Geometrical Modeling from Multiple Stereo Views

The components of the Sheffield Artificial Intelligence Vision Research Unit (AIVRU) three-dimensional (3D) vision sys tem, which currently supports model-based object recognition and location, are described. Its potential for robotics applica tions is demonstrated by its guidance of a Universal Machine Intelligence robot arm in a pick-and-place task. The system comprises (1) the recovery of a sparse depth map using edge- based, passive stereo triangulation; (2) the grouping, descrip tion, and segmentation of edge segments to recover a 3D representation of the scene geometry in terms of straight lines and circular arcs; (3) the statistical combination of 3D de scriptions for object model creation from multiple stereo views and the propagation of constraints for within-view re finement ; and (4) the matching of 3D wireframe object models to 3D scene descriptions in order to recover an initial estimate of their position and orientation.

Computation of Binocular Eye Position from Vertical Disparities with the use of Probabilistic Place Coding

Stereoscopic vision exploits the fact that points in a 3-D scene will in general project to different locations in the images in the left and the right eye. The differences in retinal locations, measured horizontally and vertically, are called horizontal ( H) and vertical ( V) disparities respectively. Their size is affected by the positions of the eyes which determine the viewing geometry parameters, that is distance to the fixation point ( d) and the angle of gaze ( g). H is also affected by the depth of the scene point relative to fixation distance, which is why one can recover 3-D scene structure using binocular vision. Achieving metric reconstruction requires knowledge of d and g to allow for their influence on H. Computational analyses have shown that d and g can in principle be recovered from V because of its relative insensitivity to scene depth variations. As d and g are the only two unknowns in the equation for V, in theory only two measurements of V (at suitable retinal locations) are needed. A practical system, however, dealing with noisy images composed of many points, needs to pool information from measurements of V at numerous retinal locations. A place-coding algorithm of the Hough transform type is well suited to this purpose (S A Peek, J E W Mayhew, J P Frisby, 1984 Image and Vision Computing2 180 – 190), but it has not hitherto been used in a way which deals appropriately with measurement noise. We describe how this can be done and demonstrate with computer simulations greatly improved estimation of d and g as well as improved robustness to noise. The new method also permits the solution of an important aspect of the stereo correspondence problem—that of finding epipolar lines.

Recruitment in retractor bulbi muscle during eyeblink conditioning: EMG analysis and common-drive model

To analyze properly the role of the cerebellum in classical conditioning of the eyeblink and nictitating membrane (NM) response, the control of conditioned response dynamics must be better understood. Previous studies have suggested that the control signal is linearly related to the CR as a result of recruitment within the accessory abducens motoneuron pool, which acts to linearize retractor bulbi muscle and NM response mechanics. Here we investigate possible recruitment mechanisms. Data came from simultaneous recordings of NM position and multiunit electromyographic (EMG) activity from the retractor bulbi muscle of rabbits during eyeblink conditioning, in which tone and periocular shock act as conditional and unconditional stimuli, respectively. Action potentials (spikes) were extracted and classified by amplitude. Firing rates of spikes with different amplitudes were analyzed with respect to NM response temporal profiles and total EMG spike firing rate. Four main regularities were revealed and quantified: 1) spike amplitude increased with response amplitude; 2) smaller spikes always appeared before larger spikes; 3) subsequent firing rates covaried for spikes of different amplitude, with smaller spikes always firing at higher rates than larger ones; and 4) firing-rate profiles were approximately Gaussian for all amplitudes. These regularities suggest that recruitment does take place in the retractor bulbi muscle during conditioned NM responses and that all motoneurons receive the same command signal (common-drive hypothesis). To test this hypothesis, a model of the motoneuron pool was constructed in which motoneurons had a range of intrinsic thresholds distributed exponentially, with threshold linearly related to EMG spike amplitude. Each neuron received the same input signal as required by the common-drive assumption. This simple model reproduced the main features of the data, suggesting that conditioned NM responses are controlled by a common-drive mechanism that enables simple commands to determine response topography in a linear fashion.

Where is the light? Bayesian perceptual priors for lighting direction

Perception of shaded three-dimensional figures is inherently ambiguous, but this ambiguity can be resolved if the brain assumes that figures are lit from a specific direction. Under the Bayesian framework, the visual system assigns a weighting to each possible direction, and these weightings define a prior probability distribution for light-source direction. Here, we describe a non-parametric maximum-likelihood estimation method for finding the prior distribution for lighting direction. Our results suggest that each observer has a distinct prior distribution, with non-zero values in all directions, but with a peak which indicates observers are biased to expect light to come from above left. The implications of these results for estimating general perceptual priors are discussed.

