bayesian inference accounts for the filling-in and suppression
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Bayesian inference
accounts for the
filling-in and suppression of visual perception of bars by context
Li Zhaoping1 & Li Jingling2
1University College London, 2China Medical School
Based on a publication Zhaoping & Jingling (2008) PLoS Comput. Biol.Ask me for a copy, or download from www.cs.ucl.ac.uk/staff/Zhaoping.Li/allpaper.html
Low response from V1 cells to a low
contrast bar
Higher responses from V1 cells when there is a colinear flanker
Test bar within the receptive field of a V1 cell
Contextual bar outside the receptive field
Some previously known contextual influences in vision
Colinear facilitation in V1
Nelson & Frost 1985, Kapadia et al 1995, Li, Piech, & Gilbert 2006
Human sensitivity to detect target bar enhanced by colinear flankers.
Polat & Sagi 1993, Morgan & Dresp 1995, Yu & Levi 2000, Huang et al 2006 etc
Location for the target bar to appear if it does.
Contextual bar
1st presentation interval
2st presentation interval
Humans are better at saying which interval (the 2AFC task)contains the target with the colinear contextual bars
A demo of the perception in this study: presence or absence of a vertical target in four different contexts
Bar seems present
Bar seems absent
Bar present?
Bar absent?
These three combined are contrary to what one may expect from the colinearfacilitation in V1 cells and human sensitivity for bar detection WHY???
Hints from another example of how context influence visual perception
The same input of a white patch on retina
Different perceptions inside the brain
Perception fills in the occluded part of the square
Focus of this study: Contextual influence in perceptual bias, not in input sensitivity, in visual object inference not in input image representation
Methods in the study:
Psychophysical: rather than the 2AFC method, we used one-interval method (observers answered after each one-interval stimulus presentation whether the target bar was present) to probe perceptual bias (rather than input sensitivity). Whether the perception is veridical is not an issue, since we study inference rather than input representation.
Computational: build a Bayesian inference model to understand the psychophysical data, showing that the model fits the data with fewer parameters than needed by phenomenological (e.g., logistic) models of the psychometric functions.
w
ithou
t con
text
Psychophysical investigation Ask an observer (with one interval presentation):
Is the vertical bar present? Answer: yes or no?
Target contrast Ct
P(yes| Ct)
1
Targets without context
contextual
effect
Yes rate, or psychometric function P(yes|Ct): Probability an observer answering “yes” given contrast Ct of the target bar in image
0
With context
Targets with context
Observations in an experiment: Perception of the target bar more likely when contextual contrast Cc is low
Contextual contrast Cc is lower,Yes rate P(yes|Ct) is larger
Contextual contrast Cc is higher,Yes rate P(yes|Ct) is smaller
Observations contrary to expectation, since in V1 (primary visual cortex), a neuron’s response is facilitated by the presence of colinear contextual bars. So stronger colinear context should facilitate more.
Experiment randomly interleaved trials of different target contrast Ct and contextual contrast Cc, including Cc=0 for the no context condition.
No target in image
Seeing
ghost?
target with contrast Ct
Not seen without context
seen without context
Seeing less
Perceptual suppression
Data
Perceptual
filling-in
P(yes|Ct)
In dimvague context with low Cc
Strong context with high C c
No conte
xtIn
medium
conte
xt with
C c
Two contextual configuations: colinear and orthogonal
TargetLess visible
TargetLess visible
Colinear context Orthogonal context
Two contextual configurations: colinear and orthogonal
Bright context Cc = 0.4
Dim context Cc = 0.01Colinear context
Orthogonal context
Data
suppresses perception regardless of contextual configuration
Filling-in only in co-linear contextual configuration
colinear
orthogonal
No context
No context
colinear
orthogonal
No context
No context
Dim context
Dim co
ntext
Bright c
ontext
Bright c
ontext
Again, trials of all contextual and target variations were randomly interleaved
Received visual signal: Ct: e.g.: neural activities in response
to the target bar or noise.
Making decision on: yes or no, the bar is there or not
Prior believed probabilities: P(yes), P(no) = 1-P(yes) of visual events “yes” or “no”.
Conditional Probability: P(Ct |yes), likelihood or evidence of likely contrast Ct for target present.
Decision probability: P(yes|Ct) = P(Ct|yes)P(yes)/P(Ct)
Understanding by Bayesian inference:
Decision: P(yes | Ct ) =
P(Ct |yes) P(yes)
P(Ct |yes) P(yes) + (1-P(yes)) P(Ct | no)
Note: the model above is derived from a neural level model, when input contrasts evoke neural responses, when the brain has an internal model of the likely neural responses to input contrast, and how neural responses to contextual inputs influences the priors and the “likelihood” models. Details of the derivations can be found in the published paper Zhaoping & Jingling 2008.
A Bayesian account: the priors P(yes) and the evidence (likelihood) P(Ct|yes)
Evidence P(Ct |yes) Larger Smaller
Larger prior P(yes) in aligned context
Smaller prior P(yes) in non-aligned context
Prior P(yes)Larger Smaller
When these different conditions are interleaved within the same experimental session, different priors manifest themselves in different trials ---- rapidly switching between priors!!!
