Panum's Fusional Area Research Articles

Stereoscopic 3D Visual Discomfort Prediction: A Dynamic Accommodation and Vergence Interaction Model.

The human visual system perceives 3D depth following sensing via its binocular optical system, a series of massively parallel processing units, and a feedback system that controls the mechanical dynamics of eye movements and the crystalline lens. The process of accommodation (focusing of the crystalline lens) and binocular vergence is controlled simultaneously and symbiotically via cross-coupled communication between the two critical depth computation modalities. The output responses of these two subsystems, which are induced by oculomotor control, are used in the computation of a clear and stable cyclopean 3D image from the input stimuli. These subsystems operate in smooth synchronicity when one is viewing the natural world; however, conflicting responses can occur when viewing stereoscopic 3D (S3D) content on fixed displays, causing physiological discomfort. If such occurrences could be predicted, then they might also be avoided (by modifying the acquisition process) or ameliorated (by changing the relative scene depth). Toward this end, we have developed a dynamic accommodation and vergence interaction (DAVI) model that successfully predicts visual discomfort on S3D images. The DAVI model is based on the phasic and reflex responses of the fast fusional vergence mechanism. Quantitative models of accommodation and vergence mismatches are used to conduct visual discomfort prediction. Other 3D perceptual elements are included in the proposed method, including sharpness limits imposed by the depth of focus and fusion limits implied by Panum's fusional area. The DAVI predictor is created by training a support vector machine on features derived from the proposed model and on recorded subjective assessment results. The experimental results are shown to produce accurate predictions of experienced visual discomfort.

Saliency Prediction on Stereoscopic Videos

We describe a new 3D saliency prediction model that accounts for diverse low-level luminance, chrominance, motion, and depth attributes of 3D videos as well as high-level classifications of scenes by type. The model also accounts for perceptual factors, such as the nonuniform resolution of the human eye, stereoscopic limits imposed by Panum's fusional area, and the predicted degree of (dis) comfort felt, when viewing the 3D video. The high-level analysis involves classification of each 3D video scene by type with regard to estimated camera motion and the motions of objects in the videos. Decisions regarding the relative saliency of objects or regions are supported by data obtained through a series of eye-tracking experiments. The algorithm developed from the model elements operates by finding and segmenting salient 3D space-time regions in a video, then calculating the saliency strength of each segment using measured attributes of motion, disparity, texture, and the predicted degree of visual discomfort experienced. The saliency energy of both segmented objects and frames are weighted using models of human foveation and Panum's fusional area yielding a single predictor of 3D saliency.

Mapping the “Forbidden Zone” near and Away from the Fixation Point

Burt and Julesz modified the classical view of Panum's fusional area by incorporating the concept of the disparity gradient. They found that an area of double vision, described as the forbidden zone for single vision, is present when the angular separation between two objects is small. However, Krol and van de Grind argued that Burt and Julesz's finding could be explained by the classical theories (specifically Ogle, 1932 JOSA 22 664-728) in which the probability for fusion is a function of peripheral angle and disparity magnitude. We examined whether a forbidden zone can be specified within Ogle's experimental space. We found forbidden zones (a) when fixation was placed on one of the two objects and (b) when fixation was placed away from both objects. Krol and van de Grind's arguments do not easily explain the results in (b). The size of the forbidden zones was less than the predicted disparity gradient of unity that Burt and Julesz found in their experiment.

