Motion perception and motion estimation by total-least squares

A computational model of motion perception is proposed. The model, which is gradient-based, adheres to the neural constraint that transmitted signals are positive-valued functions by posing the estimation of image motion as a quadratic programming problem combined with total-least squares: a model that assumes that image signals are contaminated by noise in both the spatial and temporal dimensions. By shrinking motion estimates with a regularizer whose subtractive effect introduces a contrast dependent speed threshold into motion computations, it is shown that the total-least squares model when posed as a quadratic programming problem, is capable of explaining both increases and decreases in perceived speed as these effects were reported by Thompson (1982) to vary as a function of image contrast and temporal frequency. The correlation that exists between the model's contrast speed response and results reported from visual psychophysics is consistent with the view that the visual system assumes that image signals may be contaminated by noise in both the spatial and the temporal domain, and that visual motion is influenced by the consequence of these assumptions.     

A mathematical model of the primary visual cortex and hypercolumn

A mathematical model of the primary visual cortex is presented. Basically, the model comprises two features. Firstly, in analogy with the principle of the computerized tomography (CT), it assumes that simple cells in each hypercolumn are not merely detecting line segments in images as features, but rather that they are as a whole representing the local image with a certain representation. Secondly, it assumes that each hypercolumn is performing spatial frequency analyses of local images using that representation, and that the resultant spectra are represented by complex cells. The model is analyzed using numerical simulations and its advantages are discussed from the viewpoint of visual information processing. It is shown that 1) the proposed processing is tolerant to shifts in position of input images, and that 2) spatial frequency filtering operations can be easily performed in the model.     

Mapping temporally varying quantitative trait loci in time-to-failure experiments

Existing methods for mapping quantitative trait loci (QTL) in time-to-failure experiments assume that the QTL effect is constant over the course of the study. This assumption may be violated when the gene(s) underlying the QTL are up- or downregulated on a biologically meaningful timescale. In such situations, models that assume a constant effect can fail to detect QTL in a whole-genome scan. To investigate this possibility, we utilize an extension of the Cox model (EC model) within an interval-mapping framework. In its simplest form, this model assumes that the QTL effect changes at some time point t0 and follows a linear function before and after this change point. The approximate time point at which this change occurs is estimated. Using simulated and real data, we compare the mapping performance of the EC model to the Cox proportional hazards (CPH) model, which explicitly assumes a constant effect. The results show that the EC model detects time-dependent QTL, which the CPH model fails to detect. At the same time, the EC model recovers all of the QTL the CPH model detects. We conclude that potentially important QTL may be missed if their time-dependent effects are not accounted for.     

A model of motion adaptation and motion after-effects based upon principal component regression

A computational model to help explain effects of adaptation to moving signals is compared with established energy (linear regression) models of motion detection. The proposed model assumes that processed image signals are subject to error in both dimensions of space and time. This assumption constrains models of motion perception to be based upon principal component regression rather than linear regression. It is shown that response suppression of model complex cell neurons that input into the model may account for (1) increases in perceived speed after adaptation to static patterns and testing with slowly moving patterns, (2) significant increases in perceived speed after adaptation to patterns moving at a medium speed and testing at high speed, and (3) decreases in perceived speed in the opponent direction to a quickly moving adapting signal. Neither of predictions (2) or (3) are general features of established accounts of motion detection by visual processes based upon linear regression. Comparisons of the proposed model's speed transfer function with existing psychophysical data suggests that the visual system processes motion signals with the tacit assumption that image measurements are subject to error in both space and time. Received: 24 January 2000 / Accepted in revised form: 8 May 2000     

Considering the Spatial Layout Information of Bag of Features (BoF) Framework for Image Classification

The spatial pooling method such as spatial pyramid matching (SPM) is very crucial in the bag of features model used in image classification. SPM partitions the image into a set of regular grids and assumes that the spatial layout of all visual words obey the uniform distribution over these regular grids. However, in practice, we consider that different visual words should obey different spatial layout distributions. To improve SPM, we develop a novel spatial pooling method, namely spatial distribution pooling (SDP). The proposed SDP method uses an extension model of Gauss mixture model to estimate the spatial layout distributions of the visual vocabulary. For each visual word type, SDP can generate a set of flexible grids rather than the regular grids from the traditional SPM. Furthermore, we can compute the grid weights for visual word tokens according to their spatial coordinates. The experimental results demonstrate that SDP outperforms the traditional spatial pooling methods, and is competitive with the state-of-the-art classification accuracy on several challenging image datasets.     

On the Distribution of the Menstruating Interval

This article is concerned with the development of some stochastic models better suited to describe the observed distributions of the menstruating interval relating to last closed-birth interval of two types of females. In this context, two models suited for couples using or not using contraception have been proposed. In the first case, the model assumes a constant conception rate (analogous to the constant hazard rate in the life-testing problem) over time whereas the second case assumes a time-dependent form of the conception rate. The models have been applied to the data collected in a survey conducted in Lucknow, and estimates of conception rate for the two types of females have also been obtained.     