Evidence from retractor bulbi EMG for linearized motor control of conditioned nictitating membrane responses

Classical conditioning of nictitating membrane (NM) responses in rabbits is a robust model learning system, and experimental evidence indicates that conditioned responses (CRs) are controlled by the cerebellum. It is unknown whether cerebellar control signals deal directly with the complex nonlinearities of the plant (blink-related muscles and peripheral tissues) or whether the plant is linearized to ensure a simple relation between cerebellar neuronal firing and CR profile. To study this question, the retractor bulbi muscle EMG was recorded with implanted electrodes during NM conditioning. Pooled activity in accessory abducens motoneurons was estimated from spike trains extracted from the EMG traces, and its temporal profile was found to have an approximately Gaussian shape with peak amplitude linearly related to CR amplitude. The relation between motoneuron activity and CR profiles was accurately fitted by a first-order linear filter, with each spike input producing an exponentially decaying impulse response with time constant of order 0.1 s. Application of this first-order plant model to CR data from other laboratories suggested that, in these cases also, motoneuron activity had a Gaussian profile, with time-of-peak close to unconditioned stimulus (US) onset and SD proportional to the interval between conditioned stimulus and US onsets. These results suggest that for conditioned NM responses the cerebellum is presented with a simplified "virtual" plant that is a linearized version of the underlying nonlinear biological system. Analysis of a detailed plant model suggests that one method for linearising the plant would be appropriate recruitment of motor units.

Long Time-Constant Behavior of the Oculomotor Plant in Barbiturate-Anesthetized Primate

The mechanics of the extraocular muscles and orbital tissue (“oculomotor plant”) can be approximated by a small number of viscoelastic (Voigt) elements in series. Recent analysis of the eye's return from displacement in lightly anesthetized rhesus monkeys has suggested a four-element plant model with time constants (TCs) of ∼0.01, 0.1, 1, and 10 s. To demonstrate directly the presence of long (1,10 s) TC elements and to assess their contribution quantitatively, horizontal eye displacement was induced in Cynomolgus monkeys under deep barbiturate anesthesia that prevented interference from spontaneous eye movements. The displacement was maintained for either a prolonged (30 s) or brief (0.2 s) period before release. Return to resting position took 20–30 s after prolonged displacement but only 1–2 s after brief displacement, consistent with the presence of long TC elements that would only be substantially stretched in the former condition. Quantitative fitting of the release curves after prolonged displacement indicated that the two long TC elements contribute a substantial proportion (∼30%) of the total plant compliance. A model based on the estimated compliance values is shown to account quantitatively both for our release data and for Goldstein and Robinson's data on hysteresis of ocular motoneuron firing rates measured after centripetal saccades following prolonged eccentric fixation. Long time-constant elements in the plant thus make a substantial contribution to some types of eye movement, and their inclusion in plant models can help interpret the firing patterns of single units in the oculomotor system.

Spatiotemporal independent component analysis of event-related fMRI data using skewed probability density functions

We introduce two independent component analysis (ICA) methods, spatiotemporal ICA (stICA) and skew-ICA, and demonstrate the utility of these methods in analyzing synthetic and event-related fMRI data. First, stICA simultaneously maximizes statistical independence over both time and space. This contrasts with conventional ICA methods, which maximize independence either over time only or over space only; these methods often yield physically improbable solutions. Second, skew-ICA is based on the assumption that images have skewed probability density functions (pdfs), an assumption consistent with spatially localized regions of activity. In contrast, conventional ICA is based on the physiologically unrealistic assumption that images have symmetric pdfs. We combine stICA and skew-ICA, to form skew-stICA, and use it to analyze synthetic data and data from an event-related, left-right visual hemifield fMRI experiment. Results obtained with skew-stICA are superior to those of principal component analysis, spatial ICA (sICA), temporal ICA, stICA, and skew-sICA. We argue that skew-stICA works because it is based on physically realistic assumptions and that the potential of ICA can only be realized if such prior knowledge is incorporated into ICA methods.

