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Journal Articles
Publisher: Journals Gateway
Neural Computation (2018) 30 (2): 397–427.
Published: 01 February 2018
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It has been debated whether kinematic features, such as the number of peaks or decomposed submovements in a velocity profile, indicate the number of discrete motor impulses or result from a continuous control process. The debate is particularly relevant for tasks involving target perturbation, which can alter movement kinematics. To simulate such tasks, finite-horizon models require two preset movement durations to compute two control policies before and after the perturbation. Another model employs infinite- and finite-horizon formulations to determine, respectively, movement durations and control policies, which are updated every time step. We adopted an infinite-horizon optimal feedback control model that, unlike previous approaches, does not preset movement durations or use multiple control policies. It contains both control-dependent and independent noises in system dynamics, state-dependent and independent noises in sensory feedbacks, and different delays and noise levels for visual and proprioceptive feedbacks. We analytically derived an optimal solution that can be applied continuously to move an effector toward a target regardless of whether, when, or where the target jumps. This single policy produces different numbers of peaks and “submovements” in velocity profiles for different conditions and trials. Movements that are slower or perturbed later appear to have more submovements. The model is also consistent with the observation that subjects can perform the perturbation task even without detecting the target jump or seeing their hands during reaching. Finally, because the model incorporates Weber's law via a state representation relative to the target, it explains why initial and terminal visual feedback are, respectively, less and more effective in improving end-point accuracy. Our work suggests that the number of peaks or submovements in a velocity profile does not necessarily reflect the number of motor impulses and that the difference between initial and terminal feedback does not necessarily imply a transition between open- and closed-loop strategies.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2015) 27 (5): 1058–1082.
Published: 01 May 2015
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Modeling stereo transparency with physiologically plausible mechanisms is challenging because in such frameworks, large receptive fields mix up overlapping disparities, whereas small receptive fields can reliably compute only small disparities. It seems necessary to combine information across scales. A coarse-to-fine disparity energy model, with both position- and phase-shift receptive fields, has already been proposed. However, because each scale decodes only one disparity for each location and uses the decoded disparity to select cells at the next scale, this model cannot represent overlapping surfaces at different depths. We have extended the model to solve stereo transparency. First, we introduce multiplicative connections from cells at one scale to the next to implement coarse-to-fine computation. The connection is the strongest when the presynaptic cell’s preferred disparity matches the postsynaptic cell’s position-shift parameter, encouraging the next scale to encode residual disparities with the more reliable phase-shift mechanism. This modification not only eliminates the artificial decoding and selection steps of the original model but also enables maintenance of complete population responses throughout the coarse-to-fine process. Second, because of this modification, explicit decoding is no longer necessary but rather is for visualization only. We use a simple threshold criterion to decode multiple disparities from population energy responses instead of a single disparity in the original model. We demonstrate our model using simulations on a variety of transparent and nontransparent stereograms. The model also reproduces psychophysically observed disparity interactions (averaging, thickening, attraction, and repulsion) as the depth separation between two overlapping planes varies.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2013) 25 (3): 697–724.
Published: 01 March 2013
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Optimization models explain many aspects of biological goal-directed movements. However, most such models use a finite-horizon formulation, which requires a prefixed movement duration to define a cost function and solve the optimization problem. To predict movement duration, these models have to be run multiple times with different prefixed durations until an appropriate duration is found by trial and error. The constrained minimum time model directly predicts movement duration; however, it does not consider sensory feedback and is thus applicable only to open-loop movements. To address these problems, we analyzed and simulated an infinite-horizon optimal feedback control model, with linear plants, that contains both control-dependent and control-independent noise and optimizes steady-state accuracy and energetic costs per unit time. The model applies the steady-state estimator and controller continuously to guide an effector to, and keep it at, target position. As such, it integrates movement control and posture maintenance without artificially dividing them with a precise, prefixed time boundary. Movement pace is determined by the model parameters, and the duration is an emergent property with trial-to-trial variability. By considering the mean duration, we derived both the log and power forms of Fitts's law as different approximations of the model. Moreover, the model reproduces typically observed velocity profiles and occasional transient overshoots. For unbiased sensory feedback, the effector reaches the target without bias, in contrast to finite-horizon models that systematically undershoot target when energetic cost is considered. Finally, the model does not involve backward and forward sweeps in time, its stability is easily checked, and the same solution applies to movements of different initial conditions and distances. We argue that biological systems could use steady-state solutions as default control mechanisms and might seek additional optimization of transient costs when justified or demanded by task or context.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2004) 16 (10): 2021–2040.
