Perceptual Coherence : Hearing and Seeing

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Characteristics of Auditory and Visual Scenes 123 that are tuned to slightly different directions of movement, and the same sort of analysis could extend to any sensory property (e.g., auditory localization or frequency identification). The overall firing rate of each cell is assumed to arise from the sum of the deterministic component due to the direction of movement and the noisy random component that is assumed to vary independently from instance to instance. A Gaussian distribution models the deterministic component of the cell’s response, so that each cell will respond maximally to one direction and fire at lower rates in response to other directions. Across the population of cells, all directions would be represented roughly equally. Harper and McAlpine (2004) pointed out that for auditory localization, the optimal population distribution depends on head size and sound frequency; it may not be uniform. If there were no noise in the firing rate, then the output of every cell would provide an error-free estimate of the movement direction (actually two directions, because the firing rate is assumed to be a symmetric Gaussian curve; see figure 3.6). But given the inherent noise and variability in the firing rate of a single cell, it is impossible to separate the true direction part from the noise part. Any movement direction will yield a distribution of responses, one from each receptor. However, using the firing pattern across the population of cells can minimize the error. There are several alternative ways to estimate the direction: 1. Choose the receptor with the highest firing rate. In Bayesian theory, this is equivalent to finding the maximum likelihood function, Pr(response � stimulus direction). However, picking the direction based on the receptor with the highest firing rate would be prone to error, given the variability of the responses. 2. Choose the direction with the highest posterior probability, Pr(stimulus direction � response). In Bayesian theory, this is equivalent to multiplying the likelihood function by the prior probability of that direction. The posterior probabilities would be calculated for each receptor separately. If all directions are equally probable, then the maximum likelihood and posterior probabilities are equal. This solution would still be prone to error. 3. Derive a function based on the firing rates of all the individual cells, and then shift the function laterally to find the best fit. Two solutions are shown in figure 3.6C and 3.6D. The first is to fit a cosine function (population vector coding) at the peak of the response distribution, (C); the second is to find the template derived from the noiseless tuning functions shown in (A) that best fit the response distribution, for example, at the peak of the response distribution as in (D). The peak position corresponds to the maximum likehood estimate (Pouget et al., 2000).
124 Perceptual Coherence Figure 3.6. Population coding: The responses from a set of sensory cells with slightly different sensitivities are combined to yield a response distribution. Panel (A) illustrates direction-tuning curves for a set of 15 bell-shaped symmetric neurons. The outputs of 64 such cells to an object moving at −40° are shown in (B). This output is composed of two parts: the deterministic component shown in (A) and an independent error for each neuron. This distribution in turn is used in some way to calculate the most probable input. In Panel (C), the best fitting cosine function is fitted to the output distribution. The peak of the cosine is the estimate of the motion direction. In Panel (D), the predicted response distribution based on the individual error-free tuning curves in (A) is calculated for the set of possible directions. The predicted distribution that best fits the obtained neural response pattern is assumed to be the estimate of the movement direction. This is the maximum likelihood estimate, Pr(response � stimulus direction). From “Information Processing With Population Codes,” by A. Pouget, P. Dayan, and R. Zemel, 2000, Nature Reviews: Neuroscience, 1, 125–132. Copyright 2000 by the Nature Publishing Group. Reprinted with permission. There is an interesting parallel between the coding in the individual monopole cells and the coding in populations. In both cases, information mainly is carried by the steep part of the response curve where there is a large change in the firing rate for small changes in the stimulus value (i.e., the highest derivative). At the peaks of the response curves where the receptors
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PERCEPTUAL COHERENCE
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Perceptual Coherence Hearing and Se
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To My Family, My Parents, and the B
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Preface The purpose of this book is
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Preface ix intertwined with my own
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Contents 1. Basic Concepts 3 2. Tra
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PERCEPTUAL COHERENCE
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1 Basic Concepts In the beginning G
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Basic Concepts 5 sources moving in
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even though its appearance changes.
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sources. A single sound source is t
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straight line parallel to the actua
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continuous sound. The correspondenc
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Basic Concepts 15 overall uncertain
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problem. The “snapshots” in spa
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segments at different orientations.
