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81 nips-2007-Estimating disparity with confidence from energy neurons

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Author: Eric K. Tsang, Bertram E. Shi

Abstract: The peak location in a population of phase-tuned neurons has been shown to be a more reliable estimator for disparity than the peak location in a population of position-tuned neurons. Unfortunately, the disparity range covered by a phasetuned population is limited by phase wraparound. Thus, a single population cannot cover the large range of disparities encountered in natural scenes unless the scale of the receptive fields is chosen to be very large, which results in very low resolution depth estimates. Here we describe a biologically plausible measure of the confidence that the stimulus disparity is inside the range covered by a population of phase-tuned neurons. Based upon this confidence measure, we propose an algorithm for disparity estimation that uses many populations of high-resolution phase-tuned neurons that are biased to different disparity ranges via position shifts between the left and right eye receptive fields. The population with the highest confidence is used to estimate the stimulus disparity. We show that this algorithm outperforms a previously proposed coarse-to-fine algorithm for disparity estimation, which uses disparity estimates from coarse scales to select the populations used at finer scales and can effectively detect occlusions.

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Estimating disparity with confidence from energy neurons Eric K. [sent-1, score-1.098]

2 hk Abstract The peak location in a population of phase-tuned neurons has been shown to be a more reliable estimator for disparity than the peak location in a population of position-tuned neurons. [sent-18, score-1.432]

3 Unfortunately, the disparity range covered by a phasetuned population is limited by phase wraparound. [sent-19, score-1.004]

4 Thus, a single population cannot cover the large range of disparities encountered in natural scenes unless the scale of the receptive fields is chosen to be very large, which results in very low resolution depth estimates. [sent-20, score-0.481]

5 Here we describe a biologically plausible measure of the confidence that the stimulus disparity is inside the range covered by a population of phase-tuned neurons. [sent-21, score-1.273]

6 Based upon this confidence measure, we propose an algorithm for disparity estimation that uses many populations of high-resolution phase-tuned neurons that are biased to different disparity ranges via position shifts between the left and right eye receptive fields. [sent-22, score-1.995]

7 The population with the highest confidence is used to estimate the stimulus disparity. [sent-23, score-0.436]

8 We show that this algorithm outperforms a previously proposed coarse-to-fine algorithm for disparity estimation, which uses disparity estimates from coarse scales to select the populations used at finer scales and can effectively detect occlusions. [sent-24, score-1.747]

9 Mammalian brains appear to represent the stimulus disparity using populations of disparity-tuned neurons in the visual cortex [1][2]. [sent-26, score-1.075]

10 The binocular energy model is a first order model that explains the responses of individual disparity-tuned neurons [3]. [sent-27, score-0.365]

11 In this model, the preferred disparity tuning of the neurons is determined by the phase and position shifts between the left and right monocular receptive fields (RFs). [sent-28, score-1.208]

12 Peak picking is a common disparity estimation strategy for these neurons([4]-[6]). [sent-29, score-0.768]

13 In this strategy, the disparity estimates are computed by the preferred disparity of the neuron with the largest response among the neural population. [sent-30, score-1.77]

14 Chen and Qian [4] have suggested that the peak location in a population of phase-tuned disparity energy neurons is a more reliable estimate than the peak location in a population of position-tuned neurons. [sent-31, score-1.466]

15 It is difficult to estimate disparity from a single phase-tuned neuron population because its range of preferred disparities is limited. [sent-32, score-1.276]

16 Figure 1 shows the population response of phase-tuned neurons (vertical cross section) for different stimulus disparities. [sent-33, score-0.444]

17 If the stimulus disparity is confined to the range of preferred disparities of this population, the peak location changes linearly with the stimulus disparity. [sent-34, score-1.457]

18 Thus, we can estimate the disparity from the peak. [sent-35, score-0.768]

19 However, in natural viewing condition, the stimulus disparity ranges over ten times larger than the range of the preferred disparities of the population [7]. [sent-36, score-1.371]

20 The peak location no longer indicates the stimulus disparity, since the peaks still occur even when the stimulus disparity is outside the range of neurons’ preferred disparities. [sent-37, score-1.286]

21 The false peaks arise from two sources: the phase wrap-around due to the sinusoidal modulation in the D pref 5 0 -5 -40 -30 -20 -10 0 10 20 30 40 stimulus disparity (pixels) Fig. [sent-38, score-0.956]

