Geometry of binocular vision and a model for stereopsis

If a binocular observer looks at surfaces, the disparity is a continuous vector field defined on the manifold of cyclopean visual directions. We derive this field for the general case that the observer is presented with a curved surface and fixates an arbitrary point. We expand the disparity field in the neighbourhood of a visual direction. The first order approximation can be decomposed into congruences, similarities and deformations. The deformation component is described by the traceless part of the symmetric part of the gradient of the disparity. The deformation component carries all information concerning the slant of a surface element that is contained in the disparity field itself; it is invariant for changes of fixation, differential cyclotorsion and uniform aniseikonia. The deformation component can be found from a comparison of the orientation of surface details in the left and right retinal images. The theory provides a geometric explanation of the percepts obtained with uniform and oblique meridional aniseikonia. We utilize the geometric theory to construct a mechanistic model of stereopsis that obviates the need for internal zooming mechanisms, but nevertheless is insensitive to differential cyclotorsion or uniform aniseikonia.     

The direction of retinal motion facilitates binocular stereopsis.

Visual information from binocular disparity and from relative motion provide information about three-dimensional structure and layout of the world. Although the mechanisms that process these cues have typically been studied independently, there is now a substantial body of evidence that suggests that they interact in the visual pathway. This paper investigates one advantage of such an interaction: whether retinal motion can be used as a matching constraint in the binocular correspondence process. Stimuli that contained identical disparity and motion signals but which differed in their fine-scale correlation were created to establish whether the direction, or the speed, of motion could enhance performance in a psychophysical task in which binocular matching is a limiting factor. The results of these experiments provide clear evidence that different directions of motion, but not different speeds, are processed separately in stereopsis. The results fit well with properties of neurons early in the cortical visual pathway which are thought to be involved in determining local matches between features in the two eyes'' images.     

Binocular fusion in Panum''''s limiting case of stereopsis obeys the uniqueness constraint

In the information processing procedure of stereo vision, the uniqueness constraint has been used as one of the constraints to solve the "correspondence problem". While the uniqueness constraint is valid in most cases, whether it is still valid in some particular stimulus configuration (such as Panum's limiting case) has been a problem of widespread debate for a long time. To investigate the problem, we adopted the Panum's limiting case as its basic stimulus configuration, and delved into the phenomenon of binocular fusion from two distinct aspects: visual direction and orientation disparity. The results show that in Panum's limiting case binocular fusion does not comply with the rules governing regular binocular fusion as far as visual direction and orientation disparity are concerned. This indicates that double fusion does not happen in Panum's limiting case and that the uniqueness constraint is still valid.     

A laminar cortical model of stereopsis and 3D surface perception: closure and da Vinci stereopsis

A laminar cortical model of stereopsis and 3D surface perception is developed and simulated. The model describes how monocular and binocular oriented filtering interact with later stages of 3D boundary formation and surface filling-in in the LGN and cortical areas V1, V2, and V4. It proposes how interactions between layers 4, 3B, and 2/3 in V1 and V2 contribute to stereopsis, and how binocular and monocular information combine to form 3D boundary and surface representations. The model includes two main new developments: (1) It clarifies how surface-to-boundary feedback from V2 thin stripes to pale stripes helps to explain data about stereopsis. This feedback has previously been used to explain data about 3D figure-ground perception. (2) It proposes that the binocular false match problem is subsumed under the Gestalt grouping problem. In particular, the disparity filter, which helps to solve the correspondence problem by eliminating false matches, is realized using inhibitory interneurons as part of the perceptual grouping process by horizontal connections in layer 2/3 of cortical area V2. The enhanced model explains all the psychophysical data previously simulated by Grossberg and Howe (2003), such as contrast variations of dichoptic masking and the correspondence problem, the effect of interocular contrast differences on stereoacuity, Panum's limiting case, the Venetian blind illusion, stereopsis with polarity-reversed stereograms, and da Vinci stereopsis. It also explains psychophysical data about perceptual closure and variations of da Vinci stereopsis that previous models cannot yet explain.     

