1. Bayesian inference Li Zhaoping1 & Li Jingling2 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

2. Some previously known contextual influences in vision
Colinear facilitation in V1
Human sensitivity to detect target bar enhanced by colinear flankers.
Nelson & Frost 1985, Kapadia et al 1995,
Li, Piech, & Gilbert 2006
Polat & Sagi 1993, Morgan & Dresp 1995, Yu & Levi 2000, Huang et al 2006 etc
Test bar within the receptive field of a V1 cell
Location for the target bar to appear if it does.
Contextual bar outside the receptive field
Contextual bar
Low response from V1 cells to a low contrast bar
1st presentation interval
2st presentation interval
Higher responses from V1 cells when there is a colinear flanker
Humans are better at saying which interval (the 2AFC task)
contains the target with the colinear contextual bars

3. A demo of the perception in this study:
presence or absence of a vertical target in four different contexts
Bar seems present
Bar present?
Bar absent?
Bar seems absent
These three combined are contrary to what one may expect from the colinear
facilitation in V1 cells and human sensitivity for bar detection WHY???

4. 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

5. not in input sensitivity, in visual object inference
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.

6. Is the vertical bar present? Answer: yes or no?
Psychophysical investigation
Ask an observer (with one interval presentation):
Is the vertical bar present? Answer: yes or no?
P(yes| Ct) 1
With context
Yes rate, or psychometric function P(yes|Ct): Probability an observer answering “yes” given contrast Ct of the target bar in image
contextual effect
without context
Target contrast Ct
Targets without context
Targets with context

7. Observations in an experiment:
Perception of the target bar more likely when contextual contrast Cc is low
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.
Contextual contrast Cc is lower,
Yes rate P(yes|Ct) is larger
Contextual contrast Cc is higher,
Yes rate P(yes|Ct) is smaller
Experiment randomly interleaved trials of different target contrast Ct and contextual contrast Cc, including Cc=0 for the no context condition.

8. Data filling-in P(yes|Ct) suppression low Cc with context vague In dim
Seeing ghost? Cc
seen without context
medium
with
Perceptual
filling-in
Perceptual
suppression
context In
No context
Seeing less
high Cc
Not seen without context
with
context
Strong
No target in image
target with contrast Ct

9. Two contextual configuations: colinear and orthogonal
Colinear context
Orthogonal context
Target
Less visible
Target
Less visible

10. Two contextual configurations: colinear and orthogonal
Data
Dim context Cc = 0.01
Filling-in only in co-linear contextual configuration
Colinear context
Dim context
colinear
No context
No context
orthogonal
Bright context
Orthogonal context
suppresses perception regardless of contextual configuration
Bright context Cc = 0.4
No context
No context
Dim context
colinear
Bright context
orthogonal
Again, trials of all contextual and target variations were randomly interleaved

11. Understanding by Bayesian inference:
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)
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.

12. A Bayesian account: the priors P(yes) and the evidence (likelihood) P(Ct|yes)
Evidence P(Ct |yes)
Larger Smaller
Prior P(yes)
Larger Smaller
Larger prior P(yes) in aligned context
Smaller prior P(yes) in non-aligned context
When these different conditions are interleaved within the same experimental session, different priors manifest themselves in different trials ---- rapidly switching between priors!!!

13. Bayesian model formulation:
Context influences decision in two ways:
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
Additionally: P(Ct|no) ~ exp(-Ct/ σn) a model of noise contrast
P(Ct |yes) P(yes)
Decision: P(yes | Ct ) =
P(Ct |yes) P(yes) + (1-P(yes)) P(Ct | no)
3 Parameters: k, σn, P(yes) can completely model a given contextual configuration to give P(yes|Ct) for all Ct and Cc
Note: P(Ct|yes) is not the probability of the experimenter presenting a contrast Ct for the target, nor is P(yes) the prob. of experimenter presenting a target. Both P(Ct|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.

14. Bayesian decision by combining input evidences with prior beliefs
Decision: P(yes | Ct ) =
P(Ct |yes) P(yes)
P(Ct |yes) P(yes) + (1-P(yes)) P(Ct | no)
Evidence P(Ct|yes) for target is higher for target contrast Ct resembling the contextual contrast Cc.
Evidence P(Ct|no) for non-target is higher when target contrast Ct is close to zero
P(Ct|no)
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)
P(Ct|yes) Ct
Ct = Cc

15. Effect of contextual contrast Cc Effect of prior P(yes)
P(yes|Ct)
Weaker Cc --- larger P(Ct | yes)
P(yes|Ct)
Higher P(yes)
Stronger Cc
--- smaller P(Ct |yes)
Lower P(yes)
Weaker contextual contrast Cc and/no higher prior P(yes)
bias the response to “yes”

16. The Bayesian model can fit the data well
Fitting data from a colinear context ---
a total of 3 model parameters (k, P(yes), σn) to fit all 3 psychometric curves
Solid curves are the results of the Bayesian fit
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
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.

17. Colinear context, data and fits Orthogonal context, data and fits
Bayesian model fitting data from the exp. including both colinear and orthogonal contexts
Colinear context, data and fits
Orthogonal context, data and fits
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.

18. Comparing Bayesian and logistic fitting results:
Weak context
Strong context
Dashed curves: Logistic fits --- using 8 parameters
Solid curves: Bayesian fits --- using 4 parameters
Mean Fitting Error in units of error bar size = for logistic
Mean Fitting Error in units of error bar size = for Bayesian

19. Another example: more subtle difference in context or P(yes)

20. Data fitting for 3 different contexts,
3 different Contextual contrasts
Cc = 0.01, 0.05, 0.4.
5 Bayesian parameters,
18 Logistic parameters.
Mean Fitting Error in units of error bar size
= for logistic fits (dashed curves)
= for Bayesian fits (solid curves)
Fitted Priors P(yes)

21. 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

22. 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.

23. 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)