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     

Applicability of quadratic and threshold models to motion discrimination in the rabbit retina

Computational and behavioral studies suggest that visual motion discrimination is based on quadratic nonlinearities. This raises the question of whether the behavior of motion sensitive neurons early in the visual system is actually quadratic. Theoretical studies show that mechanisms proposed for retinal directional selectivity do not behave quadratically at high stimulus contrast. However, for low contrast stimuli, models for these mechanisms may be grouped into three categories: purely quadratic, quadratic accompanied by a rectification, and models mediated by a high level threshold. We discriminated between these alternatives by analyzing the extracellular responses of ON-OFF directionally selective ganglion cells of the rabbit retina to drifting periodic gratings. The data show that purely-quadratic or high-threshold systems do not account for the behavior of these cells. However, their behavior is consistent with a rectified-quadratic model.     

Adaptive, fast walking in a biped robot under neuronal control and learning

Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (>3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks.     

Associative learning and discrimination of motion cues in the harnessed honeybee Apis mellifera L.

We previously studied a conditioning paradigm to associate the proboscis extension reflex (PER) with monochromatic light (conditioned stimulus; CS) in harnessed honeybees. Here, we established a novel conditioning paradigm to associate the PER with a motion cue generated using graphics interchange format (GIF) animations with a speed of 12 mm/s speed and a frame rate of 25 Hz as the CS, which were projected onto a screen consisting of a translucent circular cone that largely covered the visual field of the harnessed bee using two liquid crystal projectors. The acquisition rate reached a plateau at approximately 40% after seven trials, indicating that the bees were successfully conditioned with the motion cue. We demonstrated four properties of the conditioning paradigm. First, the acquisition rate was enhanced by antennae deprivation, suggesting that sensory input from the antennae interferes with the visual associative learning. Second, bees conditioned with a backward-direction motion cue did not respond to the forward-direction, suggesting that bees can discriminate the two directions in this paradigm. Third, the bees can retain memory for motion cue direction for 48 h. Finally, the acquisition rate did not differ significantly between foragers and nurse bees. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A computational approach to motion perception

In this paper it is shown that the computation of the optical flow from a sequence of timevarying images is not, in general, an underconstrained problem. A local algorithm for the computation of the optical flow which uses second order derivatives of the image brightness pattern, and that avoids the aperture problem, is presented. The obtained optical flow is very similar to the true motion field — which is the vector field associated with moving features on the image plane — and can be used to recover 3D motion information. Experimental results on sequences of real images, together with estimates of relevant motion parameters, like time-to-crash for translation and angular velocity for rotation, are presented and discussed. Due to the remarkable accuracy which can be achieved in estimating motion parameters, the proposed method is likely to be very useful in a number of computer vision applications.     

Deep learning for computational biology

Technological advances in genomics and imaging have led to an explosion of molecular and cellular profiling data from large numbers of samples. This rapid increase in biological data dimension and acquisition rate is challenging conventional analysis strategies. Modern machine learning methods, such as deep learning, promise to leverage very large data sets for finding hidden structure within them, and for making accurate predictions. In this review, we discuss applications of this new breed of analysis approaches in regulatory genomics and cellular imaging. We provide background of what deep learning is, and the settings in which it can be successfully applied to derive biological insights. In addition to presenting specific applications and providing tips for practical use, we also highlight possible pitfalls and limitations to guide computational biologists when and how to make the most use of this new technology.     

Role of ACh-GABA cotransmission in detecting image motion and motion direction

Starburst amacrine cells (SACs) process complex visual signals in the retina using both acetylcholine (ACh) and gamma-aminobutyric acid (GABA), but the synaptic organization and function of ACh-GABA corelease remain unclear. Here, we show that SACs make cholinergic synapses onto On-Off direction-selective ganglion cells (DSGCs) from all directions but make GABAergic synapses onto DSGCs only from the null direction. ACh and GABA were released differentially in a Ca(2+) level-specific manner, suggesting the two transmitters were released from different vesicle populations. Despite the symmetric cholinergic connection, the light-evoked cholinergic input to a DSGC, detected at both light onset and offset, was motion- and direction-sensitive. This input was facilitated by two-spot apparent motion in the preferred direction but supressed in the null direction, presumably by a GABAergic mechanism. The results revealed a high level of synaptic intricacy in the starburst circuit and suggested differential, yet synergistic, roles of ACh-GABA cotransmission in motion sensitivity and direction selectivity.     

