Neural correlates of contrast detection at threshold

Human psychophysical studies have demonstrated that, for stimuli near the threshold of visibility, detection of motion in one direction is unaffected by the superimposition of motion in the opposite direction. To investigate the neural basis for this perceptual phenomenon, we recorded from directionally selective neurons in macaque visual area MT (middle temporal visual area). Contrast thresholds obtained for single gratings moving in a neuron's preferred direction were compared with those obtained for motion presented simultaneously in the neuron's preferred and antipreferred directions. A simple model based on probability summation between neurons tuned to opposite directions could sufficiently account for contrast thresholds revealed psychophysically, suggesting that area MT is likely to provide the neural basis for contrast detection of stimuli modulated in time.     

Dark rearing alters the normal development of spatiotemporal response properties but not of contrast detection threshold in mouse retinal ganglion cells

The mouse visual system is immature when the eyes open two weeks after birth. As in other mammals, some of the maturation that occurs in the subsequent weeks is known to depend on visual experience. Development of the retina, which as the first stage of vision provides the visual information to the brain, also depends on light‐driven activity for proper development but has been less well studied than visual cortical development. The critical properties for retinal encoding of images include detection of contrast and responsiveness to the broad range of temporal stimulus frequencies present in natural stimuli. Here we show that contrast detection threshold and temporal frequency response characteristics of ON and OFF retinal ganglion cells (RGCs), which are poor at eye opening, subsequently undergo maturation, improving RGC performance. Further, we find that depriving mice of visual experience from before birth by rearing them in the dark causes ON and OFF RGCs to have smaller receptive field centers but does not affect their contrast detection threshold development. The modest developmental increase in temporal frequency responsiveness of RGCs in mice reared on a normal light cycle was inhibited by dark rearing only in ON but not OFF RGCs. Thus, these RGC response characteristics are in many ways unaffected by the experience‐dependent changes to synaptic and spontaneous activity known to occur in the mouse retina in the two weeks after eye opening, but specific differences are apparent in the ON vs. OFF RGC populations. © 2014 Wiley Periodicals, Inc. Develop Neurobiol 74: 692–706, 2014     

Area summation in human vision at and above detection threshold

The initial image-processing stages of visual cortex are well suited to a local (patchwise) analysis of the viewed scene. But the world's structures extend over space as textures and surfaces, suggesting the need for spatial integration. Most models of contrast vision fall shy of this process because (i) the weak area summation at detection threshold is attributed to probability summation (PS) and (ii) there is little or no advantage of area well above threshold. Both of these views are challenged here. First, it is shown that results at threshold are consistent with linear summation of contrast following retinal inhomogeneity, spatial filtering, nonlinear contrast transduction and multiple sources of additive Gaussian noise. We suggest that the suprathreshold loss of the area advantage in previous studies is due to a concomitant increase in suppression from the pedestal. To overcome this confound, a novel stimulus class is designed where: (i) the observer operates on a constant retinal area, (ii) the target area is controlled within this summation field, and (iii) the pedestal is fixed in size. Using this arrangement, substantial summation is found along the entire masking function, including the region of facilitation. Our analysis shows that PS and uncertainty cannot account for the results, and that suprathreshold summation of contrast extends over at least seven target cycles of grating.     

A vector-magnitude model of contrast detection

A model of contrast detection is proposed in which the visibility of a low-contrast stimulus is determined by a non-Euclidean magnitude of the vector composed of the responses of a large number of independent channels. Although the vector-magnitude model is quite different from the probability-summation model which has been suggested previously, the contrast thresholds and psychometric functions predicted by the two models can be in agreement within 10% for up to 10⁵ channels in the system. Presently available experimental evidence is insufficient to establish the correctness of either model, but the computational simplicity of the vector-magnitude model makes it interesting, if only as a useful approximation to the probability-summation model.     

Feature detection in human vision: a phase-dependent energy model

This paper presents a simple and biologically plausible model of how mammalian visual systems could detect and identify features in an image. We suggest that the points in a waveform that have unique perceptual significance as 'lines' and 'edges' are the points where the Fourier components of the waveform come into phase with each other. At these points 'local energy' is maximal. Local energy is defined as the square root of the sum of the squared response of sets of matched filters, of identical amplitude spectrum but differing in phase spectrum by 90 degrees: one filter type has an even-symmetric line-spread function, the other an odd-symmetric line-spread function. For a line the main contribution to the local energy peak is in the output of the even-symmetric filters, whereas for edges it is in the output of the odd-symmetric filters. If both filter types respond at the peak of local energy, both edges and lines are seen, either simultaneously or alternating in time. The model was tested with a series of images, and shown to predict well the position of perceived features and the organization of the images.     