Binocular Coordination during Reading of Blurred and Nonblurred Text

Reading a text requires vergence angle adjustments, so that the images in the two eyes fall on corresponding retinal areas. Vergence adjustments bring the two retinal images into Panum's fusional area and therefore, small remaining errors or regulations do not lead to double vision. The present study evaluated dynamic and static aspects of the binocular coordination when upcoming text was blurred. Binocular eye movements and accommodation responses were simultaneously measured for 20 participants while reading single, nonblurred sentences and while the text was blurred as if it were seen by a person in whom the combination of refraction and accommodation deviated from the stimulus plane by 0.5 D. Text comprehension did not change, even though fixation times increased for reading blurred sentences. The disconjugacy during saccades was also not affected by blurred text presentations, but the vergence adjustment during fixations was reduced. Further, for blurred text, the overall vergence angle shifted in the exo direction, and this shift correlated with the individual heterophoria. Accommodation measures showed that the lag of accommodation was slightly larger for reading blurred sentences and that the shift in vergence angle was larger when the individual lag of accommodation was also larger. The results suggest that reading comprehension is robust against changes in binocular coordination that result from moderate text degradation; nevertheless, these changes are likely to be linked to the development of fatigue and visual strain in near reading conditions.

Potential hazards of viewing 3‐D stereoscopic television, cinema and computer games: a review

The visual stimulus provided by a 3-D stereoscopic display differs from that of the real world because the image provided to each eye is produced on a flat surface. The distance from the screen to the eye remains fixed, providing a single focal distance, but the introduction of disparity between the images allows objects to be located geometrically in front of, or behind, the screen. Unlike in the real world, the stimulus to accommodation and the stimulus to convergence do not match. Although this mismatch is used positively in some forms of Orthoptic treatment, a number of authors have suggested that it could negatively lead to the development of asthenopic symptoms. From knowledge of the zone of clear, comfortable, single binocular vision one can predict that, for people with normal binocular vision, adverse symptoms will not be present if the discrepancy is small, but are likely if it is large, and that what constitutes 'large' and 'small' are idiosyncratic to the individual. The accommodation-convergence mismatch is not, however, the only difference between the natural and the artificial stimuli. In the former case, an object located in front of, or behind, a fixated object will not only be perceived as double if the images fall outside Panum's fusional areas, but it will also be defocused and blurred. In the latter case, however, it is usual for the producers of cinema, TV or computer game content to provide an image that is in focus over the whole of the display, and as a consequence diplopic images will be sharply in focus. The size of Panum's fusional area is spatial frequency-dependent, and because of this the high spatial frequencies present in the diplopic 3-D image will provide a different stimulus to the fusion system from that found naturally.

Dichoptic motion within Panum's fusional area?

Purpose. Recent computational and neurophysiological findings suggest the existence of binocular complex cells that jointly encode motion and stereoscopic depth. Dichoptically presented gratings flickering in spatio-temporal quadrature can induce directional motion perception but the existence of an early binocular motion system is a debated issue. Here we investigated perception of dichoptic motion for stimuli defined on different depth planes. Methods. Stimuli were presented to the left and right eye on a calibrated CRT display with a refresh rate of 120 Hz using a split-screen Wheatstone configuration. On each trial Ss verged on a fixation-cross flanked by nonius lines before two vertical sine-wave gratings of 1.1 c/deg were presented in dichoptic view. The gratings were displayed in a circular aperture for 200 msec flickering in temporal quadrature. After each presentation Ss indicated whether direction of motion was left or right. In three conditions disparity of the stimulus was set to −8, 0, or +8 arc min whereas spatial phase offset between gratings varied between pi/2 and 3pi/2 in randomly intermixed trials. Spatial and temporal phase of the gratings were randomised across trials. Results. Although stimuli appeared on different depth planes psychometric functions shifted systematically with disparity. Discrimination of motion direction was best when phase offset together with horizontal disparity resulted in spatial quadrature. No reliable discrimination performance was obtained for stimuli with static pedestal, flicker frequencies beyond 4 Hz, and disparities outside Panum's fusional area. Conclusions. The present result does not support the notion of an early binocular motion system that can integrate dichoptic motion at different depth planes.