Temporal discrimination learning by pigeons

Memory for time by animals appears to undergo a systematic shortening. This so-called choose-short effect can be seen in a conditional temporal discrimination when a delay is inserted between the sample and comparison stimuli. We have proposed that this temporal shortening may result from a procedural artifact in which the delay appears similar to the intertrial interval and thus, produces an inadvertent ambiguity or 'instructional failure'. When this ambiguity is avoided by distinguishing the intertrial interval from the delay, as well as the samples from the delay, the temporal shortening effect and other asymmetries often disappear. By avoiding artifacts that can lead to a misinterpretation of results, we may understand better how animals represent time. An alternative procedure for studying temporal discriminations is with the psychophysical bisection procedure in which following conditional discrimination training, intermediate durations are presented and the point of subjective equality is determined. Research using the bisection procedure has shown that pigeons represent temporal durations not only as their absolute value but also relative to durations from which they must be discriminated. Using this procedure, we have also found that time passes subjectively slower when animals are required to respond to the to-be-timed stimulus.     

A computational framework for cortical learning

Recent physiological findings have revealed that long-term adaptation of the synaptic strengths between cortical pyramidal neurons depends on the temporal order of presynaptic and postsynaptic spikes, which is called spike-timing-dependent plasticity (STDP) or temporally asymmetric Hebbian (TAH) learning. Here I prove by analytical means that a physiologically plausible variant of STDP adapts synaptic strengths such that the presynaptic spikes predict the postsynaptic spikes with minimal error. This prediction error model of STDP implies a mechanism for cortical memory: cortical tissue learns temporal spike patterns if these spike patterns are repeatedly elicited in a set of pyramidal neurons. The trained network finishes these patterns if their beginnings are presented, thereby recalling the memory. Implementations of the proposed algorithms may be useful for applications in voice recognition and computer vision.     

The computational neurobiology of learning and reward

Following the suggestion that midbrain dopaminergic neurons encode a signal, known as a 'reward prediction error', used by artificial intelligence algorithms for learning to choose advantageous actions, the study of the neural substrates for reward-based learning has been strongly influenced by computational theories. In recent work, such theories have been increasingly integrated into experimental design and analysis. Such hybrid approaches have offered detailed new insights into the function of a number of brain areas, especially the cortex and basal ganglia. In part this is because these approaches enable the study of neural correlates of subjective factors (such as a participant's beliefs about the reward to be received for performing some action) that the computational theories purport to quantify.     

Matched filtering in motion detection and discrimination

When humans detect and discriminate visual motion, some neural mechanism extracts the motion information that is embedded in the noisy spatio-temporal stimulus. We show that an ideal mechanism in a motion discrimination experiment cross-correlates the received waveform with the signals to be discriminated. If the human visual system uses such a cross-correlator mechanism, discrimination performance should depend on the cross-correlation between the two signals. Manipulations of the signals' cross-correlation using differences in the speed and phase of moving gratings produced the predicted changes in the performance of human observers. The cross-correlator's motion performance improves linearly as contrast increases and human performance is similar. The ideal cross-correlator can be implemented by passing the stimulus through linear spatio-temporal filters matched to the signals. We propose that directionally selective simple cells in the striate cortex serve as matched filters during motion detection and discrimination.     

Similarity and discrimination learning in humans

In an experiment involving a new behavioural preparation the role played by similarity in discrimination learning was examined using visual patterns (i.e., paintings) that might share common elements (specifically, A, BC, and ABC). A-C were small stars of three specific colours (target colours), which were intermixed with other stars of two different colours (distracting colours). The target colours were balanced through A-C. Students received discrimination training in which a fictitious painter was the author of paintings A and BC, while paintings ABC were assigned to a second fictitious painter. During training, the students had to make a choice, in the presence of each pattern, between two response keys, each of them indicating one of the painters. The time taken to respond was also measured. Feedback was always given after each key-press. The results showed that while at times the A+ ABC- discrimination was acquired more readily than was the BC+ ABC- discrimination, on other occasions the reverse was also true, the critical factor being the way in which the colours were combined.     

Contribution to the theory of discrimination learning

In the first two sections, which deal, respectively, with simple and double (or successive) discrimination, a comparison is made between the theory presented and certain experiments on time discrimination. Section III sets forth a possible theoretical approach to multiple choice discrimination.     

A motion direction map in macaque V2

In mammals, the perception of motion starts with direction-selective neurons in the visual cortex. Despite numerous studies in monkey primary and second visual cortex (V1 and V2), there has been no evidence of direction maps in these areas. In the present study, we used optical imaging methods to study the organization of motion response in macaque V1 and V2. In contrast to the findings in other mammals (e.g., cats and ferrets), we found no direction maps in macaque V1. Robust direction maps, however, were found in V2 thick/pale stripes and avoided thin stripes. In many cases direction maps were located within thick stripes and exhibited pinwheel or linear organizations. The presence of motion maps in V2 points to a newfound prominence of V2 in motion processing, for contributing to motion perception in the dorsal pathway and/or for motion cue-dependent form perception in the ventral pathway.     

Theoretical and computational models of ion channels

Computational studies can make meaningful contributions to our understanding of biological ion channels. A wide variety of methods, at different levels of approximation, can be used. Over the past few years, progress in the experimental determination of three-dimensional structures has given a fresh impetus to the theorists. Noteworthy progress has been made in carefully constructing realistic models of a number of complex biological channels to address important questions about their function.