Exploring sequential stereopsis for co-planarity tasks

We used the sequential stereopsis paradigm and apparatus described by Enright (Vision Research, 36, (1996) 307-312). The observer's task was to set targets to equidistance in Experiments 1-3, and to make them co-planar in Experiment 4. However, it is argued that in all experiments observers exploited a co-planarity setting strategy. Sequential stereopsis produced good performance throughout in terms of low disparity thresholds when head position was varied by rotations around three axes: vertical (azimuth condition); horizontal (elevation); and midline (tilt). It also produced good performance when the targets were shifted in position so that they both lay on one side of the median plane of the head. These results cannot be accounted for by Enright's isovergence hypothesis unless it is extended to incorporate other information about eye positions. Performance was better but not greatly so in control simultaneous stereopsis conditions, nor did it deteriorate much when the observer's view was restricted solely to the targets by removing visibility of the room in which the apparatus was located. Target settings were typically located on a concave arc centred on the median plane. This effect was quantitatively modelled using disparity correction for a relief task of co-planarity (Gârding, Porrill, Mayhew, & Frisby. Vision Research, 35 (1995) 703-722). This modelling indicated over-estimations of c.10-20 cm in fixation distance for target distances in the range 71.5-112.5 cm.

A simple control law generates Listing's positions in a detailed model of the extraocular muscle system

The neural commands for maintaining static Listing's positions were identified using a detailed model of extraocular muscle based on Miller and Shamaeva (Orbit 1.5 gaze mechanics simulation 1995). The commands were approximately separable, suggesting a simple control law whereby independent horizontal and vertical commands are combined to generate tertiary positions. Tests showed that this control law (i) generated Listing' s positions to reasonable accuracy over+/-30 deg, provided pulleys were represented in the model; (ii) if driven by retinal coordinates, produced errors close to the theoretical minimum for a commutative system. The proposed commands appear consistent with electrophysiological evidence.

When is now? Perception of simultaneity

We address the following question: Is there a difference (D) between the amount of time for auditory and visual stimuli to be perceived? On each of 1000 trials, observers were presented with a light-sound pair, separated by a stimulus onset asynchrony (SOA) between -250 ms (sound first) and +250 ms. Observers indicated if the light-sound pair came on simultaneously by pressing one of two (yes or no) keys. The SOA most likely to yield affirmative responses was defined as the point of subjective simultaneity (PSS). PSS values were between -21 ms (i.e. sound 21 ms before light) and +150 ms. Evidence is presented that each PSS is observer specific. In a second experiment, each observer was tested using two observer-stimulus distances. The resultant PSS values are highly correlated (r = 0.954, p = 0.003), suggesting that each observer's PSS is stable. PSS values were significantly affected by observer-stimulus distance, suggesting that observers do not take account of changes in distance on the resultant difference in arrival times of light and sound. The difference RTd in simple reaction time to single visual and auditory stimuli was also estimated; no evidence that RTd is observer specific or stable was found. The implications of these findings for the perception of multisensory stimuli are discussed.

The 'ecological' probability density function for linear optic flow: implications for neurophysiology

A theoretical analysis of the recovery of shape from optic flow highlights the importance of the deformation components; however, pure deforming stimuli elicit few responses from flow-sensitive neurons in the medial superior temporal (MST) area of the cerebral cortex. This finding has prompted the conclusion that MST cells are not involved in shape recovery. However, this conclusion may be unjustified in view of the emerging consensus that MST cells perform nonlinear pattern matching, rather than linear projection as implicitly assumed in many neurophysiological studies. Artificial neural models suggest that the input probability density function (PDF) is crucial in determining the distribution of responses shown by pattern-matching cells. This paper therefore describes a Monte-Carlo study of the joint PDF for linear optic-flow components produced by ego-motion in a simulated planar environment. The recent search for deformation-selective cells in MST is then used to illustrate the importance of the input PDF in determining cell characteristics. The results are consistent with the finding that MST cells exhibit a continuum of responses to translation, rotation, and divergence. In addition, there are negative correlations between the deformation and conformal components of optic flow. Consequently, if cells responsible for shape analysis are present in the MST area, they should respond best to combinations of deformation with other first-order flow components, rather than to the pure stimuli used in previous neurophysiological studies.

