectory. It is nevertheless useful to imagine this process as the pictured 3D pipe-like structure, spanning all 4 different spaces within which we defined and perturbed the visual stimuli. When the process is probed within each individual stimulus space, its characteristics can be adequately approximated by a linear model. A comprehensive account of its collective properties spanning all 4 spaces, however, cannot be achieved using a linear approximator: the system may appear linear every time it is probed from a different direction, yet its underlying structure remains highly nonlinear.