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in amplitude across time (analogous
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Basic Concepts 23 visual experience
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we would expect the correlation to
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Transformation of Sensory Informati
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Table 2.1 Derivation of the Recepti
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Figure 2.7. Continued
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Page 86 and 87: Transformation of Sensory Informati
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(A) (B) (C) The Transition Between
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The Transition Between Noise and St
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(A) (B) Warbleness The Transition B
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2000 Hz with a single action potent
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The same problem of the multiplicit
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order to create the appearance of s
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Perception of Motion 199 Figure 5.2
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Perception of Motion 203 together.
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Perception of Motion 205 (The two f
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again, two perceptions can result a
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Perception of Motion 211 notes of t
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Perception of Motion 213 Braddick (
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larger arrays and Baddeley and Tirp
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Perception of Motion 217 the judgme
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Perception of Motion 219 one color
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To review, neurons sensitive to mot
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Transparency aftereffects do occur
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Perception of Motion 225 stimuli, t
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Perception of Motion 231 perception
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Perception of Motion 237 same direc
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Time 1, Tone 1 is turned off, at Ti
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6 Gain Control and External and Int
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a signal-to-noise ratio), and Barlo
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Gain Control and External and Inter
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Suppose we have a background that h
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R Gain Control and External and Int
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Makous (1997) pointed out how diffi
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contrast that defines the boundarie
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per Second Figure 6.10. Continued G
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ane was linear, the higher sound pr
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(C. D. Geisler, 1998; C. D. Geisler
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noise visual field. 4 The S + N inp
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B. Murray, Bennett, and Sekular (20
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The authors proposed that the four
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Efficiency and Noise in Auditory Pr
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etween samples). Spiegel and Green
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In sum, the masking release is grea
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The Perception of Quality: Visual C
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Visual Worlds Modeling the Light Re
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Indirect Illumination Causing Specu
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of an object but also require the c
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assumed, so that the surface irradi
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Relative Power of Basis Functions S
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that the reflectance of the test co
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amount of light transmitted through
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light reflected by all surfaces in
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magenta to white). Then Bloj et al.
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Why is there opponent processing? O
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8 The Perception of Quality: Audito
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exists at several levels: (a) descr
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The Perception of Quality: Auditory
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mode is proportional to the relativ
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The overall result is that the rela
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obvious. The tension on the vocal c
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(termed the amplitude envelopes) ar
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obviously misplaced). The majority
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Pastore (1991) investigated whether
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experience. Erickson (2003) found t
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Rhythmic patterning usually gives i
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Let me summarize at this point. The
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the oddball note to be the one most
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9 Auditory and Visual Segmentation
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Auditory and Visual Segmentation 37
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processes (e.g., basilar membrane v
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same time, the difficulty of detect
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elease (discussed in chapter 6) dem
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(A) Target Rhythm Target + Masking
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to grouping by perceived position d
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4. Convexity: Convex figures usuall
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filter inferred from the background
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Jackson (1953) found that the sound
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a speaking face is located in front
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was high, then the resolution of th
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Listeners were more likely to repor
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10 Summing Up Perceiving is the con
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Summing Up 423 course of the stimul
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References Adelson, E. H. (1982). S
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References 427 Bermant, R. I., & We
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References 429 Crawford, B. H. (194
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References 431 Feldman, J., & Singh
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References 433 and male voices in t
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References 435 Isabelle, S. K., & C
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References 437 Laughlin, S. B. (200
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References 439 McAdams, S., Winsber
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References 441 Pittinger, J. B., Sh
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References 443 Shamma, S. (2001). O
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References 445 Troost, J. M. (1998)
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References 447 Welch, R. B. (1999).
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Index Boldfaced entries refer to ci
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Barbour, D. L., 83, 367, 426 Barlow
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Color reflectance 1/f c amplitude f
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Figure-ground auditory, 373, 421 in
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Hallikainen, J., 304, 440 Handel, S
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K-order statistics. See Visual text
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separation of things, 5 See also Pe
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Recanzone, G. H., 409-412, 441, 443
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Stream segregation default assumpti
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vibration frequencies of air masses
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Wavelet analysis. See Sparse coding
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