Charles H. Anderson’s research while affiliated with Washington University in St. Louis and other places

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Publications (50)


Does the brain de-jitter retinal images?
  • Article

November 2010

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26 Reads

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2 Citations

Proceedings of the National Academy of Sciences

Bruno A Olshausen

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Charles H Anderson

As anyone who has taken a photograph with shaky hands can attest, camera movement creates image blur. Because photosensors must integrate over a finite interval to acquire a noise-free image, any motion that occurs during that interval will blur over the spatial details of an object by the amount of space traversed (Fig. 1). This simple fact creates headaches for engineers designing scientific imaging systems and commercial digital cameras. It is also a problem that the nervous system of any animal with moving eyes—from jumping spiders to humans—must deal with in processing images, but little is currently known about how they do it. In PNAS, Burak et al. (1) propose a potential neural mechanism for solving this problem in the human visual system.


Figure S1
  • Data
  • File available

November 2009

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9 Reads

(A) Linear output of the gain-modulated gammatone filter (measured as root-mean-square, RMS), as a function of average binaural level of a broadband noise. (B) Cross-correlation vector as a function of average binaural level. (C) Tolerance to ILD of the cross-correlation vector. (0.17 MB PDF)

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Figure 1.  Input-Output response of an ICx neuron.
The mapping from the average membrane potential of an ICx neuron over the presentation of a sound stimulus to the number of spikes produced is fit with a power function (dotted line) and a threshold-sigmoid function (solid line). The threshold-sigmoid function is used as the input-output nonlinearity for model ICcl and ICx neurons.
Figure 1. Input-Output response of an ICx neuron. The mapping from the average membrane potential of an ICx neuron over the presentation of a sound stimulus to the number of spikes produced is fit with a power function (dotted line) and a threshold-sigmoid function (solid line). The threshold-sigmoid function is used as the input-output nonlinearity for model ICcl and ICx neurons. doi:10.1371/journal.pone.0008015.g001 
Figure 2.  Block diagram of model.
The initial components of the model extract time-dependent localization cues using a running cross-correlation, denoted x, and the interaural level difference, denoted z, from auditory input signals. A network model of spiking neurons uses these cues, along with a measure of stimulus intensity given by an energy envelope (y), as input to neurons in the lateral shell of the central nucleus of the inferior colliculus (ICcl), which converge on the external nucleus of the inferior colliculus (ICx). ICcl neurons add a function of the running cross-correlation with another function of the interaural level difference and energy envelope and pass the result through a spiking nonlinearity to produce the probability of spiking. The two central assumptions of the ICx model are, first, that frequency integration at the subthreshold level is linear [29] and, second, that multiplication between ITD- and ILD-dependent signals occurs only within frequency channels. Connection weights between ICcl neurons and the target ICx neuron are selected to enforce these assumptions.
Figure 3.  Accuracy of the multiplicative model as a function of spiking threshold in ICcl.
The relative accuracy of the additive and multiplicative models of ITD-ILD interaction, summarized by the correlation between the multiplicative fit and the response (A) and the multiplication index (B), depends systematically on the difference between the threshold value of the input-output curve and the center of the dynamic range of the neuron's membrane potential response to ITD and ILD, denoted as Δthreshold. Δthreshold is illustrated for positive (C) and negative (D) values. (E,G,I) ITD-ILD response matrices of model ICcl neurons with different thresholds. (F,H,J) Experimentally measured ITD-ILD response matrices [7].
Figure 3. Accuracy of the multiplicative model as a function of spiking threshold in ICcl. The relative accuracy of the additive and multiplicative models of ITD-ILD interaction, summarized by the correlation between the multiplicative fit and the response (A) and the multiplication index (B), depends systematically on the difference between the threshold value of the input-output curve and the center of the dynamic range of the neuron's membrane potential response to ITD and ILD, denoted as D threshold. D threshold is illustrated for positive (C) and negative (D) values. (E,G,I) ITD-ILD response matrices of model ICcl neurons with different thresholds. (F,H,J) Experimentally measured ITD-ILD response matrices [7]. doi:10.1371/journal.pone.0008015.g003 