An evaluation of methods for modelling species distributions

Aim Various statistical techniques have been used to model species probabilities of occurrence in response to environmental conditions. This paper provides a comprehensive assessment of methods and investigates whether errors in model predictions are associated to specific kinds of geographical and environmental distributions of species. Location Portugal, Western Europe. Methods Probabilities of occurrence for 44 species of amphibians and reptiles in Portugal were modelled using seven modelling techniques: Gower metric, Ecological Niche Factor Analysis, classification trees, neural networks, generalized linear models, generalized additive models and spatial interpolators. Generalized linear and additive models were constructed with and without a term accounting for spatial autocorrelation. Model performance was measured using two methods: sensitivity and Kappa index. Species were grouped according to their spatial (area of occupancy and extent of occurrence) and environmental (marginality and tolerance) distributions. Two‐way comparison tests were performed to detect significant interactions between models and species groups. Results Interaction between model and species groups was significant for both sensitivity and Kappa index. This indicates that model performance varied for species with different geographical and environmental distributions. Artificial neural networks performed generally better, immediately followed by generalized additive models including a covariate term for spatial autocorrelation. Non‐parametric methods were preferred to parametric approaches, especially when modelling distributions of species with a greater area of occupancy, a larger extent of occurrence, lower marginality and higher tolerance. Main conclusions This is a first attempt to relate performance of modelling techniques with species spatial and environmental distributions. Results indicate a strong relationship between model performance and the kinds of species distributions being modelled. Some methods performed generally better, but no method was superior in all circumstances. A suggestion is made that choice of the appropriate method should be contingent on the goals and kinds of distributions being modelled.     

Host-feeding strategies of parasitoid wasps

Summary Three models of the evolution of host-feeding behaviour in parasitoid wasps are developed. The first assumes that the wasp host feeds purely to obtain resources to mature eggs (limited resource model) while the second assumes that host feeding provides energy for maintenance (pro-ovigenic model). The third model assumes that host feeding provides resources for both maintenance and egg maturation (resource pool model). Two variants of the third model are examined: the first assumes that the risk of mortality is constant and state-independent, the second that resource-depleted individuals suffer a higher risk of mortality. The models are analysed using a combination of stochastic dynamic programming and analytical techniques. The models make different predictions about the relationships between the probability of host feeding and egg load and host density. The available experimental evidence best supports the resource pool model.     

Ecological interpretations of the mid-domain effect

The suggestion that spatial gradients in species richness are influenced by geometric constraints resulting in the mid‐domain effect has been investigated by null models. The technical aspects of making such null models are well explored, but the implicit ecological assumptions behind these models are less explored. Four ecological models that all assume that species ranges are constrained by hard boundaries are made: evolutionary model, source‐sink model, dynamic‐environment model, and range‐size model. These models give different predictions that make it possible to separate the models from each other, and from a model that assumes that hard boundaries are not important.     

Contrast adaptation and contrast masking in human vision.

After a preliminary study of visual evoked potentials (VEPS) to a test grating seen in the presence of masks at different orientations, psychophysical data are presented showing the effects of adaptation and of masking on thresholds for detecting the same test grating. The test is a vertical grating of spatial frequency 2 cycles per degree; adapting and masking gratings differ from the test either in orientation or in spatial frequency. The effects of adaptation and masking are explained by a single mechanism model that assumes: (i) adaptation and masking both alter the contrast response (or transducer) function of the mechanism that detects the test; (ii) masks, but not adaptors, stimulate the mechanism that detects the test; and (iii) a test is detectable when it raises response level by a constant amount. The model incorporates two distinct tuning functions, a broad adaptive contrast function and a narrow effective contrast function. It accounts adequately for all the data, including the location and size of the facilitative dip found in some masking functions, the constant slopes of the threshold elevation segments of adaptation functions and the varying slopes of masking functions. It also predicts the sometimes surprising joint effects of adaptation followed by masking and of two masks operating simultaneously.     

Simplified models for packed-bed biofilm reactors

For a packed-bed biofilm reactor two reactor models are proposed. One model is for the limiting case of a biofilm with a constant biofilm thickness in which diffusion within the biofilm is shown to be negligible. The second model assumes that the thickness of the biofilm is limited by the concentration of substrate within the biofilm. The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exact differential equations.     