A Bayesian model of stereopsis depth and motion direction discrimination

 The extraction of stereoscopic depth from retinal disparity, and motion direction from two-frame kinematograms, requires the solution of a correspondence problem. In previous psychophysical work [Read and Eagle (2000) Vision Res 40: 3345–3358], we compared the performance of the human stereopsis and motion systems with correlated and anti-correlated stimuli. We found that, although the two systems performed similarly for narrow-band stimuli, broad-band anti-correlated kinematograms produced a strong perception of reversed motion, whereas the stereograms appeared merely rivalrous. I now model these psychophysical data with a computational model of the correspondence problem based on the known properties of visual cortical cells. Noisy retinal images are filtered through a set of Fourier channels tuned to different spatial frequencies and orientations. Within each channel, a Bayesian analysis incorporating a prior preference for small disparities is used to assess the probability of each possible match. Finally, information from the different channels is combined to arrive at a judgement of stimulus disparity. Each model system – stereopsis and motion – has two free parameters: the amount of noise they are subject to, and the strength of their preference for small disparities. By adjusting these parameters independently for each system, qualitative matches are produced to psychophysical data, for both correlated and anti-correlated stimuli, across a range of spatial frequency and orientation bandwidths. The motion model is found to require much higher noise levels and a weaker preference for small disparities. This makes the motion model more tolerant of poor-quality reverse-direction false matches encountered with anti-correlated stimuli, matching the strong perception of reversed motion that humans experience with these stimuli. In contrast, the lower noise level and tighter prior preference used with the stereopsis model means that it performs close to chance with anti-correlated stimuli, in accordance with human psychophysics. Thus, the key features of the experimental data can be reproduced assuming that the motion system experiences more effective noise than the stereoscopy system and imposes a less stringent preference for small disparities. Received: 2 March 2001 / Accepted in revised form: 5 July 2001     

A binocular model for the simple cell

We authors propose a mathematical model for simple cell binocular response. It comprises two Gabor-type receptive fields (RF) having the same RF center, preferred spatial frequency, and preferred orientation. The model integrates the equally weighted signals from both eyes and performs a threshold operation. Poggio and Fischer (1977) classified binocular disparity cells in the striate cortex into four groups: tuned excitatory (TE), tuned inhibitory (TI), near, and far cells. They also found that most of the TE cells are ocularly balanced and that the other three types are usually unbalanced. This model can imitate these four types of disparity sensitivities and their ocular dominance tendency. We perform model fittings to Poggio's data using the “simulated annealing” method and discuss parameter dependence of the model's response. The model can also respond with exceptional disparity sensitivity: i.e., flat type, alternating type, and intermediate type.     

A model of neural network extracting binocular parallax

A model of neural network extracting binocular parallax is proposed. It is a multilayered network composed of analog threshold elements. Three types of binocular neurons are included in this model. They are binocular simple neurons, binocular gate neurons and binocular depth neurons. The final layers of this model consist of elements which correspond to the binocular depth neurons. The performance of the model has been simulated on a digital computer. The results of the computer simulation show that every element of this model acts like neurons found in cat's and monkey's visual system and this model extracts binocular parallax caused by simple line components satisfactorily.     

Binocular fusion in Panum’s limiting case of stereopsis obeys the uniqueness constraint

In the information processing procedure of stereo vision, the uniqueness constraint has been used as one of the constraints to solve the “correspondence problem”. While the uniqueness constraint is valid in most cases, whether it is still valid in some particular stimulus configuration (such as Panum’s limiting case) has been a problem of widespread debate for a long time. To investigate the problem, we adopted the Panum’s limiting case as its basic stimulus configuration, and delved into the phenomenon of binocular fusion from two distinct aspects: visual direction and orientation disparity. The results show that in Panum’s limiting case binocular fusion does not comply with the rules governing regular binocular fusion as far as visual direction and orientation disparity are concerned. This indicates that double fusion does not happen in Panum’s limiting case and that the uniqueness constraint is still valid.     

A stochastic model of cancer initiation including a bystander effect

A stochastic model of cancer initiation is considered. The model is used to evaluate whether a bystander effect may be important in the pre-malignant and malignant stages of carcinogenesis, and furthermore, on the basis of epidemiological data, to estimate the mutation rates of genes involved in the development of oral leukoplakias. The bystander effect is defined here as the capability of oncogenic mutations to increase the mutation probability of neighbouring (bystander) cells, thus leading potentially to a cascade of neighbouring mutated and neoplastic cells as a pre-stage in the development to leukoplakias and cancer. We find that incidence data for oral cancer are indeed in accordance with a significant bystander effect, operating either alone or in combination with genomic instability in the early stages of carcinogenesis, i.e. the development of neoplasia. Simulations performed gave a picture of how mutations and neoplasia may spread in a tissue, to form characteristic leukoplakias with a core of neoplastic cells. The model also showed that the probability of finding at least one neoplastic cell in the tissue after a given number of years is more sensitive to changes in genomic instability within the cell itself than to changes in a bystander effect. Based on epidemiological data we also calculate the maximum number of oncogenic genes that may be involved in the bystander effect and development of genomic instability. Even if capable of explaining the initial development of oncogenic mutations towards neoplastic cells, the bystander model could not reproduce the observed incidence rates of leukoplakia without assuming a carcinogen mutation probability per cell per year of neoplastic cells practically equal to one. This means that the bystander effect, to be of substantial importance in the final development of neoplastic cells towards leukoplakias, requires a very significant increase in mutation probabilities for bystanders to neoplastic cells. Alternatively, additional mechanisms such as abnormal cell differentiation and uncontrolled proliferation and apoptotis in the neoplastic stage may be of major importance during the development to cancerization.     

