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PubMed1991

Inverse perspective mapping simplifies optical flow computation and obstacle detection.

We present a scheme for obstacle detection from optical flow which is based on strategies of biological information processing. Optical flow is established by a local "voting" (non-maximum suppression) over the outputs of correlation-type motion detectors similar to those found in the fly visual system. The computational theory of obstacle detection is discussed in terms of space-variances of the motion field. An efficient mechanism for the detection of disturbances in the expected motion field is based on "inverse perspective mapping", i.e., a coordinate transform or retinotopic mapping applied to the image. It turns out that besides obstacle detection, inverse perspective mapping has additional advantages for regularizing optical flow algorithms. Psychophysical evidence for body-scaled obstacle detection and related neurophysiological results are discussed.

Algorithms↗
PubMed1991

A self-organizing multiple-view representation of 3D objects.

We explore representation of 3D objects in which several distinct 2D views are stored for each object. We demonstrate the ability of a two-layer network of thresholded summation units to support such representations. Using unsupervised Hebbian relaxation, the network learned to recognize ten objects from different viewpoints. The training process led to the emergence of compact representations of the specific input views. When tested on novel views of the same objects, the network exhibited a substantial generalization capability. In simulated psychophysical experiments, the network's behavior was qualitatively similar to that of human subjects.

Cybernetics↗
PubMed1991

On mental rotations and cortical activity patterns. A linear representation is still wanted.

Carlton (1988) has proposed an attractive hypothesis to link perceived visual images to brain electrical patterns via a linear representation of the Euclidean group onto an appropriate functional space. We show that the construction she proposes is (1) biologically restrictive, and (2) cannot be completed in the desired way. We conclude by presenting other possible means to pursue Carlton's approach.

Depth Perception↗
PubMed1994

A model of synchronization of motor acts to a stimulus sequence. I. Timing and error corrections.

A closed-loop timing model is proposed that accounts for several phenomena observed in tasks which require production of a sequence of motor acts in synchrony with a sequence of stimuli. In contrast to the previous models, variables available to the central nervous system of a subject (internal variables) and externally measurable variables are distinguished, and several physiologically justifiable internal variables are included. The model assumes the existence of (a) an internal timekeeper producing a reference interval that is used in a motor-control unit for timing of the next motor command; (b) an intrinsic (subjective) synchrony that relies on some a posteriori (feedback) information about the already executed onset of the motor act. A two-way error-corrective mechanism is hypothesized: (1) period (inverted frequency) corrections--the reference interval (period) is set at the beginning of the task according to the interstimulus-onset interval(s) and later corrected for differences between its duration and the actual duration of s; (2) phase corrections--internal synchronization errors (i.e., time gaps between the central temporal availability of internal representations of stimuli and of some feedback aspect of responses) are corrected for directly in the motor-control unit. Objectively measured systematic asynchrony of responses and stimuli is determined by the internal delays in information transduction. Finally, the model is used for making predictions of a subject's performance in some other experimental settings of the synchronization task.

Acoustic Stimulation↗
PubMed1994

A model of synchronization of motor acts to a stimulus sequence. II. Stability analysis, error estimation and simulations.

In Part I (Mates 1994), a linear model of timing and error-corrections was constructed that aims at an explanation of the mechanisms underlying a subject's performance in an experimental paradigm, in which the task is to synchronize a sequence of motor acts to a sequence of stimuli. The model consists of two error-corrective mechanisms: (1) corrections of period (inverted frequency) of the sequence of responses; (2) corrections of phase shift of that sequence (synchronization error). In this paper, the influence of the physiologically justifiable model variables and of initial conditions on the steady-state response sequence as well as the stability of performance of the model are analyzed. The model is stable for error-correction gains in the range from 0 to 2. Comparison with known empirical data supports the assumption that reasonable values are less than 1. Furthermore, an alternative to the basic linear model is introduced in which the possible character of the process of subjective acquisition of the synchronization error is discussed. On the basis of findings from other experimental paradigms (fusion and order threshold) it can be assumed that the subjective estimate is a nonlinear function of the difference between the temporal central availability of internal representations of the stimulus and response-feedback events. Some other known synchronization data are simulated by the nonlinear modification of the model in this paper. A good fit of the simulation results achieved further justifies the model structure proposed. Finally, the possible effect of the subjective synchronization-error estimation on empirical data is discussed.

