1. October 1st, 20071 Shared computational mechanism for tilt compensation accounts for biased verticality percepts in motion and pattern vision Maaike de Vrijer Pieter Medendorp Jan van Gisbergen October 1st, 2007

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3. 3 Visual stability and spatial perception Maintaining a veridical percept of allocentric visual orientations despite changes in eye, head and body orientation Introduction

4. October 1st, 20074 Visual stability Introduction

5. October 1st, 20075 Subjective Visual Vertical (SVV) Introduction Aubert (1861) was first to observe substantial errors in the perception of world-centered orientation of visual lines Errors of undercompensation

6. October 1st, 20076 Subjective Visual Vertical (SVV) from: Van Beuzekom, Medendorp & Van Gisbergen, 2001 Introduction roll angle [deg] B E-effect A-effect response error [deg]

7. October 1st, 20077 Introduction Verticality percept ≠ Body tilt percept from: Van Beuzekom, Medendorp & Van Gisbergen, 2001 roll angle [deg] response error [deg] subjective verticaltilt estimates

8. October 1st, 20078 Subjective Motion Vertical (SMV) Introduction Can the brain compensate for head tilt when judging the spatial direction of motion? If so, does the same pattern of errors occur as in the perception of line orientation? Not trivial: motion and pattern vision involve different neural areas

9. October 1st, 20079 Methods

10. October 1st, 200710 Vestibular chair Methods

11. October 1st, 200711 Two tasks Methods Line task Polarized line Motion task Random dot pattern of 30% coherence

12. October 1st, 200712 Experimental run Methods

13. October 1st, 200713 Experimental setup Eight subjects (7 male, 1 female), aged 31 ± 13 years 13 tilt angles: -120º to 120º with steps of 20º Total of 26 conditions (13 tilts x 2 tasks) Each condition was measured 12 times in a single run Task: adjust motion or line to world vertical Methods

14. October 1st, 200714 Results

15. October 1st, 200715 One subject All subjects Results Compensation for static head tilt in both tasks Compensation angle β [deg] Tilt angle ρ [deg]

16. October 1st, 200716 SMV Errors = SVV Errors Results Thus: common signal processing!

17. October 1st, 200717 Results What causes systematic errors if body tilt signal and retinal signal are unbiased? Mittelstaedt’s idiotropic model (1983) Bayesian model Models for verticality perception

18. October 1st, 200718 Modeling

19. October 1st, 200719 Mittelstaedt’s idiotropic model Modeling Utricle and saccule contain different numbers of hair cells

20. October 1st, 200720 Mittelstaedt’s idiotropic model Modeling Idiotropic vector mtmt Parameters: S = saccular gain M z = length idiotropic vector

21. October 1st, 200721 Fit results idiotropic model Modeling

22. October 1st, 200722 Scatter fit idiotropic model Modeling

23. October 1st, 200723 Questions raised by assumptions: Why would the brain not be able to cope with unequal distribution of hair cells? Why would the brain not use the unbiased tilt signal? Idiotropic model Modeling

24. October 1st, 200724 Bayesian model Bayes’ rule states: p(T|S)=p(S|T)p(T) Optimal estimate of variable T is based on sensory evidence AND on prior knowledge. Bayesian models have been found useful to explain perceptual bias phenomena Do verticality errors reflect a Bayesian strategy? Modeling 20º 25º 30º P(T) P(S|T) 20º 25º 30º 20º 25º 30º

25. October 1st, 200725 Bayesian framework from: Carandini, 2006 Single trial Roll angle Sensory head tilt signal: Provided by several sensory systems like the vestibular system, somato- sensory afferents and proprioception Accurate but noisy Prior knowledge: Small tilt angles are more likely than large angles Multiple trials Roll angle Modeling

26. October 1st, 200726 Bayesian model Head tilt signal is unbiased but noisy Noise increases with tilt angle Result: less noise but biased signal Modeling

27. October 1st, 200727 Assumptions (1) Tilt signal is contaminated by Gaussian noise, which increases linearly with tilt angle: σ tilt = a 0 + a 1 ∙ |  | Prior is normally distributed with μ = 0 and σ = σ p Optimal estimate of tilt is obtained by taking the maximum of the posterior distribution (MAP) Modeling

28. October 1st, 200728 Assumptions (2) Visual signal is contaminated by Gaussian noise, which differs in SVV and SMV task: –σ vl for line task (SVV) –σ vm for motion task (SMV) Spatial direction of visual stimulus is obtained by summing the retinal direction and the estimated head tilt angle Modeling

29. October 1st, 200729 Bayesian model fits The model was fitted to motion and line data simultaneously Parameters: –a 0 : Tilt noise at ρ=0º (offset) –a 1 : Tilt noise increase (slope) –σ p : Prior width –σ vl : Visual noise in line task –σ vm : Visual noise in motion task Modeling

30. October 1st, 200730 Systematic error fits Modeling

31. October 1st, 200731 All subjects Bayesian model and idiotropic model can both account accurately (R 2 >0.81) for systematic SVV/SMV errors Modeling

32. October 1st, 200732 Scatter Modeling

33. October 1st, 200733 Discussion (1) Overestimation of SVV/SMV scatter –Possible underestimation of scatter due to approach of collecting all responses in a single run –Psychometric measurement of scatter would improve SVV/SMV scatter estimates Discussion

34. October 1st, 200734 Discussion (2) Errors of underestimation (A-effects) and errors of overestimation (E-effects) –This Bayesian model cannot explain E-effects  Additional mechanism uncompensated counterroll of the eyes –Idiotropic model can account for both types of errors Discussion

35. October 1st, 200735 Discussion (3) Paradox: Why no large systematic errors in body tilt estimate? –Mittelstaedt model: other sensors –Bayesian model: Precision/Accuracy trade-off Visual stability Balance Discussion

36. October 1st, 200736 Conclusions Identical errors in SMV and SVV  shared computational mechanism Bayesian approach is promising and should be further tested Conclusions

37. October 1st, 200737 Current projects Accurate (psychometric) testing of scatter in SVV at several tilt angles Accurate (psychometric) testing of scatter in body tilt percept at several tilt angles –Does noise in tilt percept increase with tilt angle? –Scatter SVV < Scatter tilt percept ? Does Bayesian model still fit these data? Preliminary

38. October 1st, 200738 Preliminary results Psychometric measurement of SVV Eight subjects (5 male, 3 female) 9 tilt angles: -120º to 120º with steps of 30º SVV was measured psychometrically at each tilt angle Forced-choice task (left/right) Preliminary

39. October 1st, 200739 One subject Preliminary

40. October 1st, 200740 All subjects Preliminary

41. October 1st, 200741 Fits (1) Preliminary E-effects

42. October 1st, 200742 Fits (2) Preliminary

43. October 1st, 200743 Noise in body tilt percept Frank van Wamel performed psychometric experiments to measure body tilt percept around 0º and 90º tilt. His work will be presented on October 29 th Currently, investigations on incorporating ocular counterroll (OCR) to account for E-effects Preliminary

44. October 1st, 200744 Thank you!

45. October 1st, 200745 Idiotropic model Idiotropic vector M compensates for the distortion at small tilts at the expense of increasing systematic errors for larger tilt angles. Extra

46. October 1st, 200746 Idiotropic model Extra  

47. October 1st, 200747 Ocular counterroll (OCR) Sinusoidal behaviour –~10% of roll angle, maximally 10º (on average) at 90º roll tilt Preliminary: Bayesian fits improved Extra Without OCRWith OCR

48. October 1st, 200748 Ocular counterroll (OCR) Extra With OCR Scatter: Without OCR