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Bayesian decision theory and psychophysics
Open accessAbstract
We argue that Bayesian decision theory provides a good theoretical framework for visual perception. Such a theory involves a likelihood function specifying how the scene generates the image(s), a prior assumption about the scene, and a decision rule to determine the scene interpretation. This is illustrated by describing Bayesian theories for individual visual cues and showing that perceptual biases found in psychophysical experiments can be interpreted as biases towards prior assumptions made by the visual system. We then describe the implications of this framework for the integration of different cues. We argue that the dependence of cues on prior assumptions means that care must be taken to model these dependencies during integration. This suggests that a number of proposed schemes for cue integration, which only allow weak interaction between cues, are not adequate and instead stronger coupling is often required. These theories require the choice of decision rules and we argue that this choice is important since these rules help capture the task dependent nature of vision. This is illustrated by analysing the generic viewpoint assumption. Finally, we suggest that the visual system uses a set of competing prior assumptions, rather than the single generic priors, or natural constraints, commonly used in computational theories of vision.
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The reduced sensitivity of psychosis patients to perceptual illusions is inconsistent with the proposition that strong priors are at the root of perceptual illusions.
“which is inconsistent with the proposition that strong priors would be at the root of perceptual illusions.141,142”
From Are hallucinations due to an imbalance between excitatory and inhibitory influences on the brain? (2016) · cites this paper as [141]
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Object perception as Bayesian inference
Kersten, D., Mamassian, P., & Yuille, A. (2004) · Annual Review of Psychology · doi:10.1146/annurev.psych.55.090902.142005 · Cited by 1,269
“This can be related to notions of utility 4 , discounting a variable is equivalent to treating it as having such low utility that it is not worth estimating (Yuille & B(cid:127)ultho(cid:11) 1996), see Section 4.”
BackgroundSelf-citationMeasurement and modeling of depth cue combination: in defense of weak fusion
Landy, M. S., Maloney, L. T., Johnston, E. B., & Young, M. (1995) · Vision Research · doi:10.1016/0042-6989(94)00176-m · Cited by 996
“Yuille and Biilthoff (1995) demonstrate that some forms of weak coupling approximate a weighted linear rule of combination when cues are not too discrepant.”
BackgroundBayesian decision theory in sensorimotor control
Kording, K. P., & Wolpert, D. M. (2006) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2006.05.003 · Cited by 911
Decision theory, reinforcement learning, and the brain
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“…and Clark, 1989; Montague, 2006; Gold and Shadlen, 2002, 2007; Glimcher, 2004; Körding, 2007; Gittins, 1989; Berry and Fristedt, 1985; Wald, 1947; Yuille and Bülthoff, 1996; McNamara and Houston, 1980), and is therefore a critical tool for modeling, understanding and predicting psychological…”
BackgroundMethodInfluentialNeural correlates of multisensory cue integration in macaque MSTd
Gu, Y., Angelaki, D. E., & DeAngelis, G. C. (2008) · Nature Neuroscience · doi:10.1038/nn.2191 · Cited by 554
“Multisensory integration in human behavior often follows predictions of a quantitative framework that applies Bayesian statistical inference to the problem of cue integratio”
BackgroundBrainard, D. H., & Freeman, W. T. (1997) · Journal of the Optical Society of America A · doi:10.1364/josaa.14.001393 · Cited by 525
Bayesian integration of visual and auditory signals for spatial localization
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Pouget, A., Deneve, S., & Duhamel, J.-R. (2002) · Nature Reviews Neuroscience · doi:10.1038/nrn914 · Cited by 413
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Learning to integrate arbitrary signals from vision and touch
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Optimal integration of texture and motion cues to depth
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The Interface Theory of Perception
Hoffman, D. D., Singh, M., & Prakash, C. (2015) · Psychonomic Bulletin & Review · doi:10.3758/s13423-015-0890-8 · Cited by 329
“Yuille and Bülthoff (1996) for instance: BWe define vision as perceptual inference, the estimation of scene properties from an image or sequence of images…there is insufficient information in the image to determine uniquely the scene.”
BackgroundBayesian models of object perception
Kersten, D., & Yuille, A. (2003) · Current Opinion in Neurobiology · doi:10.1016/s0959-4388(03)00042-4 · Cited by 320
“It has been argued [38] that strong coupling of visual cues [40] is required to model a range of visual phenomena [48].”