A Model of Temporal Encoding of Stimulus Orientation by Neuronal Responses in the Primary Visual Cortex

It has been shown experimentally that the stimulus orientation that elicits the optimal response in an orientation column in the primary visual cortex (area V1) undergoes rapid systemic changes that last 10–100 ms. These changes allow different orientation columns to encode information from multiple items in the visual space (the so-called temporal encoding). However, the mechanism of these changes is still unknown. In addition, most of the modern biophysical models are unable to reproduce these changes; the peak orientation of their responses is constant over time. In this paper, we suggest a method to improve the firing-rate ring model of the orientation hypercolumn by replacing the spatial symmetric distribution of local connections with a spatial anti-symmetric distribution. As a result, we obtained a more perfect model that is capable of reproducing such changes. Moreover, their amplitude is proportional to the extent of asymmetry in the spatial distribution of local connections.     

Visual ground pattern modulates flight speed of male Oriental fruit moth Grapholita molesta

Insects flying in a horizontal pheromone plume must attend to visual cues to ensure that they make upwind progress. Moreover, it is suggested that flying insects will also modulate their flight speed to maintain a constant retinal angular velocity of terrestrial contrast elements. Evidence from flies and honeybees supports such a hypothesis, although tests with male moths and beetles flying in pheromone plumes are not conclusive. These insects typically fly faster at higher elevations above a high‐contrast ground pattern, as predicted by the hypothesis, although the increase in speed is not sufficient to demonstrate quantitatively that they maintain constant visual angular velocity of the ground pattern. To test this hypothesis more rigorously, the flight speed of male oriental fruit moths (OFM) Grapholita molesta Busck (Lepidoptera: Tortricidae) flying in a sex pheromone plume in a laboratory wind tunnel is measured at various heights (5–40 cm) above patterns of different spatial wavelength (1.8–90°) in the direction of flight. The OFM modulate their flight speed three‐fold over different patterns. They fly fastest when there is no pattern in the tunnel or the contrast elements are too narrow to resolve. When the spatial wavelength of the pattern is sufficiently wide to resolve, moths fly at a speed that tends to maintain a visual contrast frequency of 3.5 ± 3.2 Hz rather than a constant angular velocity, which varies from 57 to 611° s^?1. In addition, for the first time, it is also demonstrated that the width of a contrast pattern perpendicular to the flight direction modulates flight speed.     

Increasing neural network robustness improves match to macaque V1 eigenspectrum,spatial frequency preference and predictivity

Task-optimized convolutional neural networks (CNNs) show striking similarities to the ventral visual stream. However, human-imperceptible image perturbations can cause a CNN to make incorrect predictions. Here we provide insight into this brittleness by investigating the representations of models that are either robust or not robust to image perturbations. Theory suggests that the robustness of a system to these perturbations could be related to the power law exponent of the eigenspectrum of its set of neural responses, where power law exponents closer to and larger than one would indicate a system that is less susceptible to input perturbations. We show that neural responses in mouse and macaque primary visual cortex (V1) obey the predictions of this theory, where their eigenspectra have power law exponents of at least one. We also find that the eigenspectra of model representations decay slowly relative to those observed in neurophysiology and that robust models have eigenspectra that decay slightly faster and have higher power law exponents than those of non-robust models. The slow decay of the eigenspectra suggests that substantial variance in the model responses is related to the encoding of fine stimulus features. We therefore investigated the spatial frequency tuning of artificial neurons and found that a large proportion of them preferred high spatial frequencies and that robust models had preferred spatial frequency distributions more aligned with the measured spatial frequency distribution of macaque V1 cells. Furthermore, robust models were quantitatively better models of V1 than non-robust models. Our results are consistent with other findings that there is a misalignment between human and machine perception. They also suggest that it may be useful to penalize slow-decaying eigenspectra or to bias models to extract features of lower spatial frequencies during task-optimization in order to improve robustness and V1 neural response predictivity.     

DETERMINATION OF STEADY STATE GENERATION TIME DISTRIBUTIONS FROM LABELLED MITOSIS EXPERIMENTAL DATA

The proper application of detailed deterministic cell kinetic models depends on the way in which cells are assigned their generation times. A method is presented for the determination of population generation time distributions from labelled mitoses experiments. the model assumes that the generation time of each new cell is a function of both the steady-state generation time distribution function of the population, and also the generation time frequency-function of the previous generation of cells. This approach is applied to two different cell types to successfully simulate extended labelled mitoses curves using a population balance model with constant maturation rates.     

Invasion speeds for structured populations in fluctuating environments

We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly variable environments will be estimates of their rates of spatial spread and the associated uncertainty of these estimates. Using stochastic, stage-structured, integrodifference equation models, we show analytically that invasion speeds are asymptotically normally distributed with a variance that decreases in time. We apply our methods to a simple juvenile–adult model with stochastic variation in reproduction and an illustrative example with published data for the perennial herb, Calathea ovandensis. These examples buttressed by additional analysis reveal that increased variability in vital rates simultaneously slow down invasions yet generate greater uncertainty about rates of spatial spread. Moreover, while temporal autocorrelations in vital rates inflate variability in invasion speeds, the effect of these autocorrelations on the average invasion speed can be positive or negative depending on life history traits and how well vital rates “remember” the past.     

