Rapid reaching to a target is generally accurate but also contains random and systematic error. Random errors result from noise in visual measurement, motor planning, and reach execution. Systematic error results from systematic changes in the mapping between the visual estimate of target location and the motor command necessary to reach the target (e.g., new spectacles, muscular fatigue). Humans maintain accurate reaching by recalibrating the visuomotor system, but no widely accepted computational model of the process exists. Given certain boundary conditions, a statistically optimal solution is a Kalman filter. We compared human to Kalman filter behavior to determine how humans take into account the statistical properties of errors and the reliability with which those errors can be measured. For most conditions, human and Kalman filter behavior was similar: Increasing measurement uncertainty caused similar decreases in recalibration rate; directionally asymmetric uncertainty caused different rates in different directions; more variation in systematic error increased recalibration rate. However, behavior differed in one respect: Inserting random error by perturbing feedback position causes slower adaptation in Kalman filters but had no effect in humans. This difference may be due to how biological systems remain responsive to changes in environmental statistics. We discuss the implications of this work.
A great challenge of systems neuroscience is to understand the computations that underlie perceptual constancies, the ability to represent behaviorally relevant stimulus properties as constant even when irrelevant stimulus properties vary. As signals proceed through the visual system, neural states become more selective for properties of the environment, and more invariant to irrelevant features of the retinal images. Here, we describe a method for determining the computations that perform these transformations optimally, and apply it to the specific computational task of estimating a powerful depth cue: binocular disparity. We simultaneously determine the optimal receptive field population for encoding natural stereo images of locally planar surfaces and the optimal nonlinear units for decoding the population responses into estimates of disparity. The optimal processing predicts well-established properties of neurons in cortex. Estimation performance parallels important aspects of human performance. Thus, by analyzing the photoreceptor responses to natural images, we provide a normative account of the neurophysiology and psychophysics of absolute disparity processing. Critically, the optimal processing rules are not arbitrarily chosen to match the properties of neurophysiological processing, nor are they fit to match behavioral performance. Rather, they are dictated by the task-relevant statistical properties of complex natural stimuli. Our approach reveals how selective invariant tuning-especially for properties not trivially available in the retinal images-could be implemented in neural systems to maximize performance in particular tasks.
The nervous system often combines visual and haptic information about object properties such that the combined estimate is more precise than with vision or haptics alone. We examined how the system determines when to combine the signals. Presumably, signals should not be combined when they come from different objects. The likelihood that signals come from different objects is highly correlated with the spatial separation between the signals, so we asked how the spatial separation between visual and haptic signals affects their combination. To do this, we first created conditions for each observer in which the effect of combination--the increase in discrimination precision with two modalities relative to performance with one modality--should be maximal. Then under these conditions, we presented visual and haptic stimuli separated by different spatial distances and compared human performance with predictions of a model that combined signals optimally. We found that discrimination precision was essentially optimal when the signals came from the same location, and that discrimination precision was poorer when the signals came from different locations. Thus, the mechanism of visual-haptic combination is specialized for signals that coincide in space.
Defocus blur is nearly always present in natural images: Objects at only one distance can be perfectly focused. Images of objects at other distances are blurred by an amount depending on pupil diameter and lens properties. Despite the fact that defocus is of great behavioral, perceptual, and biological importance, it is unknown how biological systems estimate defocus. Given a set of natural scenes and the properties of the vision system, we show from first principles how to optimally estimate defocus at each location in any individual image. We show for the human visual system that highprecision, unbiased estimates are obtainable under natural viewing conditions for patches with detectable contrast. The high quality of the estimates is surprising given the heterogeneity of natural images. Additionally, we quantify the degree to which the sign ambiguity often attributed to defocus is resolved by monochromatic aberrations (other than defocus) and chromatic aberrations; chromatic aberrations fully resolve the sign ambiguity. Finally, we show that simple spatial and spatio-chromatic receptive fields extract the information optimally. The approach can be tailored to any environment-vision system pairing: natural or man-made, animal or machine. Thus, it provides a principled general framework for analyzing the psychophysics and neurophysiology of defocus estimation in species across the animal kingdom and for developing optimal image-based defocus and depth estimation algorithms for computational vision systems.optics | sensor sampling | Bayesian statistics | depth perception | auto-focus
We introduce a novel framework for estimating visual sensitivity using a continuous target-tracking task in concert with a dynamic internal model of human visual performance. Observers used a mouse cursor to track the center of a two-dimensional Gaussian luminance blob as it moved in a random walk in a field of dynamic additive Gaussian luminance noise. To estimate visual sensitivity, we fit a Kalman filter model to the human tracking data under the assumption that humans behave as Bayesian ideal observers. Such observers optimally combine prior information with noisy observations to produce an estimate of target position at each time step. We found that estimates of human sensory noise obtained from the Kalman filter fit were highly correlated with traditional psychophysical measures of human sensitivity (R2 > 97%). Because each frame of the tracking task is effectively a "minitrial," this technique reduces the amount of time required to assess sensitivity compared with traditional psychophysics. Furthermore, because the task is fast, easy, and fun, it could be used to assess children, certain clinical patients, and other populations that may get impatient with traditional psychophysics. Importantly, the modeling framework provides estimates of decision variable variance that are directly comparable with those obtained from traditional psychophysics. Further, we show that easily computed summary statistics of the tracking data can also accurately predict relative sensitivity (i.e., traditional sensitivity to within a scale factor).
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