22 1: Sample population responses of the phase-tuned disparity neurons for different disparities. [sent-39, score-1.106]

23 This was generated by presenting the left image of the “Cones” stereogram shown in Figure 5a to both eyes but varying the disparity by keeping the left image fixed and shifting the right image. [sent-40, score-0.91]

24 At each point, the image intensity represents the response of a disparity neuron tuned to a fixed preferred disparity (vertical axis) in response to a fixed stimulus disparity (horizontal axis). [sent-41, score-2.812]

25 The dashed vertical lines indicate the stimulus disparities that fall within the range of preferred disparities of the population ( ± 8 pixels). [sent-42, score-0.799]

26 Although a single population can cover a large disparity range, the large size of the required receptive fields results in very low resolution depth estimates. [sent-44, score-1.028]

27 To address this problem, Chen and Qian [4] proposed a coarse-to-fine algorithm which refines the estimates computed from coarse scales using populations tuned to finer scales. [sent-45, score-0.239]

28 Here we present an alternative way to estimate the stimulus disparity using a biologically plausible confidence measure that indicates whether the stimulus disparity lies inside or outside the range of preferred disparities in a population of phase tuned neurons. [sent-46, score-2.545]

29 2 Features of the phase-tuned disparity population In this section, we define different features of a population of phase-tuned neurons. [sent-50, score-1.123]

30 These features will be used to define the confidence measure. [sent-51, score-0.235]

31 Figure 2a illustrates the binocular disparity energy model of a phase-tuned neuron [3]. [sent-52, score-0.986]

32 The response of a binocular simple cell is modelled by summing of the outputs of linear monocular Gabor filters applied to both left and right images, followed by a positive or negative half squaring nonlinearity. [sent-54, score-0.326]

33 The response of a binocular complex cell is the sum of the four simple cell responses. [sent-55, score-0.249]

34 The disparity d is the difference between the locations of corresponding points in the left and right images, i. [sent-57, score-0.808]

35 We can compactly express the pairs of left and right monocular responses as the real and imaginary parts of V l(ψ l) = V l e jψ l and jψ V r(ψ r) = V r e r , where with a slight abuse of notation, we define Vl = ∫ g(x)e jΩx Ul(x) dx and Vr = ∫ g(x)e jΩx Ur(x) dx (2) (a) U l(x) h(x, ψ l) Re. [sent-62, score-0.219]

36 2: (a) Binocular disparity energy model of a disparity neuron in the phase-shift mechanism. [sent-67, score-1.617]

37 The phase-shift ψ r – ψ l between the left and right monocular RFs determines the preferred disparity of the neuron. [sent-68, score-0.952]

38 The neuron shown is tuned to a negative disparity of – π ⁄ ( 2Ω ) . [sent-69, score-0.872]

39 (b) The population response of the phase-tuned neurons E d(Δψ) centered at a retinal location with the phase-shifts Δψ ∈ [ – π, π ] can be characterized by three features S, P and ΔΦ . [sent-70, score-0.381]

40 The response of the binocular complex cell (the disparity energy) is the squared modulus of the sum of the monocular responses: E d(Δψ) = V l e jψ l + Vr e jψ r 2 * = V l 2 + V l V r e – j Δψ + V l* V r e jΔψ + V r 2 (3) where the * superscript indicates the complex conjugation. [sent-71, score-1.052]

41 The phase-shift between the right and left neurons Δψ = ψ r – ψ l controls the preferred disparity D pref ( Δψ ) ≈ – Δψ ⁄ Ω of the binocular complex cell [6]. [sent-72, score-1.206]

42 If we fix the stimulus and allow Δψ to vary between ± π , the function E d(Δψ) in (3) describes the population response of phase-tuned neurons whose preferred disparities range between – π ⁄ Ω and π ⁄ Ω . [sent-73, score-0.761]

43 The population response can be completely specified by three features S , P and ΔΦ [4][5]. [sent-74, score-0.235]

44 The feature ΔΦ is the peak location of the population response. [sent-79, score-0.289]

45 We find this confidence measure by analyzing the empirical joint densities of S and the ratio R = P ⁄ S conditioned on the two disparity classes. [sent-84, score-0.953]

46 guishing between DIN and DOUT, since Figure 1 shows that the phase ranges between – π and π for both disparity classes. [sent-111, score-0.826]

47 Bayesian classifiers compare the conditional probabilities of the two disparity classes (DIN and DOUT) given the observed feature values. [sent-115, score-0.813]