Humans↗
PubMed1992

The parameter identification problem for the somatic shunt model.

The somatic shunt model, a generalized version of the Rall equivalent cylinder model, is used commonly to describe the passive electrotonic properties of neurons. Procedures for determining the parameters of the somatic shunt model that best describe a given neuron typically rely on the response of the cell to a small step of hyperpolarizing current injected by an intrasomatic recording electrode. In this study it is shown that the problem of estimating model parameters for the somatic shunt model using physiological data is ill-posed, in that very small errors in measured data can lead to large and unpredictable errors in parameter estimates. If the somatic shunt is assumed to be a real property of the intact neuron, the effects of these errors are not severe when predicting EPSP waveshapes resulting from synaptic input at a given location. However, if the somatic shunt is assumed to be a consequence of a leakage pathway around the recording electrode, and a correction for the shunt is applied, then the instability of the inverse problem can introduce large errors in estimates of EPSP waveshape as a function of synaptic location in the intact cell. Morphological constraints can be used to improve the accuracy of the inversion procedure in terms of both parameter estimates and predicted EPSP responses.

Mathematics↗
PubMed1989

Perceptual spatial frequency--orientation surface: psychophysics and line element theory.

We have investigated the discriminability of gratings which simultaneously vary in spatial frequency and orientation. Thirteen and nine reference gratings were used with two observers, and bivariate discrimination probability surfaces were determined around each grating. These data were then fitted to a general bivariate Gaussian function. The results clearly demonstrate local separability in this log frequency and orientation discrimination domain. Our results also show that the factor contributing most to the non-Euclidean nature of such frequency/orientation discrimination is orientation anisotropia, although we also find some evidence for smaller changes in the associated Riemannian line-element at different frequency ranges. These results cast doubt upon claims for a "pseudo line-element" for frequency discrimination based upon the nonlinear outputs of a fixed set of detectors.

Discrimination, Psychological↗
PubMed1991

Coverage and the design of striate cortex.

Hubel and Wiesel (1977) suggested that ocular dominance and orientation columns in the macaque monkey striate cortex might be bands of uniform width that intersected orthogonally. They pointed out that if this were the case, there would be an equal allocation of cells of different orientation preference to each eye and to each point in visual space. However, orientation and ocular dominance columns have a more complex structural organization than is implied by this model: for example, iso-orientation domains do not intersect ocular dominance stripes at right angles and the two columnar systems have different periodicities. This raises the question as to how well the striate cortex manages to allocate equal numbers of neurons of different orientation preference to each eye and to each region of visual space, a factor referred to here as coverage. This paper defines a measure of uniformity of coverage, c', and investigates its dependence on several different parameters of columnar organisation. Calculations were done first using a simplified one-dimensional model of orientation and ocular dominance columns and were then repeated using more realistic two-dimensional models, generated with the algorithms described in the preceding paper (Swindale 1991). Factors investigated include the relative periodicities of the two columnar systems, the size of the cortical point image, the width of orientation tuning curves, whether columns are spatially anisotropic or not, and the role of the structural relationships between columns described by Blasdel and Salama (1986). The results demonstrate that coverage is most uniform when orientation hypercolumns are about half the size of ocular dominance hypercolumns. Coverage is most uneven when the hypercolumns are the same size, unless they are related in the way described by Blasdel and Salama, in which case coverage gets only slightly worse as the size ratio (ori/od) increases above 0.5. The minimum diameter of cortical point image that ensures reasonably uniform coverage is about twice the size of an ocular dominance hypercolumn i.e. about 1.5-2.0 mm.

Animals↗
PubMed1988

Pattern recognition and associative memory as dynamical processes in a synergetic system. I. Translational invariance, selective attention, and decomposition of scenes.

We consider a model for associative memory and pattern recognition which was devised by Haken (1987b). This model treats the activity of the neurons as continuous variables and exploits an analogy with pattern formation in synergetic systems. The capability of such a system to act as associative memory is demonstrated by the reconstruction of faces which are partially offered to the system, and which are restored by the corresponding dynamical process. We demonstrate how this model can be cast into a form which is translation invariant and how partially hidden faces in scenes can be recognized by means of the control of attention parameters of specific patterns.

Cybernetics↗
PubMed1991

Optimising synaptic learning rules in linear associative memories.