BackgroundSelf-citationProbability matching as a computational strategy used in perception
Wozny, D. R., Beierholm, U. R., & Shams, L. (2010) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000871 · Cited by 265
“This strategy in the context of our task translates into model selection [17,18].”
MethodMultimodal Saliency and Fusion for Movie Summarization Based on Aural, Visual, and Textual Attention
Evangelopoulos, G., Zlatintsi, A., Potamianos, A., Maragos, P. A., Rapantzikos, K. E., Σκούμας, Γ., & Avrithis, Y. (2013) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2013.2267205 · Cited by 263
Contributions of ideal observer theory to vision research
Geisler, W. S. (2010) · Vision Research · doi:10.1016/j.visres.2010.09.027 · Cited by 270
Towal, R. B., Mormann, M. M., & Koch, C. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1304429110 · Cited by 270
Bayesian integration of visual and vestibular signals for heading
Butler, J. S., Smith, S. T., Campos, J. L., & Bulthoff, H. H. (2010) · Journal of Vision · doi:10.1167/10.11.23 · Cited by 250
Illusions, perception and Bayes
Geisler, W. S., & Kersten, D. (2002) · Nature Neuroscience · doi:10.1038/nn0602-508 · Cited by 249
Weighted linear cue combination with possibly correlated error
Oruç, İ., Maloney, L. T., & Landy, M. S. (2003) · Vision Research · doi:10.1016/s0042-6989(03)00435-8 · Cited by 227
“5 Yuille and B€ ulthoff (1996) consider the case where the posterior”
BackgroundCrossmodal influences on visual perception
Shams, L. B., & Kim, R. S. (2010) · Physics of Life Reviews · doi:10.1016/j.plrev.2010.04.006 · Cited by 252
“The traditional model of cue combination [46,116] and multisensory integration [23,29,43,114] assumes that the sensory signals are all caused by the same object (see Fig.”
BackgroundBayesian models: the structure of the world, uncertainty, behavior, and the brain
Vilares, I., & Kording, K. P. (2011) · Annals of the New York Academy of Sciences · doi:10.1111/j.1749-6632.2011.05965.x · Cited by 236
Circular inferences in schizophrenia
Jardri, R., & Denève, S. (2013) · Brain · doi:10.1093/brain/awt257 · Cited by 201
“This phenomenon accounts specifically for many perceptual illusions (Yuille and Bülthoff, 1996; Weiss et al., 2002; Bogadhi et al., 2011).”
BackgroundA Bayesian model of the disambiguation of gravitoinertial force by visual cues
MacNeilage, P. R., Banks, M. S., Berger, D. R., & Bülthoff, H. (2006) · Experimental Brain Research · doi:10.1007/s00221-006-0792-0 · Cited by 208
Self-citationPeters, M. A. K., & Lau, H. (2015) · eLife · doi:10.7554/elife.09651 · Cited by 197
Sensory transformations and the use of multiple reference frames for reach planning
McGuire, L. M., & Sabes, P. N. (2009) · Nature Neuroscience · doi:10.1038/nn.2357 · Cited by 197
Observer biases in the 3D interpretation of line drawings
Mamassian, P., & Landy, M. S. (1998) · Vision Research · doi:10.1016/s0042-6989(97)00438-0 · Cited by 197
“Several decision rules are commonly used in statistical decision theory [32,26].”
MethodKnill, D. C. (2007) · Journal of Vision · doi:10.1167/7.7.5 · Cited by 194
“The fundamental observation underlying the approach is that most cues rely on a mixture of possible prior assumptions or constraints about objects in the world (Knill, 2003; Yuille & Bulthoff, 1996).”
BackgroundMa, W. J., Zhou, X., Ross, L. A., Foxe, J. J., & Parra, L. C. (2009) · PLoS ONE · doi:10.1371/journal.pone.0004638 · Cited by 199
The combination of vision and touch depends on spatial proximity
Gepshtein, S., Burge, J., Ernst, M. O., & Banks, M. S. (2005) · Journal of Vision · doi:10.1167/5.11.7 · Cited by 186
Bayesian Modelling of Visual Perception
Mamassian, P., Landy, M., & Maloney, L. T. (2002) · Probabilistic Models of the Brain · doi:10.7551/mitpress/5583.003.0005 · Cited by 210
What determines visual cue reliability?