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Multiplicative Auditory Spatial Receptive Fields Created by a Hierarchy of Population Codes

November 2009

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156 Reads

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26 Citations

A multiplicative combination of tuning to interaural time difference (ITD) and interaural level difference (ILD) contributes to the generation of spatially selective auditory neurons in the owl's midbrain. Previous analyses of multiplicative responses in the owl have not taken into consideration the frequency-dependence of ITD and ILD cues that occur under natural listening conditions. Here, we present a model for the responses of ITD- and ILD-sensitive neurons in the barn owl's inferior colliculus which satisfies constraints raised by experimental data on frequency convergence, multiplicative interaction of ITD and ILD, and response properties of afferent neurons. We propose that multiplication between ITD- and ILD-dependent signals occurs only within frequency channels and that frequency integration occurs using a linear-threshold mechanism. The model reproduces the experimentally observed nonlinear responses to ITD and ILD in the inferior colliculus, with greater accuracy than previous models. We show that linear-threshold frequency integration allows the system to represent multiple sound sources with natural sound localization cues, whereas multiplicative frequency integration does not. Nonlinear responses in the owl's inferior colliculus can thus be generated using a combination of cellular and network mechanisms, showing that multiple elements of previous theories can be combined in a single system.


Figure 1 of 1
Time and Frequency Characteristics of Purkinje Cell Complex Spikes in the Awake Monkey Performing a Nonperiodic Task

June 2008

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58 Reads

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12 Citations

Journal of Neurophysiology

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Scott A Norris

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[...]

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W Thomas Thach

A number of studies have been interpreted to support the view that the inferior olive climbing fibers send periodic signals to the cerebellum to time and pace behavior. In a direct test of this hypothesis in macaques performing nonperiodic tasks, we analyzed continuous recordings of complex spikes from the lateral cerebellar hemisphere. We found no periodicity outside of a 100-ms relative refractory period.


Solving the Problem of Negative Synaptic Weights in Cortical Models

June 2008

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55 Reads

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87 Citations

In cortical neural networks, connections from a given neuron are either inhibitory or excitatory but not both. This constraint is often ignored by theoreticians who build models of these systems. There is currently no general solution to the problem of converting such unrealistic network models into biologically plausible models that respect this constraint. We demonstrate a constructive transformation of models that solves this problem for both feedforward and dynamic recurrent networks. The resulting models give a close approximation to the original network functions and temporal dynamics of the system, and they are biologically plausible. More precisely, we identify a general form for the solution to this problem. As a result, we also describe how the precise solution for a given cortical network can be determined empirically.



A Logarithmic, Scale-Invariant Representation of Speed in Macaque Middle Temporal Area Accounts for Speed Discrimination Performance

November 2005

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255 Reads

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169 Citations

The Journal of Neuroscience : The Official Journal of the Society for Neuroscience

Human speed discrimination thresholds follow Weber's law over a large range of reference (i.e., pedestal) speeds, that is, the just-noticeable-difference in speed scales in proportion to the reference speed. We analyzed the neural representation of speed information in macaque middle temporal visual area (MT) to determine whether this representation can account for the basic form of psychophysical data. Based on theoretical considerations, we hypothesized: (1) that the speed tuning curves of MT neurons should be bell-shaped (Gaussian) as a function of the logarithm of speed, (2) that the set of speed-tuning curves should be approximately scale-invariant, (3) that the distribution of speed preferences should be approximately uniform in log speed, and (4) that response variability should be independent of speed preference. Our quantitative analysis of data from 501 MT neurons shows that the neural representation of speed approximately obeys these constraints, with modest deviations particularly at slow speeds. We then used the MT data to predict how speed discrimination thresholds should depend on pedestal speed. The shape of this prediction matches very closely to that of human psychophysical data, accounting for constant Weber fractions over a large range of intermediate speeds as well as a marked departure from Weber's law at slow speeds. Moreover, we show that deviations of the MT representation from the above constraints are important for predicting how psychophysical thresholds depart from Weber's law at slow speeds. These findings support the notion that a logarithmic, approximately scale-invariant representation of speed in area MT limits perceptual speed discrimination.