Self-Organized Shape and Frontal Density of Fish Schools

Models of swarming (based on avoidance, alignment and attraction) produce patterns of behaviour also seen in schools of fish. However, the significance of such similarities has been questioned, because some model assumptions are unrealistic [e.g. speed in most models is constant with random error, the perception is global and the size of the schools that have been studied is small (up to 128 individuals)]. This criticism also applies to our former model, in which we demonstrated the emergence of two patterns of spatial organization, i.e. oblong school form and high frontal density, which are supposed to function as protection against predators. In our new model we respond to this criticism by making the following improvements: individuals have a preferred ‘cruise speed’ from which they can deviate in order to avoid others or to catch up with them. Their range of perception is inversely related to density, with which we take into account that high density limits the perception of others that are further away. Swarm sizes range from 10 to 2000 individuals. The model is three‐dimensional. Further, we show that the two spatial patterns (oblong shape and high frontal density) emerge by self‐organization as a side‐effect of coordination at two speeds (of two or four body lengths per second) for schools of sizes above 20. Our analysis of the model leads to the development of a new set of hypotheses. If empirical data confirm these hypotheses, then in a school of real fish these patterns may arise as a side‐effect of their coordination in the same way as in the model.     

Are direction and speed coded independently by the visual system? Evidence from visual search.

Three visual search experiments examined whether motion is coded as two separate features, speed and direction. Increasing the heterogeneity of the directions in which stimuli moved disrupted detection of a target defined by speed (fast among medium and slow nontargets), suggesting that speed is coded integrally with direction. However, heterogeneity in speed did not disrupt detection of a target moving in a particular direction among nontargets with different directions. This suggests that direction is coded independently of speed. The apparent paradox raised by these contrasting conclusions is consistent with neurophysiological and computational models of motion-detection, which suggest that low-levels of the visual system contain direction-detectors insensitive to speed, while speed is coded at higher levels by detectors which are also sensitive to direction. Evidence consistent with the existence of the latter conjunction detectors was obtained in a final experiment which found search for a conjunction of speed and direction to be parallel.     

Malaria in Africa: vector species' niche models and relative risk maps

A central theoretical goal of epidemiology is the construction of spatial models of disease prevalence and risk, including maps for the potential spread of infectious disease. We provide three continent-wide maps representing the relative risk of malaria in Africa based on ecological niche models of vector species and risk analysis at a spatial resolution of 1 arc-minute (9 185 275 cells of approximately 4 sq km). Using a maximum entropy method we construct niche models for 10 malaria vector species based on species occurrence records since 1980, 19 climatic variables, altitude, and land cover data (in 14 classes). For seven vectors (Anopheles coustani, A. funestus, A. melas, A. merus, A. moucheti, A. nili, and A. paludis) these are the first published niche models. We predict that Central Africa has poor habitat for both A. arabiensis and A. gambiae, and that A. quadriannulatus and A. arabiensis have restricted habitats in Southern Africa as claimed by field experts in criticism of previous models. The results of the niche models are incorporated into three relative risk models which assume different ecological interactions between vector species. The "additive" model assumes no interaction; the "minimax" model assumes maximum relative risk due to any vector in a cell; and the "competitive exclusion" model assumes the relative risk that arises from the most suitable vector for a cell. All models include variable anthrophilicity of vectors and spatial variation in human population density. Relative risk maps are produced from these models. All models predict that human population density is the critical factor determining malaria risk. Our method of constructing relative risk maps is equally general. We discuss the limits of the relative risk maps reported here, and the additional data that are required for their improvement. The protocol developed here can be used for any other vector-borne disease.     

Quantification of phase synchronization phenomena and their importance for verbal memory processes

The tangential neurons in the lobula plate region of the flies are known to respond to visual motion across broad receptive fields in visual space.When intracellular recordings are made from tangential neurons while the intact animal is stimulated visually with moving natural imagery,we find that neural response depends upon speed of motion but is nearly invariant with respect to variations in natural scenery. We refer to this invariance as velocity constancy. It is remarkable because natural scenes, in spite of similarities in spatial structure, vary considerably in contrast, and contrast dependence is a feature of neurons in the early visual pathway as well as of most models for the elementary operations of visual motion detection. Thus, we expect that operations must be present in the processing pathway that reduce contrast dependence in order to approximate velocity constancy.We consider models for such operations, including spatial filtering, motion adaptation, saturating nonlinearities, and nonlinear spatial integration by the tangential neurons themselves, and evaluate their effects in simulations of a tangential neuron and precursor processing in response to animated natural imagery. We conclude that all such features reduce interscene variance in response, but that the model system does not approach velocity constancy as closely as the biological tangential cell.