The variation of torsion with vergence and elevation

Two recently developed kinematic models of human eye movements predict systematic departures from Listing's law which are associated with changes in vergence. This vergence-dependent torsion t is proportional to elevation e and vergence v, that is t = kev/2. The proposed value for k is either 1 (Van Rijn, L. J., & Van den Berg, A. V. (1993). Vision Research, 33, 691-708) or 1/2 (Minken, A. W. H., Gielen, C. C. A. M., & Van Gisbergen, J. A. M. (1995). Vision Research, 35, 93-102). One implication of both models is that an eye with a constant fixation direction should exhibit systematic torsional variation during movements of the other eye. This paper therefore examines the torsion produced by moving a fixation target inwards and outwards along the line-of-sight of the right eye at five different viewing elevations (0, +/- 15 and +/- 30 degrees). In a monocular analysis, each eye generally showed intorsion during convergence at positive elevation angles, whereas extorsion occurred at negative elevations; the opposite was true during divergence. However, the torsion response was visibly different between the five subjects, and depended on the direction of target motion. In a binocular analysis, cycloversion (mean of left and right eye torsion) varied dramatically both between subjects and between convergence and divergence; however, cyclovergence (torsional difference) was much less variable. Least-squares methods were used to estimate the constant k from monocular torsion, yielding values between 0.2 and 1.0; however, corresponding estimates based on cyclovergence were all close to 1/2. These findings support suggestions that a binocular control system couples the three-dimensional movements of the eyes, and that an existing model of monocular torsion should be generalised to the binocular case.

Instability of torsion during smooth asymmetric vergence

Several categories of torsional eye movements obey Listing's law; however, systematic deviations from this law occur during vergence. Two kinematic models attempt to incorporate these deviations, both of which are supported by experimental evidence; however, they lead to different torsion predictions. These discrepancies have been explained in terms of experimental procedures, but it now seems likely from several recent studies that individual differences in torsion patterns may also be important. This study therefore examines the variation of torsion during a smooth asymmetric vergence task in which a fixation target was moved along the line-of-sight of the right eye at 15 degrees elevation; each of five subjects observed five trials of both inward and outward target motion, repeated in two sessions several weeks apart. There were no significant group differences in left or right eye torsion between trials or sessions, suggesting that monocular torsion patterns were relatively stable over time. When examined more closely, however, the torsion patterns shown by some individuals did vary for inward versus outward target motion. Hence, monocular torsion was idiosyncratic and depended on the direction in which fixation was changing (convergence or divergence). In a binocular analysis, cycloversion varied dramatically between subjects and depended on the direction of target motion; however, this was not the case for cyclovergence. In summary, cyclovergence is relatively stable and depends on where the eyes are looking, whereas cycloversion (and hence monocular torsion) is relatively unstable and depends on how they came to be in that particular horizontal and vertical orientation. These findings help to explain the controversy surrounding the torsional behaviour of the human eye during vergence.

An orientation anisotropy in the effects of scaling vertical disparities

Gårding et al. (Vis Res 1995;35:703-722) proposed a two-stage theory of stereopsis. The first uses horizontal disparities for relief computations after they have been subjected to a process called disparity correction that utilises vertical disparities. The second stage, termed disparity normalisation, is concerned with computing metric representations from the output of stage one. It uses vertical disparities to a much lesser extent, if at all, for small field stimuli. We report two psychophysical experiments that tested whether human vision implements this two-stage theory. They tested the prediction that scaling vertical disparities to simulate different viewing distances to the fixation point should affect the perceived amplitudes of vertically but not horizontally oriented ridges. The first used elliptical half-cylinders and the 'apparently circular cylinder' judgement task of Johnston (Vis Res 1991;31:1351-1360). The second experiment used parabolic ridges and the amplitude judgement task of Buckley and Frisby (Vis Res 1993;33:919-934). Both studies broadly confirmed the anisotropy prediction by finding that large scalings of vertical disparities simulating near distances had a strong effect on the perceived amplitudes of the vertically oriented stimuli but little effect on the horizontal ones. When distances > 25 cm were simulated there were no significant differential effects and various methodological reasons are offered for this departure from expectations.

Optimality of position commands to horizontal eye muscles: A test of the minimum-norm rule

