A BAYESIAN PERSPECTIVE ON SPATIAL PERCEPTION

Maaike de Vrijer

Jan van Gisbergen

February 20, 2008

VISUAL STABILITY

Brain must combine visual and vestibular information to preserve a stable percept of the world when we make head movements

SEMICIRCULAR CANALS

Three set of mutually perpendicular canals measure rotations in three dimensions

High-pass properties

FUNCTION OF THE OTOLITHS

Sensitive to tilt and translation

Nerve fibers code deflection of the hair cell cilia (gravito-inertial force)

EXPERIMENTS

PERCEPTION OF VERTICALITY

How well can a tilted subject adjust a line to the direction of gravity?

Van Beuzekom & Van Gisbergen (2000) J. Neurophysiol.

Kaptein & Van Gisbergen (2004) J. Neurophysiol.

PASSIVE TILT EXPERIMENTS

RESULTS LINE ADJUSTMENT

”adjust the line to the direction of gravity”

De Vrijer et al. (2008)

SYSTEMATIC ERRORS LINE TASK

is tilt angle underestimated?

ACTIVE TILT RESULTS REVEAL PARADOX

tilt estimates are quite accurate

but large errors in line task

line task body tilt estimate

SPATIAL PERCEPTION TESTS

Paradox: subject knows tilt angle but has biased line settings

estimate body tilt adjust line to direction of gravity

BAYESIAN STRATEGY

BAYESIAN MODEL

OPTIMAL OBSERVER THEORY

De Vrijer et al. (2008)

• Noisy otolith signal would spoil precise visual signal

• Most of the time, the head is near upright (prior knowledge)

• Brain takes prior knowledge into account when using the sensory tilt signal

BAYES MODEL OPTIMAL OBSERVER

1) The incoming (noisy) otolith signal may have been caused by a range of possible tilt angles (likelihood function)

2) On a priori grounds, not all tilt angles are equally probable: mostly the head is near upright (prior)

3) The most likely tilt angle is the product of likelihood en prior (posterior)

BAYESIAN MODEL

Noisy tilt signal causes uncertainty about the actual tilt angle (likelihood)

Brain applies correction, based on experience of which tilt angles are most common (prior)

Result is a weighted compromise (posterior)

BAYESIAN MODEL FITS

De Vrijer et al. (2008)

tilt compensation

error

MODEL ASSUMPTIONS

1. Prior has a fixed width, independent of tilt angle

2. Noise in tilt signal increases with tilt angle: ………true?

MEASURING UNCERTAINTY:

PSYCHOPHYSICAL EXPERIMENTS

De Vrijer & Van Wamel (2007)

PSYCHOMETRIC CURVE OF 0o BODY TILT PERCEPT

Subject is tilted at various angles around 0o

Makes right or left judgment (forced-choice)

No sharply defined threshold, due to noise in tilt signal

NOISE IN TILT SIGNAL AT 00

Psychometric curve

Noise in tilt signal

NOISE BODY TILT SIGNAL AT 0o AND 90o

more noise at 90o

NOISE AT 0o AND 90o

results 5 subjects

more noise at 90o

VISUAL VERTICAL AND BODY TILT SIGNAL AT 90o

less accuracy but better precision in visual vertical

VISUAL VERTICAL AND BODY TILT SIGNAL

visual vertical

body tilt

Rechtop is de perceptie van lijnoriëntatie bijna foutloos

gekantelde proefpersoon ziet de visuele wereld geroteerd

klokschaal methode

Effect van sensor ruis

prior heeft des te meer effect op het percept naarmate de sensorische meting ruiziger is

Bayes model visuele verticaal

de Vrijer et al. (2007)

Oculomotor verticaal

Van Beuzekom & Van Gisbergen (2000)

fouten in visuele en oculomotor verticaal zijn vergelijkbaar

RENS VINGERHOETS

AMBIGUITY PROBLEM OTOLITHS

Detect gravito-inertial force (GIF)

No distinction between tilt and translation

tilt

translation

models vestibular signal processing

SOLVING THE AMBIGUITY PROBLEM: TWO MODELS

Two putative strategies for decomposition of the otolith signal:

• frequency-filtering model

• canal-otolith interaction model

inverse problem

CANAL-OTOLITH INTERACTION

• canals respond to rotation during tilt

• brain can use their signal to decompose otolith signal

SPATIAL ORIENTATION ILLUSIONS

PILOT AIRCRAFT CARRIER

pilot is upright during launch in the dark, but feels tilted backward

ROTATION IN DARKNESS

rotation percept decays slowly; after stop subject feels rotation in opposite direction

reflection of cupula mechanics

EXPERIMENTS

Percepts during rotation about a tilted axis

Vingerhoets et al. (2006) J. Neurophysiol.

Vingerhoets et al. (2007) J. Neurophysiol.

THE ACTUAL MOTION

- rotation about tilted axis

- in darkness

- constant velocity

PERCEIVED MOTION

Results support canal-otolith interaction model

rotation percept

translation percept

TRANSLATION AND ROTATION PERCEPT

rotation percept

translation percept

MODEL SIMULATION

otolith signal, actually caused by tilt changes, is partially ascribed to translation when the rotation signal dies out

SPATIAL PERCEPTION TESTS

Paradox: subject knows tilt angle but has biased line settings

estimate body tilt adjust line to direction of gravity