Spatial characteristics of movement detection mechanisms in human vision

Visual detection of targets moving against structured background fields has been studied with near-monochromatic stimuli, selected so as to isolate the different increment threshold spectral response mechanisms. It is shown that for foveal vision, the red-and green-sensitive mechanisms (₅ and ₄ respectively) yield IMG functions (Barbur and Ruddock, 1980), similar to those found with white light. In contrast, the blue-sensitive (₁) mechanism yields a low-frequency IMG response quite unlike that found for the other mechanisms. There is also considerable variation between subjects in this case. Measurements taken 30° off-axis with low (1.4 log trolands) background illumination level, yield a low frequency response IMG function for both rod and cone spectral mechanisms, similar to those found with white light stimuli. At high illumination levels (>2.2 log trolands), the IMG function for the ₅-mechanism is shifted to higher spatial frequencies, as is also observed with white light stimuli. A wavelength-selective binocular interaction effect, manifested in the detection of moving targets, is also described, and it is suggested that this may be of value in the study of defective colour vision.     

Neuronal model for stereoscopic vision

A neuronal model for stereopsis is described and simulated. Without the assumption of specific feature detectors, objects are unambiguously located in three-dimensional visual space. Random-dot stereograms are correctly resolved in depth with stimulus details conserved within planar contours.     

Mosaic model for color vision

Color vision in man is based upon three different cone types, which are quite likely arranged in a semi-ordered array in the retina. The model proposes that this ordering is an inherent part of the genetic code that sets up the color vision mechanism, and that the specification for each cone type (red, green or blue) also includes a specification for its place in the larger structure of which it is a part. One possible positional mosaic for the three cone types is proposed, together with its degeneracies into anomalous (red-green) color mechanisms. Assuming only one fixed probability for a degenerate transition, the population frequencies for color anomalies predicted from the model agree closely with the observed frequencies.     

A spatiotemporal stochastic process model for species spread

We use a spatiotemporal Markov process to model the spread of an ecological population through its environment over time. Available habitat is divided into sites, and a parametric function of spatial variables is used to model the probability that one site is colonized from another. This allows us both to make predictions about the future spread of a population, and to determine which are the important factors governing colonizations. The model evolves in discrete time, allowing the population distribution to change seasonally in accordance with breeding patterns. Discrete time formulations are natural for ecological populations, but are problematic due to difficulties of fitting and predicting over irregular time intervals. The model described here can accommodate years of missing data and can therefore fit and predict at irregular intervals. Two methods of approximating the likelihood are described and applied to ornithological survey data for the woodlark, Lullula arborea, from Thetford Forest in the U.K.     

A mixed mover-stayer model for spatiotemporal two-state processes

Studies of recurring infection or chronic disease often collect longitudinal data on the disease status of subjects. Two-state transitional models are useful for analysis in such studies where, at any point in time, an individual may be said to occupy either a diseased or disease-free state and interest centers on the transition process between states. Here, two additional features are present. The data are spatially arranged and it is important to account for spatial correlation in the transitional processes corresponding to different subjects. In addition there are subgroups of individuals with different mechanisms of transitions. These subgroups are not known a priori and hence group membership must be estimated. Covariates modulating transitions are included in a logistic additive framework. Inference for the resulting mixture spatial Markov regression model is not straightforward. We develop here a Monte Carlo expectation maximization algorithm for maximum likelihood estimation and a Markov chain Monte Carlo sampling scheme for summarizing the posterior distribution in a Bayesian analysis. The methodology is applied to a study of recurrent weevil infestation in British Columbia forests.     

Energy functions for early vision and analog networks

This paper describes attempts to model the modules of early vision in terms of minimizing energy functions, in particular energy functions allowing discontinuities in the solution. It examines the success of using Hopfield-style analog networks for solving such problems. Finally it discusses the limitations of the energy function approach.     

A model of neural network for spatiotemporal pattern recognition

A model of neural network to recognize spatiotemporal patterns is presented. The network consists of two kinds of neural cells: P-cells and B-cells. A P-cell generates an impulse responding to more than one impulse and embodies two special functions: short term storage (STS) and heterosynaptic facilitation (HSF). A B-cell generates several impulses with high frequency as soon as it receives an impulse. In recognizing process, an impulse generated by a P-cell represents a recognition of stimulus pattern, and triggers the generation of impulses of a B-cell. Inhibitory impulses with high frequency generated by a B-cell reset the activities of all P-cells in the network.Two examples of spatiotemporal pattern recognition are presented. They are achieved by giving different values to the parameters of the network. In one example, the network recognizes both directional and non-directional patterns. The selectivities to directional and non-directional patterns are realized by only adjusting excitatory synaptic weights of P-cells. In the other example, the network recognizes time series of spatial patterns, where the lengths of the series are not necessarily the same and the transitional speeds of spatial patterns are not always the same. In both examples, the HSF signal controls the total activity of the network, which contributes to exact recognition and error recovery. In the latter example, it plays a role to trigger and execute the recognizing process. Finally, we discuss the correspondence between the model and physiological findings.     