Six muscles control the position of the eye, which has three degrees of freedom. Daunicht proposed an optimization rule for solving this redundancy problem, whereby small changes in eye position are maintained by the minimum possible change in motor commands to the eye (the minimum-norm rule). The present study sought to test this proposal for the simplified one-dimensional case of small changes in conjugate eye position in the horizontal plane. Assuming such changes involve only the horizontal recti, Daunicht's hypothesis predicts reciprocal innervation with the size of the change in command matched to the strength of the recipient muscle at every starting position of the eye. If the motor command to a muscle is interpreted as the summed firing rate of its oculomotor neuron (OMN) pool, the minimum-norm prediction can be tested by comparing OMN firing rates with forces in the horizontal recti. The comparison showed 1) for the OMN firing rates given by Van Gisbergen and Van Opstal and the muscle forces given by Robinson, there was good agreement between the minimum-norm prediction and experimental observation over about a +/-30 degrees range of eye positions. This fit was robust with respect to variations in muscle stiffness and in methods of calculating muscle innervation. 2) Other data sets gave different estimates for the range of eye-positions within which the minimum-norm prediction held. The main sources of variation appeared to be disagreement about the proportion of OMNs with very low firing-rate thresholds (i.e., less than approximately 35 degrees in the OFF direction) and uncertainty about eye-muscle behavior for extreme (>30 degrees ) positions of the eye. 3) For all data sets, the range of eye positions over which the minimum-norm rule applied was determined by the pattern of motor-unit recruitment inferred for those data. It corresponded to the range of eye positions over which the size principle of recruitment was obeyed by both agonist and antagonist muscles. It is argued that the current best estimate of the oculomotor range over which minimum-norm control could be used for conjugate horizontal eye position is approximately +/-30 degrees. The uncertainty associated with this estimate would be reduced by obtaining unbiased samples of OMN firing rates. Minimum-norm control may result from reduction of the image movement produced by noise in OMN firing rates.

Robust and optimal use of information in stereo vision

Differences between the left and right eye's views of the world carry information about three-dimensional scene structure and about the position of the eyes in the head. The contemporary Bayesian approach to perception implies that human performance in using this source of eye-position information can be analysed most usefully by comparison with the performance of a statistically optimal observer. Here we argue that the comparison observer should also be statistically robust, and we find that this requirement leads to qualitatively new behaviours. For example, when presented with a class of stereoscopic stimuli containing inconsistent information about eccentricity of gaze, estimates of this gaze parameter recorded from one robust ideal observer bifurcate at a critical value of stimulus inconsistency. We report an experiment in which human observers also show this phenomenon and we use the experimentally determined critical value to estimate the vertical acuity of the visual system. The Bayesian analysis also provides a highly reliable and biologically plausible algorithm that can recover eye positions even before the classic stereo-correspondence problem is solved, that is, before deciding which features in the left and right images are to be matched.

Sequential stereopsis using high-pass spatial frequency filtered textures

Enright [(1995). Perception, 24 (suppl.), 32-33; (1996). Vision Research, 36, 307-312] described a simple piece of equipment for demonstrating a perceptual mechanism he called sequential stereopsis. The equipment requires an observer to set two textured targets seen behind a pair of small viewing ports to appear equi-distant. The principle upon which the apparatus depends is the use of textures whose elements cannot be resolved in peripheral vision at the eccentricity determined by the target separation. Enright used a fine sandpaper for this purpose. We have conducted two similar experiments using high bandpass filtered textures which eliminate any possibility that the low spatial frequency content of sandpaper textures could play a role. Our results corroborate Enright's general conclusions on sequential stereopsis, while at the same time showing that high-pass textures do not give wholly similar results to sandpaper.

Sequential Stereopsis Demonstrated with High-Bandpass Spatial-Frequency Filtered Textures

Enright (1995 Vision Research36 307 – 312; 1995 Perception24 Supplement, 32 – 33) described a simple piece of equipment for demonstrating a highly sensitive perceptual mechanism that he called sequential stereopsis. The apparatus prevents ‘conventional’ stereopsis mechanisms from operating as it prevents the comparisons of disparities of targets seen at the same time. Enright suggested that the mechanism of sequential stereopsis relies on a comparison of disparities before and after isovergent saccades between fixations of the two targets. In his apparatus, the observer makes fixations between two textured targets seen behind a pair of viewing ports and the task is to adjust these to appear equidistant. The principle upon which the apparatus depends is the use of textures whose elements cannot be resolved in peripheral vision at the eccentricity determined by the target separation. Enright used a fine sandpaper for this purpose. We describe two similar experiments ( N=3 in both) with high-bandpass filtered textures which eliminate any possibility of the low-spatial-frequency content of sandpaper textures playing a role. Our results corroborate Enright's general conclusions on sequential stereopsis while at the same time showing that high-bandpass textures do not give wholly similar results to sandpaper. Possible reasons for this are discussed.