48 We constructed a population of phase-tuned neurons at each pixel. [sent-122, score-0.272]

49 The disparity neurons had the same spatial frequency and standard deviation, and were selective to vertical orientations. [sent-123, score-0.99]

50 The range of the preferred disparities (DIN) of the population is between ± 8 pixels. [sent-128, score-0.461]

51 The features S and R computed from population were separated into two classes (DIN and DOUT) according to the ground truth in Figure 5b. [sent-131, score-0.216]

52 Figure 3a-b show the empirically estimated joint conditional densities for the two disparity classes. [sent-132, score-0.768]

53 Given the disparity within the range of preferred disparities (DIN), the joint density concentrates at small S and large R . [sent-136, score-1.085]

54 For the out-of-range disparities (DOUT), the joint density shifts to both large S and small R . [sent-137, score-0.219]

55 Given the prior class probability phase tuned population E d(Δψ) R 128, ΔΦ 128 Δc = 128 E d(Δψ) Δc = 0 E d(Δψ) Winner take all U l(x) R Δc* ΔΦ Δc* R > TR DIN /DOUT d est U r(x) Δc = – 128 Fig. [sent-144, score-0.265]

56 4: Proposed disparity estimator with the validation of disparity estimates. [sent-145, score-1.536]

57 Thus, R can be used as a confidence measure for distinguishing DIN and DOUT. [sent-149, score-0.185]

58 4 Hybrid position-phase model for disparity estimation with validation Our analysis above shows that R is a simple indicator to distinguish between in-range and out-ofrange disparities. [sent-151, score-0.768]

59 In this section, we describe a model that uses this feature to estimate the stimulus disparity with validation. [sent-152, score-0.913]

60 Figure 4 shows the proposed model, which consists of populations of hybrid tuned disparity neurons tuned to different phase-shifts Δψ and position-shifts Δc . [sent-153, score-1.09]

61 For each population tuned to the same position-shift but different phase-shifts (phase-tuned population), we compute the ratio R Δc = P Δc ⁄ S Δc . [sent-154, score-0.201]

62 The feature P Δc can be computed by subtracting the peak response S Δc + P Δc of the phase tuned population with the average activation S Δc . [sent-156, score-0.409]

63 The disparity estimate is further refined by the peak location ΔΦ Δc* by ΔΦ Δc* d est = Δc* – ---------------Ω (8) In additional to estimate the stimulus disparity, we also validate the estimates by comparing R Δc* with a threshold T R . [sent-158, score-1.121]

64 1 Disparity estimation with confidence We applied the proposed model to estimate the disparity of the “Cones” and the “Teddy” stereograms, shown in Figure 5a. [sent-161, score-0.936]

65 The spatial frequency and the spatial standard deviation of the neurons left right (b) (c) Teddy Cones (a) (d) -100 estimate error (e) 0 estimate 100 error Fig. [sent-162, score-0.298]

66 (b) The ground truth disparity maps with respect to the left images, obtained by the structured light method. [sent-164, score-0.871]

67 (d) The disparity maps and the error maps computed by the coarse-tofine approach. [sent-166, score-0.877]

68 (e) The disparity maps and the error maps computed by the proposed model. [sent-167, score-0.877]

69 The detected invalid estimates are labelled in black in the disparity maps. [sent-168, score-0.831]

70 We also performed spatial pooling and orientation pooling to improve the estimation. [sent-170, score-0.219]

71 The range of the position-shifts for the populations was set to the largest disparity range, ± 128 pixels, according to the ground truth. [sent-173, score-0.874]

72 In this model, an initial disparity estimate computed from a population of phase-tuned neurons at the coarsest scale is successively refined by the populations of phase-tuned neurons at the finer scales. [sent-175, score-1.36]

73 By choosing the coarsest scale large enough, the disparity range covered by this method can be arbitrarily large. [sent-176, score-0.856]

74 Same spatial pooling and orientation pooling were applied on each scale. [sent-180, score-0.219]

75 Figure 5d-e show the estimated disparity maps and the error maps of the two approaches. [sent-181, score-0.86]

76 The error maps show the regions where the disparity estimates exceed 1 pixel of error in the disparity. [sent-182, score-0.84]

77 Both models correctly recover the stimulus disparity at most locations with gradual disparity changes, but tend to make errors at the depth boundaries. [sent-183, score-1.737]