Associative matrix memories with real-valued synapses have been studied in many incarnations. We consider how the signal/noise ratio for associations depends on the form of the learning rule, and we show that a covariance rule is optimal. Two other rules, which have been suggested in the neurobiology literature, are asymptotically optimal in the limit of sparse coding. The results appear to contradict a line of reasoning particularly prevalent in the physics community. It turns out that the apparent conflict is due to the adoption of different underlying models. Ironically, they perform identically at their co-incident optima. We give details of the mathematical results, and discuss some other possible derivations and definitions of the signal/noise ratio.

Animals↗
PubMed1996

Recognition-by-parts: a computational approach to human learning and generalization of shapes.

In this paper human pattern recognition is modeled in terms of how human observers learn to describe patterns in terms of their perceived parts, their unary (part) and binary (relational) attributes and the way in which such attribute states "evidence' different classes of shapes. This approach, originally developed in the area of computer vision, is concerned with algorithms which enable the learning of shape descriptions from examples and the classification of new data (generalization) efficiently and accurately. An object in such an "evidence-based' system is represented by a set of rules, where each rule provides a certain amount of evidence for each object class in the database. The accumulated class evidence over all activated rules can then be used to determine the classification probability. We have examined how well this model reflects human perception by training observers to classify compound Gabor patterns and then testing them with versions of such patterns which were segmented (gray-level transformed) versions of the original training set. If the observers were to construct rules to define each pattern class in terms of perceived parts and their relations, then it should be expected that classification performance would generalize to these new patterns from the original set. Results confirm this hypothesis and the specific feature extraction, learning and rule generation model used to predict performance.

Attention↗
PubMed1991

Sequential configuration model for firing patterns in local neural networks.

This paper presents a sequential configuration model to represent the coordinated firing patterns of memory traces in groups of neurons in local networks. Computer simulations are used to study the dynamic properties of memory traces selectively retrieved from networks in which multiple memory traces have been embedded according to the sequential configuration model. Distinct memory traces which utilize the same neurons, but differ only in temporal sequencing are selectively retrievable. Firing patterns of constituent neurons of retrieved memory traces exhibit the main properties of neurons observed in multi microelectrode recordings. The paper shows how to adjust relative synaptic weightings so as to control the disruptive influences of cross-talk in multipy-embedded networks. The theoretical distinction between (primarily anatomical) beds and (primarily physiological) realizations underlines the fundamentally stochastic nature of network firing patterns, and allows the definition of 4 degrees of clarity of retrieved memory traces.

Animals↗
PubMed1991

Cross-talk theory of memory capacity in neural networks.

The present paper presents a theory for the mechanics of cross-talk among constituent neurons in networks in which multiple memory traces have been embedded, and develops criteria for memory capacity based on the disruptive influences of this cross-talk. The theory is based on interconnection patterns defined by the sequential configuration model of dynamic firing patterns. The theory accurately predicts the memory capacities observed in computer simulated nets, and predicts that cortical-like modules should be able to store up to about 300-900 selectively retrievable memory traces before disruption by cross-talk is likely. It also predicts that the cortex may has designed itself for modules of 30,000 neurons to at least in part to optimize memory capacity.

Animals↗
PubMed1991

Symbolic grouping versus simple cell models.

The apparent line-like structure in dot patterns derives substantially from the orientation defined by pairings of adjacent dots. Two alternative models have been proposed for making these pairings, one in which the individual dots are treated as discrete grouping tokens, and the second in which the pairing orientation derives from spatial summation by simple cell receptive fields. Contradictory evidence has been found both directly in support of, and directly against, both models. Much of the debate about these two models has hinged on the degree of linearity of summation expected in the simple cell model. Recent neurophysiological evidence changes the balance of the debate, invalidating certain earlier arguments based on linearity and providing a model way of showing that simple cells do indeed play a major, but not necessarily exclusive, role in dot groupings.

Analysis of Variance↗
PubMed1992

Dead zone for express saccades.