Advantage of binocularity in the presence of external visual noise

External visual noise plays a major role in real life, for instance, when a driver tries to identify an object through a snow flurry or through a dirty windshield. The goal of the present investigation was to quantify, under such a condition, the advantage of binocular over monocular vision or, rather, the disadvantage of having only one eye. Eight observers judged the orientation of a Landolt ring (gap always 10 arcmin), partly obscured by noise particles of different sizes (5, 10 or 20 arcmin). The noise particles were presented at a stereo disparity of 62 arcmin, i.e. beyond Panum's fusional area. We compared the percentage of correct responses and the reaction time between binocular and monocular vision. Control conditions: (1) binocular vision with noise particles located immediately in front of the Landolt ring (stereo disparity +/- 0), and (2) absence of noise particles. With regard to the percentage of correct responses, an advantage of binocular over monocular observation occurred only when the obscuring particles were presented at the stereo disparity of 62 arcmin. The advantage depended on the size of the noise particles. The factor was 1.24 for particles of 5 arcmin, 1.49 for 10 arcmin and 1.59 for 20 arcmin. With regard to the reaction time, there was no difference between binocular and monocular vision. Binocular vision provides a considerable advantage over monocular vision when particles partly obstruct the view. This advantage is due to the capability of the visual system to construct a coherent percept of an object of which different parts are imaged in the right and left eye.

Normalization Enables Robust Validation of Disparity Estimates from Neural Populations

Binocular fusion takes place over a limited region smaller than one degree of visual angle (Panum's fusional area), which is on the order of the range of preferred disparities measured in populations of disparity-tuned neurons in the visual cortex. However, the actual range of binocular disparities encountered in natural scenes extends over tens of degrees. This discrepancy suggests that there must be a mechanism for detecting whether the stimulus disparity is inside or outside the range of the preferred disparities in the population. Here, we compare the efficacy of several features derived from the population responses of phase-tuned disparity energy neurons in differentiating between in-range and out-of-range disparities. Interestingly, some features that might be appealing at first glance, such as the average activation across the population and the difference between the peak and average responses, actually perform poorly. On the other hand, normalizing the difference between the peak and average responses results in a reliable indicator. Using a probabilistic model of the population responses, we improve classification accuracy by combining multiple features. A decision rule that combines the normalized peak to average difference and the peak location significantly improves performance over decision rules based on either measure in isolation. In addition, classifiers using normalized difference are also robust to mismatch between the image statistics assumed by the model and the actual image statistics.

Binocular Coordination of the Eyes during Reading

Saccadic eye movements and fixations are the behavioral means by which we visually sample text during reading. Human oculomotor control is governed by a complex neurophysiological system involving the brain stem, superior colliculus, and several cortical areas. A very widely held belief among researchers investigating primate vision is that the oculomotor system serves to orient the visual axes of both eyes to fixate the same target point in space. It is argued that such precise positioning of the eyes is necessary to place images on corresponding retinal locations, such that on each fixation a single, nondiplopic, visual representation is perceived. Vision works actively through a continual sampling process involving saccades and fixations. Here we report that during normal reading, the eyes do not always fixate the same letter within a word. We also demonstrate that saccadic targeting is yoked and based on a unified cyclopean percept of a whole word since it is unaffected if different word parts are delivered exclusively to each eye via a dichoptic presentation technique. These two findings together suggest that the visual signal from each eye is fused at a very early stage in the visual pathway, even when the fixation disparity is greater than one character (0.29 deg), and that saccade metrics for each eye are computed on the basis of that fused signal.

Disparity Limit for Binocular Fusion in Fovea

In the human visual system, binocular disparity limit must be limited within a certain fusional area, called “Panum's fusional area”; otherwise, unsuitable disparity could cause double vision. The previous studies on Panum's fusional area have focused only on the horizontal and vertical meridians. In order to measure this area in more directions, we determined its limits in 16 different directions from 0 to 360° at 22.5° steps in fovea. It was found that: (1) the horizontal disparity limit (about 32-40 arcmin) is larger than the vertical limit (about 19.2–25.6 arcmin); (2) Panum's fusional area is approximately symmetrical around the horizontal meridian; (3) however, it is not symmetrical around the vertical meridian; the nasalward disparity limits are obviously larger than temporalward disparity limits; (4) therefore, the form of Panum's fusional area in fovea could be suggested to be an ellipse off-centered toward the nasal side on the horizontal meridian.