Jacobs, R. A. (2002) · Trends in Cognitive Sciences · doi:10.1016/s1364-6613(02)01948-4 · Cited by 182
Human trimodal perception follows optimal statistical inference
Wozny, D. R., Beierholm, U., & Shams, L. B. (2008) · Journal of Vision · doi:10.1167/8.3.24 · Cited by 178
“The traditional model of sensory cue combination (Bülthoff & Mallot, 1988; Yuille & Bülthoff, 1996) has been successful in accounting for sensory integration, such as visual–haptic integration (Ernst & Banks, 2002; Hillis, Ernst, Banks, & Landy, 2002), visual–auditory integration (Alais & Burr,…”
Viewing Geometry Determines How Vision and Haptics Combine in Size Perception
Gepshtein, S., & Banks, M. S. (2003) · Current Biology · doi:10.1016/s0960-9822(03)00133-7 · Cited by 171
“The principle of maximum likelihood Berkeley, California 94720-2020 (ML) prescribes the strategy for combining visual and haptic estimates that produces the estimate of lowest variance [4–8].”
BackgroundA review of interactions between peripheral and foveal vision
Stewart, E. E. M., Valsecchi, M., & Schütz, A. C. (2020) · Journal of Vision · doi:10.1167/jov.20.12.2 · Cited by 184
“The framework in which feature-integration benefits have been measured is maximum likelihood estimation (MLE) cue combination (e.g. Landy, Maloney, Johnston, & Young, 1995; Yuille & Bülthoff, 1996).”
BackgroundFusion of visual cues is not mandatory in children
Nardini, M., Bedford, R., & Mareschal, D. (2010) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1001699107 · Cited by 161
Are hallucinations due to an imbalance between excitatory and inhibitory influences on the brain?
Jardri, R., Hugdahl, K., Hughes, M., Brunelin, J., Waters, F., Alderson-Day, B., Smailes, D., Sterzer, P., Corlett, P. R., Leptourgos, P., et al. (2016) · Schizophrenia Bulletin · doi:10.1093/schbul/sbw075 · Cited by 157
Fetsch, C. R., DeAngelis, G. C., & Angelaki, D. E. (2010) · European Journal of Neuroscience · doi:10.1111/j.1460-9568.2010.07207.x · Cited by 154
Decision-theoretic models of visual perception and action
Maloney, L. T., & Zhang, H. (2010) · Vision Research · doi:10.1016/j.visres.2010.09.031 · Cited by 147
“…has been more and more frequently used in developing models of biological perception and action (Knill & Richards, 1996; Maloney, 2002; Mamassian, Landy, & Maloney, 2002; Yuille & Bülthoff, 1996), in part because its mathematical structure resembles the ordinary ‘‘perceptual cycle” (Neisser, 1976).”
MethodBayesian learning theory applied to human cognition
Jacobs, R. A., & Kruschke, J. K. (2010) · Wiley Interdisciplinary Reviews Cognitive Science · doi:10.1002/wcs.80 · Cited by 149
Knill, D. C. (1998) · Vision Research · doi:10.1016/s0042-6989(97)00324-6 · Cited by 147
“Applying a statistical estimation approach as used here provides a framework for testing assumptions such as isotropy [9,33].”
Haptic Interaction Design for Everyday Interfaces
MacLean, K. E. (2008) · Reviews of Human Factors and Ergonomics · doi:10.1518/155723408x342826 · Cited by 157
Feldman, J. (2001) · Perception & Psychophysics · doi:10.3758/bf03194532 · Cited by 141
“…2 3 4 1 4 1 1 1 smooth = ( ) ( ) ( ) = ( ) - = - + Õ (4) places this model somewhere between weak fusion (all cues are assumed to be independent) and strong fusion (all joint densities are computed) (Yuille & Bülthoff, 1996), approximately in the style of modified weak fusion (Landy et al., 1995).”