Bayesian model formulation:
Context influences decision in two ways:
(1)Contextual configuration determines the prior prob. parameter P(yes)
(2) Contextual contrast Cc determines likelihood P(Ct|yes)
P(Ct |yes) ~ exp [ -|Ct –Cc|/ (k Cc) ] favouring targets that resemble context in contrast
3 Parameters: k, σn, P(yes) can completely model a given contextual configuration to give P(yes|Ct) for all Ct and Cc
P(Ct |yes) P(yes)
P(Ct |yes) P(yes) + (1-P(yes)) P(Ct | no) Decision: P(yes | Ct ) =
Additionally: P(Ct|no) ~ exp(-Ct/ σn) a model of noise contrast
Note: P(Ct|yes) is not the probability of the experimenter presenting a contrast C t for the target, nor is P(yes) the prob. of experimenter presenting a target. Both P(C t|yes) and P(yes) are internal models in the observer’s brain only, and “yes” and “no” refer the brain’s perceptions and assumptions rather than the external stimulus, see paper for more details.
Ct
Ct = Cc
P(Ct|no)
P(Ct|yes)
Evidence P(Ct|no) for non-target is higher when target contrast Ct is close to zero
Evidence P(Ct|yes) for target is higher for target contrast Ct resembling the contextual contrast Cc.
The decision P(yes|Ct) results from weighing the evidences P(Ct|yes) and P(Ct|no), for and against the target, weighted by the priors P(yes) and P(no)=1-P(yes)
Decision: P(yes | Ct ) =
P(Ct |yes) P(yes)
P(Ct |yes) P(yes) + (1-P(yes)) P(Ct | no)
Bayesian decision by combining input evidences with prior beliefs
Effect of contextual contrast Cc
Weaker Cc --- larger P(Ct | yes)
Stronger Cc
--- smaller P(Ct |yes)
Effect of prior P(yes)
Higher P(yes)
Lower P(yes)
Weaker contextual contrast Cc and/no higher prior P(yes) bias the response to “yes”
P(yes|Ct) P(yes|Ct)
The Bayesian model can fit the data well
No co-linear facilitation mechanism necessary for explaining the data!!!!If a 4th parameter for colinear facilitation is fitted, it returns a zero facilitation magnitude
Fitting data from a colinear context --- a total of 3 model parameters (k, P(yes), σn) to fit all 3 psychometric curves
Typically, 6 parameters would be needed to adequately fit 3 psychometric curves.Using only 3 parameters to fit the data, the Bayesian model demonstrates its adequacy.
Solid curves are the results of the Bayesian fit
Bayesian model fitting data from the exp. including both colinear and orthogonal contexts
Fitted Priors P(yes) Four model parameters: k, σn, P(yes)colinear, P(yes)orthogonal
used to fit all 4 psychometric curves
P(yes)colinear and P(yes)orthogonal are both quite big, reflecting an additional response bias by the subjects to respond roughly 50% “yes” in total.
Colinear context, data and fits Orthogonal context, data and fits
Comparing Bayesian and logistic fitting results:
Dashed curves: Logistic fits --- using 8 parametersSolid curves: Bayesian fits --- using 4 parameters
Mean Fitting Error in units of error bar size = 0.83 for logistic Mean Fitting Error in units of error bar size = 1.01 for Bayesian
Weak context Strong context
Another example: more subtle difference in context or P(yes)
Data fitting for 3 different contexts,3 different Contextual contrastsCc = 0.01, 0.05, 0.4.
5 Bayesian parameters,18 Logistic parameters.
Mean Fitting Error in units of error bar size = 0.54 for logistic fits (dashed curves) Mean Fitting Error in units of error bar size = 1.07 for Bayesian fits (solid curves)
Fitted Priors P(yes)
Summary:
Studied contextual influence in perceptual bias --- filling-in & suppression
Study uses simple stimuli, more easily controlled and modelled one interval tasks used to study bias rather than sensitivities.
Found context influences perception by (1) affecting prior expectation of perceptions (2) affecting likelihood model of sensory inputs
Findings (1) accountable by a Bayesian inference model (2) unexpected from colinear facilitation in V1, suggest mechanisms beyond V1
Other related works and issues:
Contextual influences in object recognition and attentional guidance
Contextual effects on mid-level vision assimilation and induction in the perception of motion, orientation, color, and lightness etc.
Effects of the input signal-to-noise on input encoding and perception.
Perceptual ambiguity
Relationship/difference between object inference and image representation
Bayesian inference in vision in many previous works, often with more complex stimuli (which can be difficult to manipulate and model)
Statistics of the natural scenes and adaptation
Decision making, and internal beliefs unchanged by input samples.
Etc, etc. … see detailed discussions in the published papers.
2AFC tasks remove the effects of the priors:
Visual Signal received: x1, x2, for time interval 1 and 2.
Making decision on: y
Prior expectation: P(y)
Conditional Probability: P(x1|y), P(x2|y)
Decision based on: P(y|x1) > ? < P(y|x2)
P(x1|y)P(y)/P(x1) > ? < P(x2|y)P(y)P(x2)
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