Abstract
We present a formal framework that generalizes and subsumes the standard Bayesian framework for vision. While incorporating the fundamental role of probabilistic inference, our Computational Evolutionary Perception (CEP) framework also incorporates fitness in a fundamental way, and it allows us to consider different possible relationships between the objective world and perceptual representations (e.g., in evolving visual systems). In our framework, shape is not assumed to be a “reconstruction” of an objective world property. It is simply a representational format that has been tuned by natural selection to guide adaptive behavior. In brief, shape is an effective code for fitness. Because fitness depends crucially on the actions of an organism, shape representations are closely tied to actions. We model this connection formally using the Perception-Decision-Action (PDA) loop. Among other things, the PDA loop clarifies how, even though one cannot know the effects of one’s actions in the objective world itself, one can nevertheless know the results of those effects back in our perceptions. This, in turn, explains how organisms can interact effectively with a fundamentally unknown objective world.
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- 1.
We use “action” in the broadest sense of the word—to include not only visually-guided manipulation of objects (“dorsal stream”), but also visual categorizations (“ventral stream”) that inform subsequent behavior, e.g., whether or not to eat a fruit that has some probability of being poisonous.
- 2.
Hence, formally, P is a mapping
, where 
is the event space on X. One can view P as a linear operator that maps probability measures on W to probability measures on X. In the discrete case, it would be represented by a stochastic matrix whose rows add up to 1. For more on Markovian kernels, see [3, 32]. - 3.
Thus, whereas in BDT μ X is taken to be the world prior, in CEP μ X is the pushdown, via the perceptual channel P X , of the prior μ on the objective world.
- 4.
Kernel composition is defined as follows: let M be a kernel from
to 
, and N be a kernel from 
to 
. Then the composition kernel MN from 
to 
is defined, ∀x∈X and 
, by MN(x,A)=∫
Y
M(x,dy)N(y,A). This is simply a generalization to the continuous case of the familiar multiplication of (stochastic) matrices. For details, see [32]. - 5.
In this example, a simple clustering based on fitness values was sufficient. More generally, however, multi-dimensional scaling may be required. Indeed, MDS-type solutions may also provide an explanation of how dimensional structure can arise in perceptual representations.
- 6.
The inverse optics approach allows for misperceptions—e.g., that observers tend to perceive an object from a certain viewpoint as being less elongated in depth than physical measurements of the object tell us it is. But the inverse optics approach nevertheless assumes that one of the shapes in X is the “correct” one in the objective world W. In other words, at a more fundamental level, the inverse optics approach assumes that the very property we call shape is an intrinsic property of the objective world W itself.
, where 
is the event space on X. One can view P as a linear operator that maps probability measures on W to probability measures on X. In the discrete case, it would be represented by a stochastic matrix whose rows add up to 1. For more on Markovian kernels, see [
to 
, and N be a kernel from 
to 
. Then the composition kernel MN from 
to 
is defined, ∀x∈X and 
, by MN(x,A)=∫
Y
M(x,dy)N(y,A). This is simply a generalization to the continuous case of the familiar multiplication of (stochastic) matrices. For details, see [References
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Acknowledgements
For helpful discussions, we thank Jacob Feldman, Pete Foley, Brian Marion, Justin Mark, Darren Peshek, and Kyle Stevens. MS was supported by NIH EY021494 (joint with Jacob Feldman); DH was supported by a grant from Procter & Gamble.
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Appendix: Relation to Quantum Bayesianism
Appendix: Relation to Quantum Bayesianism
One possible objection to the framework proposed in this chapter might be: “It is naive for vision scientists to propose that our perceptions are not veridical, and that therefore the objective world need not be spatiotemporal and need not contain 3D objects with shapes. Surely physicists know otherwise, and would dismiss such a proposal out of hand.”
Although some physicists might dismiss such a proposal, there are others who, in trying to best interpret the formalism of quantum theory, have been led to a view about quantum states that comports well with our proposal. These physicists, who call their approach “quantum Bayesianism,” or QBism for short, claim that quantum states are not objective representations of the external world, but rather are compendia of beliefs about possible outcomes of measurements [2, 10, 11]. As Fuchs [10] puts it, “… there is no sense in which the quantum state itself represents (pictures, copies, corresponds to, correlates with) a part or a whole of the external world, much less a world that just is” and “… a quantum state is a state of belief about what will come about as a consequence of … actions upon the system.” So, for instance, according to QBism a state function of a quantum system, represented say in the basis of the position operator, has a particular shape in space that can be used to predict the consequences of actions on that system.
This is entirely consistent with the view we propose about our perceptual experiences in general, and our experiences of shape in particular. There is no sense in which the objects in our perceptual experiences picture, copy, correspond to, or correlate with a part or a whole of the external world. Instead such objects and their shapes, and perceived space-time itself, are states of belief about what will come about as a consequence of our actions (which could include measurement). The reason is that natural selection, which has tuned our perceptions, rewards fitness and nothing else. Therefore our perceptions have been tuned to inform us of the fitness consequences of our possible actions, not to copy or picture the objective world.
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Singh, M., Hoffman, D.D. (2013). Natural Selection and Shape Perception. In: Dickinson, S., Pizlo, Z. (eds) Shape Perception in Human and Computer Vision. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-5195-1_12
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