78 This arises because the assumption that the stimulus disparity is constant over the RF of the neuron is unlikely at very large scales. [sent-189, score-0.939]

79 At boundaries, the coarse-to-fine model generates poor initial estimates, which cannot be corrected at the finer scales, because the actual stimulus disparities are outside the range considered at the finer scales. [sent-190, score-0.483]

80 In general, the responses of neurons selective to different position disparities are not comparable, since they depend upon image contrast which varies at different spatial locations. [sent-192, score-0.458]

81 Moreover, the invalid regions detected (the black regions on the disparity maps) are in excellent agreement with the error labels. [sent-194, score-0.787]

82 2 Occlusion detection In addition to validating the disparity estimates, the feature R can also be used to detect occlusion. [sent-196, score-0.811]

83 There are three possibilities for image pixels that are labelled as out of range (DOUT). [sent-201, score-0.196]

84 They are occluded pixels, pixels with valid disparities that are incorrectly estimated, and pixels with valid disparity that are correctly estimated. [sent-202, score-1.283]

85 Figure 6a shows the percentages of DOUT pixels that fall into each possibility as the threshold T R applied to R varies, e. [sent-203, score-0.214]

86 , # of occluded pixels in DOUT P1 ( occluded ) = ------------------------------------------------------------------------ × 100% total # of pixels in DOUT (9) These percentages sum to unity for any thresholds T R . [sent-205, score-0.511]

87 As the threshold increases, the detector also begins to detect incorrect disparity estimates. [sent-207, score-0.84]

88 Figure 6b shows the percentages of pixels in each possibility that are classified as DOUT as a function of T R , e. [sent-208, score-0.183]

89 , # of occluded pixels in DOUT P2 ( occluded ) = ------------------------------------------------------------------------ × 100% # of occluded pixels in image (10) For a large threshold ( T R close to unity), all estimates are labelled as DOUT, so the three percentages approach 100%. [sent-210, score-0.662]

90 3 , it identifies ~70% of the occluded pixels, ~20% of the pixels with incorrect estimates with only ~10% misclassification. [sent-213, score-0.256]

91 6: The percentages of occluded pixels (thick), pixels with incorrect disparity estimates (thin) and pixels with correct estimates (dotted) identified as DOUT. [sent-231, score-1.329]

92 5 Discussion In this paper, we have proposed an algorithm to estimate stimulus disparities based on a confidence measure computed from population of hybrid tuned disparity neurons. [sent-234, score-1.509]

93 Although there have been previously proposed models that estimate the stimulus disparity from populations of hybrid tuned neurons [4][10], our model is the first that also provides a confidence measure for these estimates. [sent-235, score-1.342]

94 Our analysis suggests that pixels with low confidence are likely to be in occluded regions. [sent-236, score-0.374]

95 The confidence measure used in the proposed algorithm can be computed using normalization, which has been used to model the responses of V1 neurons [11]. [sent-238, score-0.396]

96 Previous work has emphasized the role of normalization in reducing the effect of image contrast or in ensuring that the neural responses tuned to different stimulus dimensions are comparable [12]. [sent-239, score-0.292]

97 Our results show that, in addition to these roles, normalization also serves to make the magnitude of the neural responses more representative of the confidence in validating the hypothesis that the input disparity is close to the neurons preferred disparity. [sent-240, score-1.245]

98 An interesting question, which we are now investigating, is whether individual confidence measures computed from different locations or orientations can be combined systematically. [sent-244, score-0.223]

99 Stereoscopic depth discrimination in the visual cortex: neurons ideally suited as disparity detectors. [sent-271, score-0.954]