InfluentialIdeal cue combination for localizing texture-defined edges
Landy, M. S., & Kojima, H. (2001) · Journal of the Optical Society of America A · doi:10.1364/josaa.18.002307 · Cited by 137
The Sapir-Whorf Hypothesis and Probabilistic Inference: Evidence from the Domain of Color
Cibelli, E. S., Xu, Y., Austerweil, J. L., Griffiths, T. L., & Regier, T. (2016) · PLoS ONE · doi:10.1371/journal.pone.0158725 · Cited by 134
Zhao, M., & Warren, W. H. (2015) · Psychological Science · doi:10.1177/0956797615574952 · Cited by 112
The Interface Theory of Perception: Natural Selection Drives True Perception to Swift Extinction
Hoffman, D. D. (2009) · Cambridge University Press eBooks · doi:10.1017/cbo9780511635465.009 · Cited by 120
Implicit knowledge of visual uncertainty guides decisions with asymmetric outcomes
Whiteley, L., & Sahani, M. (2008) · Journal of Vision · doi:10.1167/8.3.2 · Cited by 114
“Bayesian decision theory gives the optimal form of this response (see Berger, 1985; Maloney, 2002; Yuille & Bultho, 1996 ).”
Foveated shot detection for video segmentation
Boccignone, G., Chianese, A., Moscato, V., & Picariello, A. (2005) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2004.842603 · Cited by 116
“As regards , under weak coupling assumption [62] of structural events , we can set .”
BackgroundStatistically Optimal Multisensory Cue Integration: A Practical Tutorial
Rohde, M., van Dam, L. C. J., & Ernst, M. O. (2015) · Multisensory Research · doi:10.1163/22134808-00002510 · Cited by 117
A review of human sensory dynamics for application to models of driver steering and speed control
Nash, C., Cole, D. J., & Bigler, R. S. (2016) · Biological Cybernetics · doi:10.1007/s00422-016-0682-x · Cited by 114
Multisensory integration: resolving sensory ambiguities to build novel representations
Green, A. M., & Angelaki, D. E. (2010) · Current Opinion in Neurobiology · doi:10.1016/j.conb.2010.04.009 · Cited by 102
No Evidence for an Item Limit in Change Detection
Keshvari, S., van den Berg, R., & Ma, W. J. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002927 · Cited by 100
Bayesian natural selection and the evolution of perceptual systems
Geisler, W. S., & Diehl, R. L. (2002) · Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences · doi:10.1098/rstb.2001.1055 · Cited by 101
Hoffman, D. D., & Prakash, C. (2014) · Frontiers in Psychology · doi:10.3389/fpsyg.2014.00577 · Cited by 103
“As Alan Yuille and Heinrich Bülthoff put it, “We define vision as perceptual inference, the estimation of scene properties from an image or sequence of images . . . ” (Yuille and Bülthoff, 1996).”
Neurobiology of Decision Making
Shadlen, M. N., Kiani, R., Hanks, T. D., & Churchland, A. K. (2008) · The MIT Press eBooks · doi:10.7551/mitpress/7735.003.0007 · Cited by 130
Interaction of visual prior constraints
Mamassian, P., & Landy, M. S. (2001) · Vision Research · doi:10.1016/s0042-6989(01)00147-x · Cited by 98
“Keywords: Visual constraints; Three-dimensional perception; Bayesian modelling; Shape from shading; Shape from contours”
BackgroundNatural selection and veridical perceptions
Mark, J. T., Marion, B. B., & Hoffman, D. D. (2010) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2010.07.020 · Cited by 97
“Yuille and Bülthoff (1996) concur, saying, ‘‘visual perception yinvolves the evolution of an organism’s visual ll rights reserved. arion@uci.edu (B.B. Marion), system to match the structure of the world and the coding scheme provided by nature.’’”
BackgroundA Bayesian approach to the evolution of perceptual and cognitive systems
Geisler, W. S., & Diehl, R. L. (2003) · Cognitive Science · doi:10.1016/s0364-0213(03)00009-0 · Cited by 125
“…stimulus factors, which were treated informally by Helmholtz, are rigorously specified in the Bayesian framework by prior probability and likelihood distributions (Freeman, 1994; Knill, Kersten, & Yuille, 1996; Yuille & Bülthoff, 1996; Brainard & Freeman, 1997; Geisler & Diehl, 2002; also seeFig.”
MethodIlluminant estimation as cue combination
Maloney, L. T. (2002) · Journal of Vision · doi:10.1167/2.6.6 · Cited by 98
“This second problem has been studied intensively only in the last 15 years (see discussions in Landy et al., 1995 and Yuille & Bülthoff, 1996), and it is in essence a statistical problem (e.g., see Geisler, 1989; Knill & Richards, 1996; Rao, Olshausen, & Lewicki, 2002).”