The Gaussian derivative model for spatial-temporal vision: I. Cortical model

How do we see the motion of objects as well as their shapes? The Gaussian Derivative (GD) spatial model is extended to time to help answer this question. The GD spatio-temporal model requires only two numbers to describe the complete three-dimensional space-time shapes of individual receptive fields in primate visual cortex. These two numbers are the derivative numbers along the respective spatial and temporal principal axes of a given receptive field. Nine transformation parameters allow for a standard geometric association of these intrinsic axes with the extrinsic environment. The GD spatio-temporal model describes in one framework the following properties of primate simple cell fields: motion properties, number of lobes in space-time, spatial orientation. location, and size. A discrete difference-of-offset-Gaussians (DOOG) model provides a plausible physiological mechanism to form GD-like model fields in both space and time. The GD model hypothesizes that receptive fields at the first stage of processing in the visual cortex approximate 'derivative analyzers' that estimate local spatial and temporal derivatives of the intensity profile in the visual environment. The receptive fields as modeled provide operators that can allow later stages of processing in either a biological or machine vision system to estimate the motion as well as the shapes of objects in the environment.     

The transducer model for contrast detection and discrimination: formal relations, implications, and an empirical test

The transducer function mu for contrast perception describes the nonlinear mapping of stimulus contrast onto an internal response. Under a signal detection theory approach, the transducer model of contrast perception states that the internal response elicited by a stimulus of contrast c is a random variable with mean mu(c). Using this approach, we derive the formal relations between the transducer function, the threshold-versus-contrast (TvC) function, and the psychometric functions for contrast detection and discrimination in 2AFC tasks. We show that the mathematical form of the TvC function is determined only by mu, and that the psychometric functions for detection and discrimination have a common mathematical form with common parameters emanating from, and only from, the transducer function mu and the form of the distribution of the internal responses. We discuss the theoretical and practical implications of these relations, which have bearings on the tenability of certain mathematical forms for the psychometric function and on the suitability of empirical approaches to model validation. We also present the results of a comprehensive test of these relations using two alternative forms of the transducer model: a three-parameter version that renders logistic psychometric functions and a five-parameter version using Foley's variant of the Naka-Rushton equation as transducer function. Our results support the validity of the formal relations implied by the general transducer model, and the two versions that were contrasted account for our data equally well.     

A hierarchical spatiotemporal analog forecasting model for count data

Analog forecasting is a mechanism‐free nonlinear method that forecasts a system forward in time by examining how past states deemed similar to the current state moved forward. Previous applications of analog forecasting has been successful at producing robust forecasts for a variety of ecological and physical processes, but it has typically been presented in an empirical or heuristic procedure, rather than as a formal statistical model. The methodology presented here extends the model‐based analog method of McDermott and Wikle (Environmetrics, 27, 2016, 70) by placing analog forecasting within a fully hierarchical statistical framework that can accommodate count observations. Using a Bayesian approach, the hierarchical analog model is able to quantify rigorously the uncertainty associated with forecasts. Forecasting waterfowl settling patterns in the northwestern United States and Canada is conducted by applying the hierarchical analog model to a breeding population survey dataset. Sea surface temperature (SST) in the Pacific Ocean is used to help identify potential analogs for the waterfowl settling patterns.     

The threshold bias model: a mathematical model for the nomothetic approach of suicide

Background

Comparative and predictive analyses of suicide data from different countries are difficult to perform due to varying approaches and the lack of comparative parameters.

Methodology/Principal Findings

A simple model (the Threshold Bias Model) was tested for comparative and predictive analyses of suicide rates by age. The model comprises of a six parameter distribution that was applied to the USA suicide rates by age for the years 2001 and 2002. Posteriorly, linear extrapolations are performed of the parameter values previously obtained for these years in order to estimate the values corresponding to the year 2003. The calculated distributions agreed reasonably well with the aggregate data. The model was also used to determine the age above which suicide rates become statistically observable in USA, Brazil and Sri Lanka.

Conclusions/Significance

The Threshold Bias Model has considerable potential applications in demographic studies of suicide. Moreover, since the model can be used to predict the evolution of suicide rates based on information extracted from past data, it will be of great interest to suicidologists and other researchers in the field of mental health.