John Porrill

The cerebellar microcircuit as an adaptive filter: experimental and computational evidence

Initial investigations of the cerebellar microcircuit inspired the Marr–Albus theoretical framework of cerebellar function. We review recent developments in the experimental understanding of cerebellar microcircuit characteristics and in the computational analysis of Marr–Albus models. We conclude that many Marr–Albus models are in effect adaptive filters, and that evidence for symmetrical long-term potentiation and long-term depression, interneuron plasticity, silent parallel fibre synapses and recurrent mossy fibre connectivity is strikingly congruent with predictions from adaptive-filter models of cerebellar function. This congruence suggests that insights from adaptive-filter theory might help to address outstanding issues of cerebellar function, including both microcircuit processing and extra-cerebellar connectivity.

When is now? Perception of simultaneity

We address the following question: Is there a difference (D) between the amount of time for auditory and visual stimuli to be perceived? On each of 1000 trials, observers were presented with a light–sound pair, separated by a stimulus onset asynchrony (SOA) between–250 ms (sound first) and 250 ms. Observers indicated if the light–sound pair came on simultaneously by pressing one of two (yes or no) keys. The SOA most likely to yield affirmative responses was defined as the point of subjective simultaneity (PSS). PSS values were between–21 ms (i.e. sound 21ms before light) and 150 ms. Evidence is presented that each PSS is observer specific. In a second experiment, each observer was tested using two observerstimulus distances. The resultant PSS values are highly correlated (r = 0.954, p = 0.003) suggesting that each observers PSS is stable. PSS values were significantly affected by observer–stimulus distance, suggesting that observers do not take account of changes in distance on the resultant difference in arrival times of light and sound. The difference RTd in simple reaction time to single visual and auditory stimuli was also estimated; no evidence that RTd is observer specific or stable was found. The implications of these findings for the perception of multisensory stimuli are discussed.

Spatiotemporal Independent Component Analysis of Event-Related fMRI Data Using Skewed Probability Density Functions

We introduce two independent component analysis (ICA) methods, spatiotemporal ICA (stICA) and skew-ICA, and demonstrate the utility of these methods in analyzing synthetic and event-related fMRI data. First, stICA simultaneously maximizes statistical independence over both time and space. This contrasts with conventional ICA methods, which maximize independence either over time only or over space only; these methods often yield physically improbable solutions. Second, skew-ICA is based on the assumption that images have skewed probability density functions (pdfs), an assumption consistent with spatially localized regions of activity. In contrast, conventional ICA is based on the physiologically unrealistic assumption that images have symmetric pdfs. We combine stICA and skew-ICA, to form skew-stICA, and use it to analyze synthetic data and data from an event-related, left-right visual hemifield fMRI experiment. Results obtained with skew-stICA are superior to those of principal component analysis, spatial ICA (sICA), temporal ICA, stICA, and skew-sICA. We argue that skew-stICA works because it is based on physically realistic assumptions and that the potential of ICA can only be realized if such prior knowledge is incorporated into ICA methods.

Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter

Abstract The use of the Kaiman filter to find optimal fits to short sections of ellipse data, and to predict confidence envelopes to facilitate search for further ellipse data, is described. The extended Kaiman filter in its usual form is shown not to reduce the well known bias to high curvature involved in least squares ellipse fitting. This problem is overcome by developing a linear bias correction for the extended Kaiman filter. The estimate covariance is used to evaluate confidence envelopes for the fitted ellipse. Performance is shown on both real and synthetic data.

Stereopsis, vertical disparity and relief transformations.