BackgroundMethodKnill, D. C. (2005) · Journal of Vision · doi:10.1167/5.2.2 · Cited by 96
“In Bayesian decision theory, task demands are enforced by specifying cost functions associated with a task and estimating a parameter like slant to minimize the expected cost of performance errors (Maloney, 2002; Yuille & Bulthoff, 1996).”
BackgroundSelf-motion leads to mandatory cue fusion across sensory modalities
Prsa, M., Gale, S., & Blanke, O. (2012) · Journal of Neurophysiology · doi:10.1152/jn.00439.2012 · Cited by 100
“Maximum likelihood estimation (MLE), derived from Bayes’ rule (Landy et al. 1995; Yuille and Bulthoff 1996), predicts that the optimal way for the brain to combine sensory cues will result in the posterior distribution being a normalized product of the visual and vestibular likelihoods P S Ivi, Ive…”
MethodRhythmicity and cross-modal temporal cues facilitate detection
ten Oever, S., Schroeder, C., Poeppel, D., et al. (2014) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2014.08.008 · Cited by 86
“…cues about a stimulus can be expressed by integrating the reliability of the perceptual estimates of individual cues, with the combination yielding higher reliability than each single cue alone (e.g. Yuille & Bülthoff, 1996; Landy, Maloney, Johnston, & Young, 1995; Oruç, Maloney, & Landy, 2003).”
A Bayesian approach to the evolution of perceptual and cognitive systems
Geisler, W. S., & Diehl, R. L. (2003) · Cognitive Science · doi:10.1207/s15516709cog2703_3 · Cited by 89
The Sapir‐Whorf hypothesis and inference under uncertainty
Regier, T., & Xu, Y. (2017) · Wiley Interdisciplinary Reviews Cognitive Science · doi:10.1002/wcs.1440 · Cited by 90
Making Decisions with Unknown Sensory Reliability
Denève, S. (2012) · Frontiers in Neuroscience · doi:10.3389/fnins.2012.00075 · Cited by 87
“Variants of diffusion models have been shown to successfully reproduce human and animal behaviour in 2AFC tasks (Ferguson 1967; Newsome, Britten et al. 1989; Yuille and Bülthoff 1996; Mazurek, Roitman et al. 2003; Ratcliff, Cherian et al. 2003; Palmer, McKinley et al. 2005; Ratcliff and McKoon 2008).”
BackgroundAn adaptive cue combination model of human spatial reorientation
Xu, Y., Regier, T., & Newcombe, N. S. (2017) · Cognition · doi:10.1016/j.cognition.2017.02.016 · Cited by 89
“This formulation for the combination of independent cues is drawn from the literature on perceptual cue integration (Ernst & Banks, 2002; Jacobs, 2002; Knill & Pouget, 2004; Yuille & Bülthoff, 1996).”
MethodThe simplicity principle in perception and cognition
Feldman, J. (2016) · Wiley Interdisciplinary Reviews Cognitive Science · doi:10.1002/wcs.1406 · Cited by 102
Multisensory Calibration Is Independent of Cue Reliability
Zaidel, A., Turner, A. H., & Angelaki, D. E. (2011) · Journal of Neuroscience · doi:10.1523/jneurosci.2732-11.2011 · Cited by 83
Linking neurons to behavior in multisensory perception: A computational review
Ma, W. J., & Pouget, A. (2008) · Brain Research · doi:10.1016/j.brainres.2008.04.082 · Cited by 86
“The model can be restated in the form of a mixed prior over pairs of stimuli (Beierholm et al., 2007; Kording et al., 2007) and is therefore an example of a mixture model ( Yuille and Bulthoff, 1996 ), used earlier to describe the combination of depth cues (Knill, 2003).”
InfluentialBayesian modeling of cue interaction: bistability in stereoscopic slant perception
van Ee, R., Adams, W. J., & Mamassian, P. (2003) · Journal of the Optical Society of America A · doi:10.1364/josaa.20.001398 · Cited by 83
High-level Vision as Statistical Inference
Kersten, D. (1999) · Cited by 99
Visual–Haptic Adaptation Is Determined by Relative Reliability
Burge, J., Girshick, A. R., & Banks, M. S. (2010) · Journal of Neuroscience · doi:10.1523/jneurosci.6427-09.2010 · Cited by 78
“where wV and wH are the combination weights and rV and rH are the reliabilities of the estimates, where reliability is defined as the inverse of the measurement variance, σ2 (Yuille and Bülthoff, 1996; Jacobs, 1999).”
