Bayesian inference accounts for the filling-in and suppression

1. 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

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 1st presentation interval 2st presentation interval Low response from V1 cells to a low contrast bar 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 absent? Bar seems absent Bar seems present Bar present? 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 Different perceptions inside the brain The same input of a white patch on retina Perception fills in the occluded part of the square

5. 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. 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 0 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 higher, Yes rate P(yes|Ct) is smaller Contextual contrast Cc is lower, Yes rate P(yes|Ct) is larger Experiment randomly interleaved trials of different target contrast Ct and contextual contrast Cc, including Cc=0 for the no context condition.

8. Data P(yes|Ct) low Cc with context vague In dim Cc Seeing ghost? 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 Orthogonal context Colinear context Target Less visible Target Less visible

10. Two contextual configurations: colinear and orthogonal Data Filling-in only in co-linear contextual configuration Dim context Cc = 0.01 Colinear context colinear Dim context No context No context orthogonal Bright context suppresses perception regardless of contextual configuration Orthogonal context Bright context Cc = 0.4 No context No context colinear Dim context 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. 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 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 prior P(yes) Effect of contextual contrast Cc Weaker Cc --- larger P(Ct | yes) P(yes|Ct) 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. 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 = 0.83 for logistic Mean Fitting Error in units of error bar size = 1.01 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 = 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)

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)