The pattern of retinal binocular disparities acquired by a fixating visual system depends on both the depth structure of the scene and the viewing geometry. This paper treats the problem of interpreting the disparity pattern in terms of scene structure without relying on estimates of fixation position from eye movement control and proprioception mechanisms. We propose a sequential decomposition of this interpretation process into disparity correction, which is used to compute three-dimensional structure up to a relief transformation, and disparity normalization, which is used to resolve the relief ambiguity to obtain metric structure. We point out that the disparity normalization stage can often be omitted, since relief transformations preserve important properties such as depth ordering and coplanarity. Based on this framework we analyse three previously proposed computational models of disparity processing; the Mayhew and Longuet-Higgins model, the deformation model and the polar angle disparity model. We show how these models are related, and argue that none of them can account satisfactorily for available psychophysical data. We therefore propose an alternative model, regional disparity correction. Using this model we derive predictions for a number of experiments based on vertical disparity manipulations, and compare them to available experimental data. The paper is concluded with a summary and a discussion of the possible architectures and mechanisms underling stereopsis in the human visual system.

Curve matching and stereo calibration

Abstract The topological obstacles to the matching of smooth curves in stereo images are shown to occur at epipolar tangencies. Matching is possible when these tangencies satisfy certain projective constraints (the tangent lines form corresponding pencils) and metric contraints dependent on the camera geometry. Such points are good matching primitives, even when the image curves correspond to smooth surface profiles. An iterative scheme for improving camera calibration based on these results is derived, and performance demonstrated on real data.

Recurrent cerebellar architecture solves the motor-error problem

Current views of cerebellar function have been heavily influenced by the models of Marr and Albus, who suggested that the climbing fibre input to the cerebellum acts as a teaching signal for motor learning. It is commonly assumed that this teaching signal must be motor error (the difference between actual and correct motor command), but this approach requires complex neural structures to estimate unobservable motor error from its observed sensory consequences. We have proposed elsewhere a recurrent decorrelation control architecture in which Marr–Albus models learn without requiring motor error. Here, we prove convergence for this architecture and demonstrate important advantages for the modular control of systems with multiple degrees of freedom. These results are illustrated by modelling adaptive plant compensation for the three–dimensional vestibular ocular reflex. This provides a functional role for recurrent cerebellar connectivity, which may be a generic anatomical feature of projections between regions of cerebral and cerebellar cortex.

Decorrelation control by the cerebellum achieves oculomotor plant compensation in simulated vestibulo-ocular reflex

We introduce decorrelation control as a candidate algorithm for the cerebellar microcircuit and demonstrate its utility for oculomotor plant compensation in a linear model of the vestibulo–ocular reflex (VOR). Using an adaptive–filter representation of cerebellar cortex and an anti–Hebbian learning rule, the algorithm learnt to compensate for the oculomotor plant by minimizing correlations between a predictor variable (eye–movement command) and a target variable (retinal slip), without requiring a motor–error signal. Because it also provides an estimate of the unpredicted component of the target variable, decorrelation control can simplify both motor coordination and sensory acquisition. It thus unifies motor and sensory cerebellar functions.

Active region models for segmenting textures and colours

This paper describes a new region-growing method that uses a closed snake driven by a pressure force that is a function of the statistical characteristics of image data. This statistical snake expands until its elements encounter pixels that lie outside user-defined limits relative to a seed region; when these limits are violated the pressure force is reversed to make the model contract. Tension and stiffness forces keep the boundary of the region model smooth, and a repulsion force prevents self-intersection. Boundary elements can be inserted and deleted in response to complexity changes, and the tension and stiffness parameters can be adjusted to preserve the energy balance of the changing model. Statistical snakes have been used to segment a variety of composite textures; they have also been used to track rigid coloured regions in real-time video by modifying the energy formalism to produce affine motion

Statistical snakes: active region models

This paper describes a new region-growing technique that uses a closed snake driven by a pressure force that is a function of the statistical characteristics of image data. This statistical snake expands until its elements encounter pixels that lie outside user-defined limits relative to a seed region; when these limits are violated the pressure force is reversed to make the model contract. Tension and stiffness forces keep the boundary of the region model smooth, and a repulsion force prevents self-intersection. Boundary elements can be added and removed in response to complexity changes, and the tension, stiffness and pressure parameters can be adjusted to preserve the energy balance of the changing model. Statistical snakes have been used to segment a variety of images including composite textures and NMR data volumes.