100 Neural encoding of binocular disparity: energy models, position shifts and phase shifts. [sent-286, score-0.241]

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These sources are chosen close to each other so that the subject can imagine that the resulting cues originate from a single source and thus implicitly have a common cause. The experimentally observed distribution is then p (ˆ|sV , sA ) = s p (ˆ|xV , xA ) p (xV |sV ) p (xA |sA ) dxV dxA s Given that s is a linear combination of two normally distributed variables, it will itself follow a ˆ sV +wA 1 2 normal distribution, with mean s = wVwV +wA sA and variance σs = wV +wA . The reason that we ˆ ˆ emphasize this point is because many authors identify the estimate distribution p (ˆ|sV , sA ) with s the posterior distribution p (s|xV , xA ). This is justiﬁed in this case because all distributions are Gaussian and the estimate is a linear combination of cues. 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In all three models, the response distribution p (ˆV , sA |sV , sA ) is obtained by idens ˆ tifying it with the posterior distribution p (sV , sA |xV , xA ). This procedure thus implicitly assumes that marginalizing over the latent variables xV and xA is not necessary, which leads to a signiﬁcant error for non-Gaussian priors. In this paper we correctly deal with these issues and in all cases marginalize over the latent variables. The parametric models used for the coupling between the cues lead to an elegant low-dimensional model of cue integration that allows for estimates of single cues that differ from one another. C C=1 SA S XA 2.3 C=2 XV SV XA XV Causal inference model In the causal inference model [24, 25], we start from the traditional cue integration model but remove the assumption that two signals are caused by the same source. Instead, the number of sources can be one or two and is itself a variable that needs to be inferred from the cues. Figure 1: Generative model of causal inference. 1 This family of Bayesian posterior distributions also includes one used to successfully model cue combination in depth perception [27, 28]. In depth perception, however, there is no notion of segregation as always a single surface is assumed. 3 If there are two sources, they are assumed to be independent. Thus, we use the graphical model depicted in Fig. 1. We denote the number of sources by C. The probability distribution over C given internal representations xV and xA is given by Bayes’ rule: p (C|xV , xA ) ∝ p (xV , xA |C) p (C) . In this equation, p (C) is the a priori probability of C. We will denote the probability of a common cause by pcommon , so that p (C = 1) = pcommon and p (C = 2) = 1 − pcommon . The probability of generating xV and xA given C is obtained by inserting a summation over the sources: p (xV , xA |C = 1) = p (xV , xA |s)p (s) ds = p (xV |s) p (xA |s)p (s) ds Here p (s) is a prior for spatial location, which we assume to be distributed as N (s; 0, σP ). Then all three factors in this integral are Gaussians, allowing for an analytic solution: p (xV , xA |C = 1) = 2 2 2 2 2 −xA )2 σP σA √ 2 2 1 2 2 2 2 exp − 1 (xV σ2 σ2 +σ2+xV+σ2+xA σV . 2 σ2 σ2 2π σV σA +σV σP +σA σP V A V P A P For p (xV , xA |C = 2) we realize that xV and xA are independent of each other and thus obtain p (xV , xA |C = 2) = p (xV |sV )p (sV ) dsV p (xA |sA )p (sA ) dsA Again, as all these distributions are assumed to be Gaussian, we obtain an analytic solution, x2 x2 1 1 V A p (xV , xA |C = 2) = exp − 2 σ2 +σ2 + σ2 +σ2 . Now that we have com2 +σ 2 2 +σ 2 p p V A 2π (σV p )(σA p) puted p (C|xV , xA ), the posterior distribution over sources is given by p (si |xV , xA ) = p (si |xV , xA , C) p (C|xV , xA ) C=1,2 where i can be V or A and the posteriors conditioned on C are well-known: p (si |xA , xV , C = 1) = p (xA |si ) p (xV |si ) p (si ) , p (xA |s) p (xV |s) p (s) ds p (si |xA , xV , C = 2) = p (xi |si ) p (si ) p (xi |si ) p (si ) dsi The former is the same as in the case of mandatory integration with a prior, the latter is simply the unimodal posterior in the presence of a prior. Based on the posterior distribution on a given trial, p (si |xV , xA ), an estimate has to be created. For this, we use a sum-squared-error cost func2 2 tion, Cost = p (C = 1|xV , xA ) (ˆ − s) + p (C = 2|xV , xA ) (ˆ − sV or A ) . Then the best s s estimate is the mean of the posterior distribution, for instance for the visual estimation: sV = p (C = 1|xA , xV ) sV,C=1 + p (C = 2|xA , xV ) sV,C=2 ˆ ˆ ˆ where sV,C=1 = ˆ −2 −2 −2 xV σV +xA σA +xP σP −2 −2 −2 σV +σA +σP and sV,C=2 = ˆ −2 −2 xV σV +xP σP . −2 −2 σV +σP If pcommon equals 0 or 1, this estimate reduces to one of the conditioned estimates and is linear in xV and xA . If 0 < pcommon < 1, the estimate is a nonlinear combination of xV and xA , because of the functional