The saccadic eye movements of three humans and one non-human primate (a male rhesus monkey) have been measured for target eccentricities between 0.3 and 15 deg. With a gap task (fixation point offset precedes target onset by 200 ms) and a target at 4 deg, all subjects produced reasonable amounts of express saccades as indicated by a clear peak in the distribution of their saccadic reaction times (SRT): about 100 ms in human subjects and 70 ms in the monkey. This peak disappeared with decreasing target eccentricity below 2 deg, but saccades of longer (regular) reaction times were still present. Thus it was found that there exists a dead zone for express saccades. In addition, small saccades have a much stronger tendency to overshoot the target and their velocity falls above the main sequence as defined by the least square fit of an exponential v = vo(1-exp(-a/ao)) to the maximal velocity (v) versus amplitude (a) relationship (vo and ao are constants fitted). It is concluded that for small saccades the express way is blocked functionally or does not exist anatomically.

Animals↗
PubMed1991

Cortical control of memory-guided saccades in man.

Memory-guided saccades were electro-oculographically recorded in 30 patients with limited unilateral cerebral infarction, documented by computerized tomographic scan and/or magnetic resonance imaging. The lesions affected either (1) the posterior parietal cortex (PPC), (2) the dorsolateral frontal cortex (DLFC), involving the frontal eye field (FEF) and/or the prefrontal cortex (PFC) (area 46 of Brodmann), or (3) the supplementary motor area in the dorsomedial frontal cortex (DMFC). Patients were divided into 6 groups according to the location (PPC, DLFC, DMFC) and side of the lesions. Both latency and accuracy (expressed as percentage of error in amplitude) of memory-guided saccades were compared in each group of patients to values obtained from 20 age-matched normal subjects. Latency was significantly increased, for both directions of saccades in the two DLFC groups and in the right PPC group, and for leftward saccades in the left PPC group. The percentage of error in amplitude was also significantly increased for both directions of saccades in the right PPC group and the left DLFC group, and for leftward saccades in the right DLFC group. Results were near the normal values in patients with lesions affecting the DMFC. Thus, both the PPC (essentially on the right side) and the DLFC appear to play a role in the control of memory-guided saccades. It is suggested that the cortical pathway involved in these saccades includes the PPC, the PFC and the FEF, successively. The PPC could have a dual role: visuospatial integration, and early selection and preparation of certain collicular cells by pre-excitation. Both functions could be ensured by two different types of cells, corresponding, in the monkey, to area 7a and to lateral intraparietal area, respectively. The DLFC could also have a dual role: memorization of visuospatial information by the PFC, and triggering of memory-guided saccades by the FEF.

Cerebral Cortex↗
PubMed1985

Reflex actions of muscle afferents on fusimotor innervation in decerebrated cats: an assessment of beta contributions.

The existence of beta innervation in many cat muscles raises the possibility that spindle afferent discharge will excite beta motoneurons, augmenting spindle afferent discharge and thereby closing a positive feedback loop. In order to evaluate the strength of such a loop through beta motoneurons and muscle spindles, the stretch responses of muscle spindle afferents from medial gastrocnemius (MG) and soleus (SOL) muscles were studied in decerebrated cats before and after dorsal root section. If a positive feedback loop were operational, the spindle afferent stretch response should be diminished following dorsal root section by an amount related to the magnitude of positive feedback. After dorsal root section, the static positional sensitivities of our MG spindle afferent sample were significantly reduced for 72% (13/18, p less than 0.05) of the afferents, and dynamic rate/length slopes were decreased for 88% (8/9) of a subset of the afferents studied. Similar reductions for 6 afferents from SOL were not found. To apportion these afferent changes to reflex excitation of either gamma or beta motoneurons, we recorded the stretch responses of gamma and alpha-type fibers in the same preparation. (We assume that the population of alpha-type fibers includes beta fibers). In keeping with other reports, alpha fibers were much more responsive to stretch than gamma fibers. The mean positional sensitivity for alpha fibers (1.29 +/- 0.92 pps/mm, n = 15) was greater (p less than 0.05) than that of gamma fibers (0.49 +/- 0.93 pps/mm, n = 18). Because of these differences in sensitivity, beta motoneurons are more likely (than gamma motoneurons) to be involved in a positive feedback loop, although some gamma contribution is also likely. Using equations based on a beta position regulating scheme, differences in spindle positional sensitivity were used to estimate beta loop gain. The average loop gain was estimated to be 0.41 (n = 18). The contribution of such a beta configuration to reducing the sensitivity of muscle to changes in load and muscle properties is evaluated.

Afferent Pathways↗