Girshick, A. R., & Banks, M. S. (2009) · Journal of Vision · doi:10.1167/9.9.8 · Cited by 81
“…has become the standard framework for sensory cue combination (Ghahramani, Wolpert, & Jordan, 1997; Landy, Maloney, Johnston, & Young, 1995; Yuille & Bülthoff, 1996), and is supported by a large body of empirical evidence (Alais & Burr, 2004; Ernst & Banks, 2002; Hillis, Watt, Landy, &…”
Burge, T. (2020) · Oxford University Press eBooks · doi:10.1093/oso/9780198713524.003.0002 · Cited by 68
Fitness Beats Truth in the Evolution of Perception
Prakash, C., Stephens, K. D., Hoffman, D. D., Singh, M., & Fields, C. (2021) · Acta Biotheoretica · doi:10.1007/s10441-020-09400-0 · Cited by 66
Probabilistic Models of the Brain.
Long, D. M. (2002) · Neurosurgery Quarterly · doi:10.1097/00013414-200212000-00005 · Cited by 67
You Don’t See What I See: Individual Differences in the Perception of Meaning from Visual Stimuli
Partos, T., Cropper, S. J., & Rawlings, D. (2016) · PLoS ONE · doi:10.1371/journal.pone.0150615 · Cited by 75
“The meaning that is imposed can depend on our internal templates of prototypical stimuli [12, 13] our expectations and learned probabilities about the visual environment [9, 14–20], contextual cues or prior visual input [21, 22] and on random neural fluctuations in functionally relevant areas of cortex [23–26].”
BackgroundThe Size-Weight Illusion is not anti-Bayesian after all: a unifying Bayesian account
Peters, M. A. K., Ma, W. J., & Shams, L. B. (2016) · PeerJ · doi:10.7717/peerj.2124 · Cited by 61
Sensory Weighting of Force and Position Feedback in Human Motor Control Tasks
Mugge, W., Schuurmans, J. H. A., Schouten, A. C., et al. (2009) · Journal of Neuroscience · doi:10.1523/jneurosci.0116-09.2009 · Cited by 64
“Many studies have shown sensory integration and weighting in the CNS (Yuille and Bülthoff, 1996; Ernst and Bülthoff, 2004).”
BackgroundCue Integration in Categorical Tasks: Insights from Audio-Visual Speech Perception
Bejjanki, V. R., Clayards, M. A., Knill, D. C., & Aslin, R. Ν. (2011) · PLoS ONE · doi:10.1371/journal.pone.0019812 · Cited by 61
Claessens, P. M. E., & Wagemans, J. P. (2008) · Journal of Vision · doi:10.1167/8.7.33 · Cited by 58
Statistics for optimal point prediction in natural images
Geisler, W. S., & Perry, J. S. (2011) · Journal of Vision · doi:10.1167/11.12.14 · Cited by 58
“…are Gaussian distributed and uncorrelated, then the optimal estimate given the combined conditional variables is x ^¼ x ^ 1 + þ x ^ 2 ð1j +Þ; ð6Þ where + = > ^ 1 / (> ^ 1 + > ^ 2 ) is the relative reliability of the two estimates (e.g., Oruç, Maloney, & Landy, 2003; Yuille & Bulthoff, 1996).”
BackgroundDirect learning in dynamic touch.
Michaels, C. F., Arzamarski, R., Isenhower, R. W., & Jacobs, D. M. (2008) · Journal of Experimental Psychology Human Perception & Performance · doi:10.1037/0096-1523.34.4.944 · Cited by 59
van Ee, R., van Dam, L. C. J., & Erkelens, C. J. (2002) · Journal of Vision · doi:10.1167/2.9.2 · Cited by 57
“…this framework to human vision (Porrill, Frisby, Adams, & Buckley, 1999; Bülthoff & Yuille, 1991; Bülthoff & Mallot, 1990; Clark & Yuille, 1990; Yuille & Bülthoff, 1996; Freeman, 1994; Freeman, 1996; Bülthoff & Yuille, 1990; Bülthoff, 1991; Yuille, Geiger, & Bülthoff, 1991; Ascher & Grzywacz,…”
(2008) · Cited by 61
Causal Inference in Multisensory Heading Estimation
de Winkel, K. N., Katliar, M., & Bülthoff, H. (2017) · PLoS ONE · doi:10.1371/journal.pone.0169676 · Cited by 60
Self-citationIntegration of vision and haptics during tool use
Takahashi, C., Diedrichsen, J., & Watt, S. J. (2009) · Journal of Vision · doi:10.1167/9.6.3 · Cited by 53
The Role of Stereo Vision in Visual–Vestibular Integration
Butler, J. S., Campos, J. L., Bülthoff, H., & Smith, S. (2011) · Seeing and Perceiving · doi:10.1163/187847511x588070 · Cited by 58
“Using a simplified form of MLE (Alais and Burr, 2004; Bülthoff and Yuille, 1991; Ernst and Banks, 2002; Ernst et al., 2000; Yuille and Bülthoff, 1996), we used the JND to estimate a Gaussian likelihood distribution for each of the unimodal cues (visual, ŜVis and vestibular, ŜVest).”