Published: 01 October 2004
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We investigated the differences between two well-known optimization principles for understanding movement planning: the minimum variance (MV) model of Harris and Wolpert (1998) and the minimum torque change (MTC) model of Uno, Kawato, and Suzuki (1989). Both models accurately describe the properties of human reaching movements in ordinary situations (e.g., nearly straight paths and bell-shaped velocity profiles). However, we found that the two models can make very different predictions when external forces are applied or when the movement duration is increased. We considered a second-order linear system for the motor plant that has been used previously to simulate eye movements and single-joint arm movements and were able to derive analytical solutions based on the MV and MTC assumptions. With the linear plant, the MTC model predicts that the movement velocity profile should always be symmetrical, independent of the external forces and movement duration. In contrast, the MV model strongly depends on the movement duration and the system's degree of stability; the latter in turn depends on the total forces. The MV model thus predicts a skewed velocity profile under many circumstances. For example, it predicts that the peak location should be skewed toward the end of the movement when the movement duration is increased in the absence of any elastic force. It also predicts that with appropriate viscous and elastic forces applied to increase system stability, the velocity profile should be skewed toward the beginning of the movement. The velocity profiles predicted by the MV model can even show oscillations when the plant becomes highly oscillatory. Our analytical and simulation results suggest specific experiments for testing the validity of the two models.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2004) 16 (8): 1545–1577.
Published: 01 August 2004
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Numerous studies suggest that the visual system uses both phase-and position-shift receptive field (RF) mechanisms for the processing of binocular disparity. Although the difference between these two mechanisms has been analyzed before, previous work mainly focused on disparity tuning curves instead of population responses. However, tuning curve and population response can exhibit different characteristics, and it is the latter that determines disparity estimation. Here we demonstrate, in the framework of the disparity energy model, that for relatively small disparities, the population response generated by the phase-shift mechanism is more reliable than that generated by the position-shift mechanism. This is true over a wide range of parameters, including the RF orientation. Since the phase model has its own drawbacks of underestimating large stimulus disparity and covering only a restricted range of disparity at a given scale, we propose a coarse-to-fine algorithm for disparity computation with a hybrid of phase-shift and position-shift components. In this algorithm, disparity at each scale is always estimated by the phase-shift mechanism to take advantage of its higher reliability. Since the phase-based estimation is most accurate at the smallest scale when the disparity is correspondingly small, the algorithm iteratively reduces the input disparity from coarse to fine scales by introducing a constant position-shift component to all cells for a given location in order to offset the stimulus disparity at that location. The model also incorporates orientation pooling and spatial pooling to further enhance reliability. We have tested the algorithm on both synthetic and natural stereo images and found that it often performs better than a simple scale-averaging procedure.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2000) 12 (2): 279–292.
Published: 01 February 2000
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The phase and energy methods for computing binocular disparity maps from stereograms are motivated differently, have different physiological relevances, and involve different computational steps. Nevertheless, we demonstrate that at the final stages where disparity values are made explicit, the simplest versions of the two methods are exactly equivalent. The equivalence also holds when the quadrature-pair construction in the energy method is replaced with a more physiologically plausible phase-averaging step. The equivalence fails, however, when the phase-difference receptive field model is replaced by the position-shift model. Additionally, intermediate results from the two methods are always quite distinct. In particular, the energy method generates a distributed disparity representation similar to that found in the visual cortex, while the phase method does not. Finally, more elaborate versions of the two methods are in general not equivalent. We also briefly compare these two methods with some other stereo models in the literature.