form of p (C|xV , xA ). The response distributions, that is the distributions of sV and sA given ˆ ˆ sV and sA over many trials, now cannot be identiﬁed with the posterior distribution on a single trial and cannot be computed analytically either. The correct way to obtain the response distribution is to simulate an experiment numerically. Note that the causal inference model above can also be cast in the form of a bisensory stimulus prior by integrating out the latent variable C, with: p (sA , sV ) = p (C = 1) δ (sA − sV ) p (sA ) + p (sA ) p (sV ) p (C = 2) However, in addition to justifying the form of the interaction between the cues, the causal inference model has the advantage of being based on a generative model that well formalizes salient properties of the world, and it thereby also allows to predict judgments of unity. 4 3 Model performance and comparison To examine the performance of the causal inference model and to compare it to previous models, we performed a human psychophysics experiment in which we adopted the same dual-report paradigm as was used in [11]. Observers were simultaneously presented with a brief visual and also an auditory stimulus, each of which could originate from one of ﬁve locations on an imaginary horizontal line (-10◦ , -5◦ , 0◦ , 5◦ , or 10◦ with respect to the ﬁxation point). Auditory stimuli were 32 ms of white noise ﬁltered through an individually calibrated head related transfer function (HRTF) and presented through a pair of headphones, whereas the visual stimuli were high contrast Gabors on a noisy background presented on a 21-inch CRT monitor. Observers had to report by means of a key press (1-5) the perceived positions of both the visual and the auditory stimulus. Each combination of locations was presented with the same frequency over the course of the experiment. In this way, for each condition, visual and auditory response histograms were obtained. We obtained response distributions for each the three models described above by numeral simulation. On each trial, estimation is followed by a step in which, the key is selected which corresponds to the position closed to the best estimate. The simulated histograms obtained in this way were compared to the measured response frequencies of all subjects by computing the R2 statistic. Auditory response Auditory model Visual response Visual model no vision The parameters in the causal inference model were optimized using fminsearch in MATLAB to maximize R2 . The best combination of parameters yielded an R2 of 0.97. The response frequencies are depicted in Fig. 2. The bisensory prior models also explain most of the variance, with R2 = 0.96 for the Roach model and R2 = 0.91 for the Bresciani model. This shows that it is possible to model cue combination for large disparities well using such models. no audio 1 0 Figure 2: A comparison between subjects’ performance and the causal inference model. The blue line indicates the frequency of subjects responses to visual stimuli, red line is the responses to auditory stimuli. Each set of lines is one set of audio-visual stimulus conditions. Rows of conditions indicate constant visual stimulus, columns is constant audio stimulus. Model predictions is indicated by the red and blue dotted line. 5 3.1 Model comparison To facilitate quantitative comparison with other models, we now ﬁt the parameters of each model2 to individual subject data, maximizing the likelihood of the model, i.e., the probability of the response frequencies under the model. The causal inference model ﬁts human data better than the other models. Compared to the best ﬁt of the causal inference model, the Bresciani model has a maximal log likelihood ratio (base e) of the data of −22 ± 6 (mean ± s.e.m. over subjects), and the Roach model has a maximal log likelihood ratio of the data of −18 ± 6. A causal inference model that maximizes the probability of being correct instead of minimizing the mean squared error has a maximal log likelihood ratio of −18 ± 3. These values are considered decisive evidence in favor of the causal inference model that minimizes the mean squared error (for details, see [25]). The parameter values found in the likelihood optimization of the causal model are as follows: pcommon = 0.28 ± 0.05, σV = 2.14 ± 0.22◦ , σA = 9.2 ± 1.1◦ , σP = 12.3 ± 1.1◦ (mean ± s.e.m. over subjects). We see that there is a relatively low prior probability of a common cause. In this paradigm, auditory localization is considerably less precise than visual localization. Also, there is a weak prior for central locations. 