In
daily life, we encounter dynamic scenes as well as static
scenes.
Both dynamic and static scenes may be visually ambiguous, but
in daily life, this ambiguity may often be resolved by changes
in view. In dynamic scenes, such changes in view may be caused by
physical changes in the scene itself.
For instance, if you encounter the scene in the next left-hand figure
and if you are asked to assess how many windows the front of
the building has, then you might answer "12 windows"
(as, in some countries, children are taught to answer) even though,
factually,
you see only 8 whole windows plus a three window-like parts that
might extend into many different things behind the truck. If the truck
moves forward, however, the visual ambiguity is resolved, yielding a
potentially unexpected answer.
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Furthermore, notice that seeing
organisms usually are able to move too, that is, the ability to see
seems to have co-evolved with the ability to move. This implies that,
also in case of static scenes,
seeing
organisms can often move around to obtain different views of a scene.
The next example illustrates that, just as above, new views may lead to
an update of the initial percept.
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| 1.
You take a first glance at a static scene |
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2.
You probably interpret it like this |
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| 3.
You move and take a second glance |
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4.
You might see this, leading to an update of your initial percept |
Formally,
such a visual update process can be modeled straightforwardly by a
recursive application of Bayes' Rule (see
Occam,
von Helmholtz, and Bayes):
- For a first view, one may multiply prior probabilities
(quantifying viewpoint-independent aspects of candidate
interpretations) and conditional probabilities (quantifying
viewpoint-dependent aspects of candidate interpretations in
relation to this first view) to obtain the interpretation with the
highest posterior probability according to Bayes' Rule.
- For a second view, the just obtained posterior probabilities
of candidate interpretations can be taken as their new
prior probabilities which, together with
the conditional
probabilities for the expanded set of views, can be used to
obtain
new posterior probabilities by again applying Bayes' rule -- and so on
for each additional view.
This recursive application of Bayes' rule implies that the effect of
the initial, or first, priors gradually fades away because the priors
are
continuously updated on the basis of the conditionals which, thereby,
become the decisive entities. Generally, just a few different views
suffice to disambiguate the
initial percept and to home in quickly on the "true" interpretation,
that is, on the interpretation which, under the employed priors and
conditionals, continues to get the highest posterior when the set of
views is expanded further.
On the one hand, the foregoing is of course convenient to model
everyday perception, be it by humans or by robots. On the other hand,
research into human perception focuses primarily on properties of the
human visual system, and one of the most interesting questions in this
respect is the question of which priors it uses for a first view. In
the dynamic situations above, these first priors may be less relevant
but, of course in combination with first conditionals, they are
relevant in completely static situations -- which are also part of
daily life. Investigating the combination of first priors and first
conditionals may reveal much about human vision (see also
T-junctions).
For instance, in the recursive application of Bayes' rule above, it is
left open where the employed probabilities come from. To merely
simulate everyday perception, they might be based on empirical data. To
explain it, they might reflect real probabilities
of occurrence in the world, as considered by the Helmholtzian
likelihood principle (though see
Bertrand's paradox), or artificial probabilities derived from
descriptive complexities, as considered by the Occamian simplicity
principle. These two principles are probably far apart regarding the
viewpoint-independent priors but seem close regarding the
viewpoint-dependent conditionals (see
Occam,
von Helmholtz, and Bayes and
Object
versus viewer).
Because the conditionals are the decisive ones in the recursive
application of Bayes' rule, this implies that either principle would do
in dynamic situations. This implies in turn, however, that
such situations are not suited to investigate the question of which of
these two principles guides the visual system and that, to this
question, the first priors are most relevant.
Hence, in sum, modeling everyday perception in dynamic situations is of
course a very interesting issue, but in human perception research, a
more relevant issue is the underlying question of which first priors
and conditionals are used by the visual system, and to investigate this
question, static situations are better suited than dynamic situations.
For an extensive discussion on these issues, see
Psychological
Bulletin
2000
For a brief discussion on these issues, see
In the
Mind's Eye
2007
For an updated brief discussion on these issues, see
Acta Psychologica
2011