MethodSelf-citationRepresentations of uncertainty: where art thou?
Koblinger, Á., Fiser, J., & Lengyel, M. (2021) · Current Opinion in Behavioral Sciences · doi:10.1016/j.cobeha.2021.03.009 · Cited by 51
Human observers are biased in judging the angular approach of a projectile
Welchman, A. E., Tuck, V., & Harris, J. M. (2004) · Vision Research · doi:10.1016/j.visres.2004.03.014 · Cited by 49
“If these two estimators were combined (Landy, Maloney, Johnston, & Young, 1995) using maximum likelihood estimation (Ernst & Banks, 2002; Yuille & B€ ulthoff, 1996), then the weight given to the looming estimator should increase as the reliability of that estimator increases (i.e. as the stimulus…”
Using psychophysics to ask if the brain samples or maximizes
Acuna, D. E., Berniker, M., Fernandes, H. L., & Kording, K. P. (2015) · Journal of Vision · doi:10.1167/15.3.7 · Cited by 50
Supervised Calibration Relies on the Multisensory Percept
Zaidel, A., Ma, W. J., & Angelaki, D. E. (2013) · Neuron · doi:10.1016/j.neuron.2013.09.026 · Cited by 52
“The prevalent theory of multisensory integration accounts for improved reliability (Yuille and Bülthoff, 1996; Ernst and Banks, 2002; van Beers et al., 2002; Knill and Pouget, 2004; Alais and Burr, 2004; Fetsch et al., 2009; Butler et al., 2010), but not for accuracy.”
Common Bayesian Models for Common Cognitive Issues
Colas, F., Diard, J., & Bessìère, P. (2010) · Acta Biotheoretica · doi:10.1007/s10441-010-9101-1 · Cited by 59
TOWARDS PRACTICAL FACIAL FEATURE DETECTION
Eckhardt, M., Fasel, I., & Movellan, J. R. (2009) · International Journal of Pattern Recognition and Artificial Intelligence · doi:10.1142/s0218001409007247 · Cited by 49
Learning and inference using complex generative models in a spatial localization task
Bejjanki, V. R., Knill, D. C., & Aslin, R. Ν. (2016) · Journal of Vision · doi:10.1167/16.5.9 · Cited by 47
“Bayesian inference provides a principled approach for accomplishing this in a statistically efficient fashion; that is, in a manner that maximally utilizes the available information (Bernardo & Smith, 1994; Cox, 1946; Yuille & Bülthoff, 1996).”
BackgroundMethod
Metadata
- Authors
- Yuille, A. L., & Bülthoff, H. H.
- Affiliations
- Harvard University (US)
- Max Planck Society (DE)
- Venue
- Perception as Bayesian Inference
- Publisher
- Cambridge University Press
- Published
- 1996-09-13
- Pages
- 123-162
- OpenAlex
- W1604979084
- Cited by
- 250
- References
- 0
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 6 · 2023: 5 · 2022: 8 · 2021: 8 · 2020: 11 · 2019: 8 · 2018: 7 · 2017: 11 · 2016: 11 · 2015: 8 · 2014: 8 · 2013: 15 · 2012: 10
- FWCI
- 7.83
- Type
- book chapter
- Language
- en
- Open access
- green
- hdl.handle.net
- Licence
- Locations
- Cambridge University Press eBooks (publishedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Vision and Imaging
- Keywords
- Bayesian decision theory, visual perception, perceptual bias, cue integration, prior assumptions, likelihood function, decision rules, natural constraints, psychophysics
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