3.2 Localization bias A useful quantity to gain more insight into the structure of multisensory data is the cross-modal bias. In our experiment, relative auditory bias is deﬁned as the difference between the mean auditory estimate in a given condition and the real auditory position, divided by the difference between the real visual position and the real auditory position in this condition. If the inﬂuence of vision on the auditory estimate is strong, then the relative auditory bias will be high (close to one). It is well-known that bias decreases with spatial disparity and our experiment is no exception (solid line in Fig. 3; data were combined between positive and negative disparities). It can easily be shown that a traditional cue integration model would predict a bias equal to σ2 −1 , which would be close to 1 and 1 + σV 2 A independent of disparity, unlike the data. This shows that a mandatory integration model is an insufﬁcient model of multisensory interactions. 45 % Auditory Bias We used the individual subject ﬁttings from above and and averaged the auditory bias values obtained from those ﬁts (i.e. we did not ﬁt the bias data themselves). Fits are shown in Fig. 3 (dashed lines). We applied a paired t-test to the differences between the 5◦ and 20◦ disparity conditions (model-subject comparison). Using a double-sided test, the null hypothesis that the difference between the bias in the 5◦ and 20◦ conditions is correctly predicted by each model is rejected for the Bresciani model (p < 0.002) and the Roach model (p < 0.042) and accepted for the causal inference model (p > 0.17). Alternatively, with a single-sided test, the hypothesis is rejected for the Bresciani model (p < 0.001) and the Roach model (p < 0.021) and accepted for the causal inference model (> 0.9). 50 40 35 30 25 20 5 10 15 Spatial Disparity (deg.) 20 Figure 3: Auditory bias as a function of spatial disparity. Solid blue line: data. Red: Causal inference model. Green: Model by Roach et al. [23]. Purple: Model by Bresciani et al. [22]. Models were optimized on response frequencies (as in Fig. 2), not on the bias data. The reason that the Bresciani model fares worst is that its prior distribution does not include a component that corresponds to independent causes. On 2 The Roach et al. model has four free parameters (ω,σV , σA , σcoupling ), the Bresciani et al. model has three (σV , σA , σcoupling ), and the causal inference model has four (pcommon ,σV , σA , σP ). We do not consider the Shams et al. model here, since it has many more parameters and it is not immediately clear how in this model the erroneous identiﬁcation of posterior with response distribution can be corrected. 6 the contrary, the prior used in the Roach model contains two terms, one term that is independent of the disparity and one term that decreases with increasing disparity. It is thus functionally somewhat similar to the causal inference model. 4 Discussion We have argued that any model of multisensory perception should account not only for situations of small, but also of large conﬂict. In these situations, segregation is more likely, in which the two stimuli are not perceived to have the same cause. Even when segregation occurs, the two stimuli can still inﬂuence each other. We compared three Bayesian models designed to account for situations of large conﬂict by applying them to auditory-visual spatial localization data. We pointed out a common mistake: for nonGaussian bisensory priors without mandatory integration, the response distribution can no longer be identiﬁed with the posterior distribution. After correct implementation of the three models, we found that the causal inference model is superior to the models with ad hoc bisensory priors. This is expected, as the nervous system actually needs to solve the problem of deciding which stimuli have a common cause and which stimuli are unrelated. We have seen that multisensory perception is a suitable tool for studying causal inference. However, the causal inference model also has the potential to quantitatively explain a number of other perceptual phenomena, including perceptual grouping and binding, as well as within-modality cue combination [27, 28]. Causal inference is a universal problem: whenever the brain has multiple pieces of information it must decide if they relate to one another or are independent. As the causal inference model describes how the brain processes probabilistic sensory information, the question arises about the neural basis of these processes. Neural populations encode probability distributions over stimuli through Bayes’ rule, a type of coding known as probabilistic population coding. Recent work has shown how the optimal cue combination assuming a common cause can be implemented in probabilistic population codes through simple linear operations on neural activities [29]. This framework makes essential use of the structure of neural variability and leads to physiological predictions for activity in areas that combine multisensory input, such as the superior colliculus. Computational