Cerebral vasomotion: a 0.1-Hz oscillation in reflected light imaging of neural activity

Imaging of scattered and reflected light from the surface of neural structures can reveal the functional architecture within large populations of neurons. These techniques exploit, as one of the principal signal sources, reflectance changes produced by local variation in blood volume and oxygen saturation related to neural activity. We found that a major source of variability in the captured light signal is a pervasive low-frequency (0.1-Hz) oscillation which apparently results from regional cerebral blood flow. This signal is present in brain parenchyma as well as the microvasculature and exhibits many characteristics of the low-frequency "vasomotion" signals observed in peripheral microcirculation. Concurrent measurements in brain with a laser Doppler flow meter contained an almost identical low-frequency signal. The presence of the 0.1-Hz oscillation in the cerebral microcirculation could underlie a portion of the previously described characteristics reported in reflected-light imaging studies. The prevalence of the oscillatory phenomena in the brain raises substantial temporal sampling issues for optical imaging and for other visualization techniques which depend on changes in regional cerebral blood dynamics, such as functional magnetic resonance imaging.

Pooling of vertical disparities by the human visual system

Two experiments are described in which the effects of scaling vertical disparities on the perceived amplitudes of dome-shaped surfaces depicted with horizontal disparities were examined. The Mayhew and Longuet-Higgins's theory and the regional-disparity-correction theory of Garding et al predict that scaling should generate a change in perceived depth appropriate to the viewing distance simulated by the scaled vertical disparities. Significant depth changes were observed, by means of a nulling task in which the vertical-disparity-scaling effect was cancelled by the observer choosing a pattern of horizontal disparities that made the dome-shaped surface appear flat. The sizes of the scaling effects were less than those predicted by either theory, suggesting that other cues to fixation distance such as oculomotor information played an appreciable role. In conditions in which 50% of the texture elements were given one value of vertical-disparity scaling and the remaining 50% were left unscaled, the size of the scaling effect on perceived depth could be accounted for by equally weighted pooling of the vertical-disparity information unless the two scalings were very dissimilar, in which case the lower scaling factor tended to dominate. These findings are discussed in terms of a Hough parameter estimation model of the vertical-disparity-pooling process.

Interaction of stereo and texture cues in the perception of three-dimensional steps

A computational method for calibrating stereo using shape-from-texture is described together with five experiments that tested whether the human visual system implements the method. The experiments all tested the prediction that the perceived size of a step between two planar and slanted real surfaces should be affected by texture slant cues projected on to them that are inconsistent with the disparity cues. The predicted effect was observed but the results could be accounted for by a new phenomenon revealed in control conditions: the perceived size of a step between two slanted planes is in part determined by the size of the slants even when texture and stereo cues are held consistent. We conclude that the hypothesis that human stereo is calibrated by texture is not confirmed.

Stereopsis, vertical disparity and relief transformations

The pattern of retinal binocular disparities acquired by a fixating visual system depends on both the depth structure of the scene and the viewing geometry. This paper treats the problem of interpreting the disparity pattern in terms of scene structure without relying on estimates of fixation position from eye movement control and proprioception mechanisms. We propose a sequential decomposition of this interpretation process into disparity correction, which is used to compute three-dimensional structure up to a relief transformation, and disparity normalization, which is used to resolve the relief ambiguity to obtain metric structure. We point out that the disparity normalization stage can often be omitted, since relief transformations preserve important properties such as depth ordering and coplanarity. Based on this framework we analyse three previously proposed computational models of disparity processing; the Mayhew and Longuet-Higgins model, the deformation model and the polar angle disparity model. We show how these models are related, and argue that none of them can account satisfactorily for available psychophysical data. We therefore propose an alternative model, regional disparity correction. Using this model we derive predictions for a number of experiments based on vertical disparity manipulations, and compare them to available experimental data. The paper is concluded with a summary and a discussion of the possible architectures and mechanisms underling stereopsis in the human visual system.

A semiautomatic tool for 3D medical image analysis using active contour models

We describe a computerized tool designed to improve the efficiency with which clinicians can delineate volumes of interest in multi slice medical data such as NMR and CT images. The tool allows a trained user to create deformable models that can be used to search for edges or regions. Models can also be copied from previously analysed images into fresh slices, and frozen so they can only translate, rotate and scale, without deforming. In this way an accurate model can be used to extract an object from several adjacent slices. Surfaces are then reconstructed from the models using conic splines. By applying these techniques to objects such as tumours, it should be possible to generate three-dimensional images that are accurate enough to use when planning surgery and radiotherapy.