The dynamic model of binocular rivalry

Binocular rivalry is an interesting phenomenon observed in the human vision. It occurs when the right and left eyes are given different stimuli (pictures). This paper describes a mathematical model which explains the mechanism of binocular rivalry. Our basic assumption is that binocular rivalry is elicited by the mutual inhibition between the right and left visual neuron systems. The mutual inhibition between two neurons is first discussed in detail, where a special emphasis is put on a fatigue effect of neurons, and then its results are applied to a simulation model of binocular rivalry.     

A dynamic model of the forearm including fatigue

A biomechanical model of the forearm, consisting of 61 muscle-tendon systems or tendons and 8 sections, is presented. The model can be used to calculate the muscle forces when resultant of the external forces and the motion is known. Calculations are based on constraints of muscle forces, joint forces, contact forces, and tendon junctions, and a load sharing principle telling which of the feasible solutions are likely and which are not. Fatigue is accounted for by updating the upper limits of the muscle forces according to the loading history. As an example, the model is used to predict the load sharing between the fingers when they are pressed against a table with a given total force.     

Neural field model of binocular rivalry waves

We present a neural field model of binocular rivalry waves in visual cortex. For each eye we consider a one-dimensional network of neurons that respond maximally to a particular feature of the corresponding image such as the orientation of a grating stimulus. Recurrent connections within each one-dimensional network are assumed to be excitatory, whereas connections between the two networks are inhibitory (cross-inhibition). Slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We derive an analytical expression for the speed of a binocular rivalry wave as a function of various neurophysiological parameters, and show how properties of the wave are consistent with the wave-like propagation of perceptual dominance observed in recent psychophysical experiments. In addition to providing an analytical framework for studying binocular rivalry waves, we show how neural field methods provide insights into the mechanisms underlying the generation of the waves. In particular, we highlight the important role of slow adaptation in providing a “symmetry breaking mechanism” that allows waves to propagate.     

Defining the importance of including transient ecosystem responses to simulate C‐cycle dynamics in a global change model

The ability of plant species to migrate is one of the critical issues in assessing accurately the future response of the terrestrial biosphere to climate change. This ability is confined by both natural and human‐induced changes in land cover. In this paper we present land‐cover and Carbon (C) cycle models designed to simulate the biospheric consequences of different types of land‐cover changes. These models, imbedded in the larger integrated assessment model IMAGE 2, were used to demonstrate the importance of considering spatial aspects for global C‐cycle modelling. A gradual‐migration, an unlimited‐migration and a no‐migration case were compared to show the range of possible consequences. Major differences between these cases were simulated for land‐cover patterns and the carbon budget. A large geographical variation in the biospheric response was also simulated. The strongest response was simulated in high‐latitude regions, especially for the migration cases in which land‐cover changes were permitted. In low‐latitudes regions the differences between the migration cases were smaller, mainly due to the effects of land‐use changes. The geographical variation among, and the different responses, the migration cases clearly demonstrate how essential it is to assess biospheric responses to climate change and land use simultaneously. Moreover, it also shows the urgent need for enhanced understanding of spatial and temporal dynamics of the biospheric responses.     

A global verification study of a quasi-static knee model with multi-bundle ligaments

The ligaments of the knee consist of fiber bundles with variable orientations, lengths and mechanical properties. In concept, however, these structures were too often seen as homogeneous structures, which are either stretched or slack during knee motions. In previous studies, we proposed a new structural concept of the ligaments of the knee. In this concept, the ligaments were considered as multi-bundle structures, with nonuniform mechanical properties and zero force lengths. The purpose of the present study was to verify this new concept.