A systems and neurobiological model of nucleus angularis and nucleus laminaris in the barn owl

October 2004

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7 Reads

The Journal of the Acoustical Society of America

The representation of binaural sound localization cues was investigated in a model of the barn owl’s auditory nerve, nucleus angularis (NA), nucleus magnocellularis (NM), nucleus laminaris (NL), and superior olivary nucleus (SON) using spiking leaky integrate and fire neurons. A phenomenological model of the barn owl’s auditory‐nerve spike response was created to reproduce responses to tonal stimuli and exhibit two‐tone rate suppression effects. The representation of stimulus level by NA was investigated by decoding the envelope of the input signal from populations of NA model neurons where the envelope was defined as in a previous computational model of sound localization in the barn owl [B.J. Fischer and C.H. Anderson, Adv. NIPS 16 (2004)]. Simulations demonstrated that inclusion of NA neurons with type IV responses increased the accuracy of the representation of the stimulus envelope. The effect of inhibition on the output of the population of NL model neurons was investigated and compared to a cross‐correlation model. The output of the model SON provides inhibitory feedback to ipsilateral NA, NM, and NL model neurons. Simulations demonstrated that inclusion of inhibition of NL neurons by SON output increased peak–trough differences in ITD tuning curves.


A computational model of sound localization in the barn owl

June 2004

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15 Reads

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1 Citation

Neurocomputing

We model the representation of auditory space in the barn owl as a posterior probability density function over location variables given cues extracted from the auditory input signals. Binaural disparity cues are introduced to the input signals through the use of head, related transfer functions. The cue extraction process is based on the extraction of temporal and intensity information in parallel pathways. Inferring locations from auditory cues relies on stimulus invariance properties of the computed location cues.


A Probabilistic Model of Auditory Space

March 2004

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8 Reads

The barn owl is a nocturnal hunter, capable of capturing prey using auditory information alone [1]. The neural basis for this localization behavior is the existence of auditory neurons with spatial receptive fields [2]. We provide a mathematical description of the operations performed on auditory input signals by the barn owl that facilitate the creation of a representation of auditory space. To develop our model, we first formulate the sound localization problem solved by the barn owl as a statistical estimation problem. The implementation of the solution is constrained by the known neurobiology.


Citations (32)


... In [7], the filtering is biased either in the vertical and horizontal directions or along the diagonal directions-with the latter chosen as giving better performance. A visual-based com- parison between the two nonlinear filter performances, was pre- sented in [4] demonstrating slight differences, with less aliasing effects evident using the isotropic Laplacian filter. ...

Reference:

Image enhancement by nonlinear extrapolation in frequency space
Image enhancement by nonlinear extrapolation in frequency space
  • Citing Conference Paper
  • February 1994

... From the partial assays of parafoveal neurons currently available, it would seem there is an over-abundance of neurons tuned to low spatial-frequencies as compared to the model (DeValois et al., 1982; Parker & Hawken, 1988; van Hateren and van der Schaaf, 1998). This discrepancy could be due to biases in sampling, or because the model is currently ignoring many other stimulus dimensions that the cortex also cares about, such as color, disparity, etc. (Olshausen & Anderson, 1995). In addition, real neurons have a certain level of precision with which they can code information in amplitude and time, whereas in the model there is no limit in precision imposed upon the coefficient amplitudes (i.e., they have essentially infinite precision in amplitude). ...

