Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Brains, it has recently been argued, are essentially prediction machines. They are bundles of cells that support perception and action by constantly attempting to match incoming sensory inputs with top-down expectations or predictions. This is achieved using a hierarchical generative model that aims to minimize prediction error within a bidirectional cascade of cortical processing. Such accounts offer a unifying model of perception and action, illuminate the functional role of attention, and may neatly capture the special contribution of cortical processing to adaptive success. This target article critically examines this "hierarchical prediction machine" approach, concluding that it offers the best clue yet to the shape of a unified science of mind and action. Sections 1 and 2 lay out the key elements and implications of the approach. Section 3 explores a variety of pitfalls and challenges, spanning the evidential, the methodological, and the more properly conceptual. The paper ends (sections 4 and 5) by asking how such approaches might impact our more general vision of mind, experience, and agency.

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Whatever next? Predictive brains, situated agents, and the future of cognitive science

Three-dimensional (3D) displays have become important for many applications including vision research, operation of remote devices, medical imaging, surgical training, scientific visualization, virtual prototyping, and more. In many of these applications, it is important for the graphic image to create a faithful impression of the 3D structure of the portrayed object or scene. Unfortunately, 3D displays often yield distortions in perceived 3D structure compared with the percepts of the real scenes the displays depict. A likely cause of such distortions is the fact that computer displays present images on one surface. Thus, focus cues-accommodation and blur in the retinal image-specify the depth of the display rather than the depths in the depicted scene. Additionally, the uncoupling of vergence and accommodation required by 3D displays frequently reduces one's ability to fuse the binocular stimulus and causes discomfort and fatigue for the viewer. We have developed a novel 3D display that presents focus cues that are correct or nearly correct for the depicted scene. We used this display to evaluate the influence of focus cues on perceptual distortions, fusion failures, and fatigue. We show that when focus cues are correct or nearly correct, (1) the time required to identify a stereoscopic stimulus is reduced, (2) stereoacuity in a time-limited task is increased, (3) distortions in perceived depth are reduced, and (4) viewer fatigue and discomfort are reduced. We discuss the implications of this work for vision research and the design and use of displays.

Vergence-accommodation conflicts hinder visual performance and cause visual fatigue.

In 1912, Max Wertheimer published his paper on phi motion, widely recognized as the start of Gestalt psychology. Because of its continued relevance in modern psychology, this centennial anniversary is an excellent opportunity to take stock of what Gestalt psychology has offered and how it has changed since its inception. We first introduce the key findings and ideas in the Berlin school of Gestalt psychology, and then briefly sketch its development, rise, and fall. Next, we discuss its empirical and conceptual problems, and indicate how they are addressed in contemporary research on perceptual grouping and figure–ground organization. In particular, we review the principles of grouping, both classical (e.g., proximity, similarity, common fate, good continuation, closure, symmetry, parallelism) and new (e.g., synchrony, common region, element and uniform connectedness), and their role in contour integration and completion. We then review classic and new image-based principles of figure–ground organization, how it is influenced by past experience and attention, and how it relates to shape and depth perception. After an integrated review of the neural mechanisms involved in contour grouping, border ownership, and figure–ground perception, we conclude by evaluating what modern vision science has offered compared to traditional Gestalt psychology, whether we can speak of a Gestalt revival, and where the remaining limitations and challenges lie. A better integration of this research tradition with the rest of vision science requires further progress regarding the conceptual and theoretical foundations of the Gestalt approach, which is the focus of a second review article.

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A Century of Gestalt Psychology in Visual Perception I. Perceptual Grouping and Figure-Ground Organization

Visual discomfort has been the subject of considerable research in relation to stereoscopic and autostereoscopic displays. In this paper, the importance of various causes and aspects of visual discomfort is clarified. When disparity values do not surpass a limit of 1°, which still provides sufficient range to allow satisfactory depth perception in stereoscopic television, classical determinants such as excessive binocular parallax and accommodation-vergence conflict appear to be of minor importance. Visual discomfort, however, may still occur within this limit and we believe the following factors to be the most pertinent in contributing to this: (1) temporally changing demand of accommodation-vergence linkage, e.g., by fast motion in depth; (2) three-dimensional artifacts resulting from insufficient depth information in the incoming data signal yielding spatial and temporal inconsistencies; and (3) unnatural blur. In order to ad- equately characterize and understand visual discomfort, multiple types of measurements, both objective and subjective, are required. © 2009 Society for Imaging Science and Technology. DOI: 10.2352/J.ImagingSci.Technol.2009.53.3.030201

Visual Discomfort and Visual Fatigue of Stereoscopic Displays: A Review

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.

The statistical determinants of adaptation rate in human reaching.

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.

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The combination of vision and touch depends on spatial proximity

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 high-precision, 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.

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Optimal defocus estimation in individual natural images

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.

Optimal disparity estimation in natural stereo images

The shape of the contour separating two regions strongly influences judgments of which region is “figure” and which is “ground.” Convexity and other figure–ground cues are generally assumed to indicate only which region is nearer, but nothing about how much the regions are separated in depth. To determine the depth information conveyed by convexity, we examined natural scenes and found that depth steps across surfaces with convex silhouettes are likely to be larger than steps across surfaces with concave silhouettes. In a psychophysical experiment, we found that humans exploit this correlation. For a given binocular disparity, observers perceived more depth when the near surface's silhouette was convex rather than concave. We estimated the depth distributions observers used in making those judgments: they were similar to the natural-scene distributions. Our findings show that convexity should be reclassified as a metric depth cue. They also suggest that the dichotomy between metric and nonmetric depth cues is false and that the depth information provided many cues should be evaluated with respect to natural-scene statistics. Finally, the findings provide an explanation for why figure–ground cues modulate the responses of disparity-sensitive cells in visual cortex.

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Johannes Burge

Papers

The statistical determinants of adaptation rate in human reaching.

The combination of vision and touch depends on spatial proximity

Optimal defocus estimation in individual natural images

Optimal disparity estimation in natural stereo images

Natural-Scene Statistics Predict How the Figure–Ground Cue of Convexity Affects Human Depth Perception