Journal Articles
Publisher: Journals Gateway
Neural Computation (1996) 8 (8): 1611–1641.
Published: 01 November 1996
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Disparity tuning of visual cells in the brain depends on the structure of their binocular receptive fields (RFs). Freeman and coworkers have found that binocular RFs of a typical simple cell can be quantitatively described by two Gabor functions with the same gaussian envelope but different phase parameters in the sinusoidal modulations (Freeman and Ohzawa 1990). This phase-parameter-based RF description has recently been questioned by Wagner and Frost (1993) based on their identification of a so-called characteristic disparity (CD) in some cells' disparity tuning curves. They concluded that their data favor the traditional binocular RF model, which assumes an overall positional shift between a cell's left and right RFs. Here we set to resolve this issue by studying the dependence of cells' disparity tuning on their underlying RF structures through mathematical analyses and computer simulations. We model the disparity tuning curves in Wagner and Frost's experiments and demonstrate that the mere existence of approximate CDs in real cells cannot be used to distinguish the phase-parameter-based RF description from the traditional position-shift-based RF description. Specifically, we found that model simple cells with either type of RF description do not have a CD. Model complex cells with the position-shift-based RF description have a precise CD, and those with the phase-parameter-based RF description have an approximate CD. We also suggest methods for correctly distinguishing the two types of RF descriptions. A hybrid of the two RF models may be required to fit the behavior of some real cells, and we show how to determine the relative contributions of the two RF models.
Journal Articles
Publisher: Journals Gateway
Neural Computation (1995) 7 (4): 735–752.
Published: 01 July 1995
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Lisberger and Sejnowski (1992) recently proposed a computational model for motor learning in the vestibular-ocular reflex (VOR) system. They showed that the steady-state gain of the system can be modified by changing the ratio of the two time constants along the feedforward and the feedback projections to the Purkinje cell unit in their model VOR network. Here we generalize their model by including two additional time constant variables and two synaptic weight variables, which were set to fixed values in their original model. We derive the stability conditions of the generalized system and thoroughly analyze its steady-state and transient behavior. It is found that the generalized system can display a continuum of behavior with the Lisberger-Sejnowski model and a static model proposed by Miles et al . (1980b) as special cases. Moreover, although mathematically the Lisberger-Sejnowski model requires two precise relationships among its parameters, the model is robust against small perturbations from the physiological point of view. Additional considerations on the gain of smooth pursuit eye movement, which is believed to share the positive feedback loop with the VOR network, suggest that the VOR network should operate in the parameter range favoring the behavior studied by Lisberger and Sejnowski. Under this condition, the steady-state gain of the VOR is found to depend on all four time constants in the network. The time constant of the Purkinje cell unit should be relatively small in order to achieve effective VOR learning through the modifications of the other time constants. Our analysis provides a thorough characterization of the system and could thus be useful for guiding further physiological tests of the model.
Journal Articles
Publisher: Journals Gateway
Neural Computation (1994) 6 (3): 390–404.
Published: 01 May 1994
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Many models for stereo disparity computation have been proposed, but few can be said to be truly biological. There is also a rich literature devoted to physiological studies of stereopsis. Cells sensitive to binocular disparity have been found in the visual cortex, but it is not clear whether these cells could be used to compute disparity maps from stereograms. Here we propose a model for biological stereo vision based on known receptive field profiles of binocular cells in the visual cortex and provide the first demonstration that these cells could effectively solve random dot stereograms. Our model also allows a natural integration of stereo vision and motion detection. This may help explain the existence of units tuned to both disparity and motion in the visual cortex.