For this purpose, laxity characteristics of a human knee joint were compared as measured in an experiment and predicted in a model simulation study. In the experiment, the varus-valgus and anterior-posterior laxities of a knee-joint specimen containing the ligaments and the articular surfaces only, were determined. From this knee-joint, geometric and mechanical parameters were derived to supply the parameters for a three-dimensional quasi-static knee-joint model. These parameters included (i) the three-dimensional insertion points of bundles, defined in the four major knee ligaments, (ii) the mechanical properties of these ligament, as functions of their relative insertion orientations and (iii) three-dimensional representations of the articular surfaces. With this model the experiments were simulated. If knee-model predictions and experimental results agree, then the multi-bundle ligament models are validated, at least with respect to their functional role in anterior-posterior and varus-valgus loading of the joint.

The model described the laxity characteristics in AP-translation and VV-rotation of the cadaveric knee-joint specimen reasonably well. Both display the same patterns of laxity changes during knee flexion. Only if a varus moment of 8 N m was applied and if the tibia was posteriorly loaded, did the model predict a slightly higher laxity than that measured experimentally.

From the model-experiment comparisons it was concluded that the proposed structural representations of the ligaments and their mechanical property distributions seem to be valid for studying the anterior-posterior and varus-valgus laxity characteristics of the human knee-joint.     

Effects of neurosteroids on a model membrane including cholesterol: A micropipette aspiration study

Amphiphilic molecules supposed to affect membrane protein activity could strongly interact also with the lipid component of the membrane itself. Neurosteroids are amphiphilic molecules that bind to plasma membrane receptors of cells in the central nervous system but their effect on membrane is still under debate. For this reason it is interesting to investigate their effects on pure lipid bilayers as model systems. Using the micropipette aspiration technique (MAT), here we studied the effects of a neurosteroid, allopregnanolone (3α,5α-tetrahydroprogesterone or Allo) and of one of its isoforms, isoallopregnanolone (3β,5α-tetrahydroprogesterone or isoAllo), on the physical properties of pure lipid bilayers composed by DOPC/bSM/chol. Allo is a well-known positive allosteric modulator of GABA_A receptor activity while isoAllo acts as a non-competitive functional antagonist of Allo modulation. We found that Allo, when applied at nanomolar concentrations (50–200 nM) to a lipid bilayer model system including cholesterol, induces an increase of the lipid bilayer area and a decrease of the mechanical parameters. Conversely, isoAllo, decreases the lipid bilayer area and, when applied, at the same nanomolar concentrations, it does not affect significantly its mechanical parameters. We characterized the kinetics of Allo uptake by the lipid bilayer and we also discussed its aspects in relation to the slow kinetics of Allo gating effects on GABA_A receptors. The overall results presented here show that a correlation exists between the modulation of Allo and isoAllo of GABA_A receptor activity and their effects on a lipid bilayer model system containing cholesterol.     

A model of neuro-musculo-skeletal system for human locomotion under position constraint condition

The human locomotion was studied on the basis of the interaction of the musculo-skeletal system, the neural system and the environment. A mathematical model of human locomotion under position constraint condition was established. Besides the neural rhythm generator, the posture controller and the sensory system, the environment feedback controller and the stability controller were taken into account in the model. The environment feedback controller was proposed for two purposes, obstacle avoidance and target position control of the swing foot. The stability controller was proposed to imitate the self-balancing ability of a human body and improve the stability of the model. In the stability controller, the ankle torque was used to control the velocity of the body gravity center. A prediction control algorithm was applied to calculate the torque magnitude of the stability controller. As an example, human stairs climbing movement was simulated and the results were given. The simulation result proved that the mathematical modeling of the task was successful.     

A bone remodelling model including the directional activity of BMUs

Bone is able to adapt itself to the mechanical and biological environment by changing its porosity and/or orientation of its internal microstructure in a process known as bone remodelling. As a consequence, a change of bone mechanical properties is produced leading to an optimum structure, able to bear the external loads with the minimum weight. This adaptation is carried out by a temporal association of cells known as BMUs (basic multicellular units) that resorb old bone and sometimes produce new organic extracellular matrix (osteoid) that is later mineralized. This involves changes in porosity, damage level (density of microcracks accumulated by cyclic loads) and mineral content. All of these features were taken into account in a previous model, but the whole process and therefore the resulting bone constitutive behaviour was considered isotropic. The model proposed herein, recognizing that bone is actually anisotropic, tries to explain how BMUs modify the anisotropy by changing their progressing direction. We check the potential of the model to predict the alignment of the bone microstructure with the external loads in different situations. Then, the model is also applied to obtain the anisotropy and mechanical properties of the human proximal femur under physiological loads with initial conditions corresponding to a heterogeneous, but otherwise isotropic bone.