The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate “causal map ” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or Bayes nets. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2to 4-year-old children construct new causal maps and that their learning is consistent with the Bayes net formalism.

A global shape judgement task was used to investigate the combination of stereopsis and kinetic depth. With botb cues present, there were no distortions of shape perception, even under conditions where either cue alone did show such distortions. We suggest that the addition of motion information overcomes the stereo distance scaling problem. However, when incongruent combinations of disparity and motion were used, the results did not match predictions of a number of combination theories. These data could be described by a model which used weighted linear combination afier correctly scaling disparities for viewing distance. When the motion cue was weakened by presenting only two frames of each motion sequence, stereo was weighted more heavily. Stereopsis Structure-from-motion Three-dimensional shape perception Integration of depth cues

Obtaining exact depth from binocular disparities is hard if camera calibration is needed. We will show that qualitative information can be obtained from stereo disparities with little computation, and without prior knowledge (or computation) of camera parameters. First, we derive two expressions that order all matched points in the images by depth in two distinct ways from image coordinates only. Using one for tilt estimation and point separation (in depth) demonstrates some anomalies observed in psychophysical experiments, most notably the "induced size effect". We apply the same approach to detect qualitative changes in the curvature of a contour on the surface of an object, with either x- or y-coordinate fixed. Second, we develop an algorithm to compute axes of zero-curvature from disparities alone. The algorithm is shown to be quite robust against violations of its basic assumptions for synthetic data with relatively large controlled deviations. It performs almost as well on real i...

The geometry of binocular projection is analyzed in relation to the primate visual system. An oculomotor parameterization that includes the classical vergence and version angles is defined. It is shown that the epipolar geometry of the system is constrained by binocular coordination of the eyes. A local model of the scene is adopted in which depth is measured relative to a plane containing the fixation point. These constructions lead to an explicit parameterization of the binocular disparity field involving the gaze angles as well as the scene structure. The representation of visual direction and depth is discussed with reference to the relevant psychophysical and neurophysiological literature. © 2008 Optical Society of America OCIS codes: 330.1400, 330.2210. 1.

Neurons in the visual cortex of monkeys respond selectively to the disparity between the images in the two eyes. Recent recordings have shown that some of the disparity-selective neurons in the primary visual cortex and the posterior parietal cortex are modulated by the distance of fixation. A population of such gain-modulated, disparity-selective neurons forms a set of basis functions of horizontal disparity and distance of fixation that can be used as an intermediate representation for computing egocentric distance. This distributed representation is consistent with psychophysical studies of human depth perception; in contrast, neurons explicitly tuned to distance are not consistent with how we perceive distance. In a population model that includes noise in the firing rates of neurons, the perceived distance is

We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distorted version of actual, physical space can be computed. This paper develops a computational geometric model that explains why such distortion might take place. The basic idea is that, both in stereo and motion, we perceive the world from multiple views. Given the rigid transformation between the views and the properties of the image correspondence, the depth of the scene can be obtained. Even a slight error in the rigid transformation parameters c...

When an object’s motion is influenced by gravity, as in the rise and fall of a thrown ball, the vertical component of acceleration is roughly constant at 9.8 m/sec 2. In principle, an observer could use this information to estimate the absolute size and distance of the object (Saxberg, 1987a; Watson, Banks, von Hofsten, & Royden, 1992). In five experiments, we examined people’s ability to utilize the size and distance information provided by gravitational acceleration. Observers viewed computer simulations of an object rising and falling on a trajectory aligned with the gravitational vector. The simulated objects were balls of different diameters presented across a wide range of simulated distances. Observers were asked to identify the ball that was presented and to estimate its distance. The results showed that observers were much more sensitive to average velocity than to the gravitational acceleration pattern. Likewise, verticality of the motion and visibility of the trajectory’s apex had negligible effects on the accuracy of size and distance judgments. People need to process the absolute distance and size of objects in order to act in the environment. For example, in order to catch and grasp a thrown ball successfully, a person must place his/her hands in the appropriate

Abstract. Binocular information about the structure of a scene is contained in the relative positions of corresponding points in the two views. If the eyes rotate, in order to fixate a different target, then the disparity at a given image location is likely to change. Quite different disparities can be produced at the same location, as the eyes move from one fixation-point to the next. The pointwise variability of the disparity map is problematic for biological visual systems, in which stereopsis is based on simple, short-range mechanisms. It is argued here that the problem can be addressed in two ways; firstly by an appropriate representation of disparity, and secondly by learning the typical pattern of image correspondences. It is shown that the average spatial structure of the disparity field can be estimated, by integrating over a series of binocular fixations. An algorithm based on this idea is tested on natural images. Finally, it is shown how the average pattern of disparities could help to put the images into binocular correspondence. 1

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We measured the ability to fuse dichoptic images of a horizontal line alone or in the presence of a textured background with different vertical disparity. Nonius-line measurements of vertical vergence were also obtained. Diplopia thresholds and vertical vergence gains were much higher in response to an isolated vertically disparate line than to one with a zero vertical-disparity background. The effect of the background was maximum when it was coplanar with the target and decreased with increasing relative horizontal disparity. We conclude that vertical disparities are integrated over a restricted range of horizontal disparities to drive vertical vergence. 2000 Elsevier Science Ltd. All rights reserved.