mechanisms for causal inference are expected have a neural substrate that generalizes these linear operations on population activities. A neural implementation of the causal inference model will open the door to a complete neural theory of multisensory perception. References [1] H.L. Pick, D.H. Warren, and J.C. Hay. Sensory conﬂict in judgements of spatial direction. Percept. Psychophys., 6:203205, 1969. [2] D. H. Warren, R. B. Welch, and T. J. McCarthy. The role of visual-auditory ”compellingness” in the ventriloquism effect: implications for transitivity among the spatial senses. Percept Psychophys, 30(6):557– 64, 1981. [3] D. Alais and D. Burr. The ventriloquist effect results from near-optimal bimodal integration. Curr Biol, 14(3):257–62, 2004. [4] R. A. Jacobs. Optimal integration of texture and motion cues to depth. Vision Res, 39(21):3621–9, 1999. [5] R. J. van Beers, A. C. Sittig, and J. J. Gon. Integration of proprioceptive and visual position-information: An experimentally supported model. J Neurophysiol, 81(3):1355–64, 1999. [6] D. H. Warren and W. T. Cleaves. Visual-proprioceptive interaction under large amounts of conﬂict. J Exp Psychol, 90(2):206–14, 1971. [7] C. E. Jack and W. R. Thurlow. Effects of degree of visual association and angle of displacement on the ”ventriloquism” effect. Percept Mot Skills, 37(3):967–79, 1973. [8] G. H. Recanzone. Auditory inﬂuences on visual temporal rate perception. J Neurophysiol, 89(2):1078–93, 2003. [9] J. P. Bresciani, M. O. Ernst, K. Drewing, G. Bouyer, V. Maury, and A. Kheddar. Feeling what you hear: auditory signals can modulate tactile tap perception. Exp Brain Res, 162(2):172–80, 2005. 7 [10] R. Gepshtein, P. Leiderman, L. Genosar, and D. Huppert. Testing the three step excited state proton transfer model by the effect of an excess proton. J Phys Chem A Mol Spectrosc Kinet Environ Gen Theory, 109(42):9674–84, 2005. [11] L. Shams, W. J. Ma, and U. Beierholm. Sound-induced ﬂash illusion as an optimal percept. Neuroreport, 16(17):1923–7, 2005. [12] G Thomas. Experimental study of the inﬂuence of vision on sound localisation. J Exp Psychol, 28:167177, 1941. [13] W. R. Thurlow and C. E. Jack. Certain determinants of the ”ventriloquism effect”. Percept Mot Skills, 36(3):1171–84, 1973. [14] C.S. Choe, R. B. Welch, R.M. Gilford, and J.F. Juola. The ”ventriloquist effect”: visual dominance or response bias. Perception and Psychophysics, 18:55–60, 1975. [15] R. I. Bermant and R. B. Welch. Effect of degree of separation of visual-auditory stimulus and eye position upon spatial interaction of vision and audition. Percept Mot Skills, 42(43):487–93, 1976. [16] R. B. Welch and D. H. Warren. Immediate perceptual response to intersensory discrepancy. Psychol Bull, 88(3):638–67, 1980. [17] P. Bertelson and M. Radeau. Cross-modal bias and perceptual fusion with auditory-visual spatial discordance. Percept Psychophys, 29(6):578–84, 1981. [18] P. Bertelson, F. Pavani, E. Ladavas, J. Vroomen, and B. de Gelder. Ventriloquism in patients with unilateral visual neglect. Neuropsychologia, 38(12):1634–42, 2000. [19] D. A. Slutsky and G. H. Recanzone. Temporal and spatial dependency of the ventriloquism effect. Neuroreport, 12(1):7–10, 2001. [20] J. Lewald, W. H. Ehrenstein, and R. Guski. Spatio-temporal constraints for auditory–visual integration. Behav Brain Res, 121(1-2):69–79, 2001. [21] M. T. Wallace, G. E. Roberson, W. D. Hairston, B. E. Stein, J. W. Vaughan, and J. A. Schirillo. Unifying multisensory signals across time and space. Exp Brain Res, 158(2):252–8, 2004. [22] J. P. Bresciani, F. Dammeier, and M. O. Ernst. Vision and touch are automatically integrated for the perception of sequences of events. J Vis, 6(5):554–64, 2006. [23] N. W. Roach, J. Heron, and P. V. McGraw. Resolving multisensory conﬂict: a strategy for balancing the costs and beneﬁts of audio-visual integration. Proc Biol Sci, 273(1598):2159–68, 2006. [24] K. P. Kording and D. M. Wolpert. Bayesian decision theory in sensorimotor control. Trends Cogn Sci, 2006. 1364-6613 (Print) Journal article. [25] K.P. Kording, U. Beierholm, W.J. Ma, S. Quartz, J. Tenenbaum, and L. Shams. Causal inference in multisensory perception. PLoS ONE, 2(9):e943, 2007. [26] Z. Ghahramani. Computational and psychophysics of sensorimotor integration. PhD thesis, Massachusetts Institute of Technology, 1995. [27] D. C. Knill. Mixture models and the probabilistic structure of depth cues. Vision Res, 43(7):831–54, 2003. [28] D. C. Knill. Robust cue integration: A bayesian model and evidence from cue conﬂict studies with stereoscopic and ﬁgure cues to slant. Journal of Vision, 7(7):2–24. [29] W. J. Ma, J. M. Beck, P. E. Latham, and A. Pouget. Bayesian inference with probabilistic population codes. Nat Neurosci, 9(11):1432–8, 2006. 8

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