A Model of the Spatial-Frequency Organization in Primate Striate Cortex
  • Citing Chapter
  • January 1995

... This is achieved by moving the center of the DVS integrated into the Speck device mounted on the FLIR PTU to foveate towards the salient point (see Figure 1). To describe this feedback control system, we use the Neural Engineering Framework (NEF) [23]. Since the camera is mounted on a PTU, we can treat the axis-aligned errors and controls separately. ...

Neural Engineering: Computation, Representation and Dynamics in Neurobiological Systems
  • Citing Book
  • January 2003

... Over the last few years, the wavelet transformation has been used successfully in many compression algorithms [1][8] [14]. The combination of multi resolution analysis and error correction schemes has been present-ed by Rakshit and Anderson, using an overcomplete pyramid image representation which shares many properties with the WT [12]. The paper is structured as follows: Section 2 describes the overall architecture and the design goals that led to the presented implementation. ...

Error correction in images using overcomplete pyramid representations
  • Citing Article
  • October 1994

Proceedings of SPIE - The International Society for Optical Engineering

... Alternatively, Anderson [1994] assumes that the true density is somehow known (strong assumption) and proposed a projection approach that aims to minimise the reconstruction error of the density functions. Given a density function p(z) and basis ψ(z), let R(r) = 1 the neural activity be the projection of p(z) on some functions, i.e. for all m ∈ [1, . . . ...

Basic elements of biological computional systems
  • Citing Article
  • April 1994

International Journal of Modern Physics C

... De manière générale, cette approche permet des analyses plus fines des points communs ainsi que des différences individuelles dans l'organisation fonctionnelle du cortex cérébral des primates. Cette reconstruction surfacique est basée sur l'algorithme SureFit (Surface Reconstruction by Filtering and Intensity Transformations) fourni dans le logiciel CARET et permet de générer rapidement des reconstructions de surface précises du cortex cérébral à partir de données d'IRM structurelles(Drury, Van Essen, et Anderson 2000). Ces surfaces peuvent alors servir à la visualisation des données préalablement analysées dans le volume mais permettent également d'analyser plus directement les données brutes dans la surface.Traitement des données en IRMf1. ...

SureFit: Software for segmenting the cerebral cortex and generating surface reconstructions
  • Citing Article
  • May 2000

NeuroImage

... In these experiments eye-movements were eliminated by instructing subjects to fixate at the center fo the screen and observe the stimulus using their peripheral vision [4,5]. However, it has been argued that the projecting to the peripheral part of the visual field may have led to a poor resolution in percieving local details than global structures [6][7][8] because peripheral vision has a lower acuity. ...

Information processing strategies and pathways in the primate retina and visual cortex
  • Citing Article
  • January 1990

... However, recent evidence suggests that this transformation process could be a gradual transformation within the body schema map(s) of the perspective taker (Kessler and Rutherford, 2010;Kessler and Thomson, 2010;Kessler and Wang, 2012) that can be described as a shift within basis function networks. Kessler (2000) proposed a network model that used shifter circuits (Van Essen and Anderson, 1990) to shift the egocentric FOR orientation via intermediate orientations into the target orientation congruent to a simulated body rotation (Kessler and Thomson, 2010), which would be equivalent to the use of sensorimotor basis function networks in a "simulation mode". That is, the anticipated sensorimotor and visuo-spatial outcomes are generated within the (individualistic) operational space by gradual orientation shifts without actually executing the usually associated movement. ...

Reference frames and dynamic remapping processes in vision
  • Citing Article
  • January 1993

... There are two primary models for simulating nerve impulse activity. The Hodgkin-Huxley model describes various ionic movements within neurons [124][125][126]. Alternatively, mathematical models such as the integrate-and-fire (IF) and the leaky integrate-and-fire (LIF) models describe changes in membrane potentials without considering ion diffusion properties [127,128]. ...

Neural Engineering (Computational Neuroscience Series): Computational, Representation, and Dynamics in Neurobiological Systems
  • Citing Article