Binocular Disparity Limit in Three-dimensional Display Systems

In three-dimensional display systems, binocular disparities must be limited within a certain fusional area, called as “Panum's fusional area. Otherwise, too larger disparity could cause double view or serious eye fatigue. However, the measurements about Panum's fusional area in the previous studies focused only on the horizontal and vertical meridian of retina. For fully measuring the Panum's fusional area in more directions, we took the measurements of the limits of Panum's fusional area, in sixteen different directions from 0 degree to 360 degrees by a step of 22.5 degrees in the fovea. It was found that the horizontal disparity limit of binocular fusional area is about 32-38.4 min of arc and the vertical limit is about 19.2-24 min of arc. The disparity limits of binocular fusional area are approximately symmetrical about horizontal meridian. However, the disparity limits are not symmetrical about vertical meridian; the nasalward disparity limits are obviously larger than temporalward disparity limits. Moreover, in the nasal side of retina, the disparity limits decrease in a monotonic fashion, and in the temporal side, however, the disparity limits have no obvious difference.

Change of Binocular Fusional Area with Retinal Shift

In three-dimensional display systems, binocular disparity must be limited within a certain area, called as “Panum's fusional area”. Otherwise, unsuitable binocular disparity can cause double view or eye fatigue. In this study we fully measured the limits of binocular fusional area in sixteen different directions from 0 degree to 360 degrees by a step of 22.5 degrees in the retinal fovea, using a three-dimensional display device. The following results were obtained: (1) the horizontal limit of Panum's fusional area in retinal fovea is larger than the vertical limit; (2) the limits of Panum's fusional area are almost symmetrical about the horizontal meridian; (3) the nasalward limits are obviously larger than the temporalward limits; (4) In nasal side of retina, the limits increase in a monotonic fashion; however in temporal side, the limits have no obvious change.

Perceiving Surfaces in Depth beyond the Fusion Limit of Their Elements

An isolated dot appears double outside a small disparity range called Panum's fusional area. In random-dot stereograms (RDSs), however, this doubling, or diplopia of dot elements is not evident at any disparity. Nevertheless, depth is perceived up to disparities that greatly exceed Panum's fusional limit. Either one is unaware of dot diplopia at disparities exceeding Panum's fusional limit or the fusion limit is extended. To examine these possibilities, we developed a novel RDS in which dichoptically color-coded dots have a distinctive color when fused, and return to their intrinsic colors when diplopic. We measured the fusion limit of dots in this RDS, and compared it to the patent stereopsis limit of the perceived surface in similar RDSs. We found that the fusional area of dots in the RDS was comparable to Panum's fusional area. Furthermore, there was clear dissociation between the fusion limit and the patent stereopsis limit in the RDS. We conclude that the elements composing a surface are not necessarily fused when a large disparity surface is perceived in depth.

Changing Binocular Fusional Area with Retinal Shift in Binocular Vision

In three-dimensional display systems, binocular disparity must be limited within a certain area, called as “Panum's fusional area”. Otherwise, unsuitable binocular disparity can cause double view or eye fatigue. In this study, we measured the binocular fusional areas in central vision, in the case of peripheral visions of retinal eccentricity of 3 degrees and 6 degrees on horizontal meridian, respectively, using a three-dimensional display. The following results were obtained, (1) in each experiment in central vision, peripheral vision of 3 degrees and 6 degrees, the disparity limit in horizontal meridian is larger than that in vertical meridian; the binocular fusional area is symmetrical about horizontal meridian and is not symmetrical about vertical meridian; the nasalward disparity limits are larger than the temporalward disparity limits; therefore, the form of the binocular fusional area is considered as an ellipse off-centered toward the nasal side on the horizontal meridian. (2) The size of the binocular fusional areas increases with the increase of retinal eccentricity, and the increase of disparity limit on horizontal meridian is faster than that on vertical meridian.

Analysis of Human Binocular Fusional Area in Retinal Fovea

In three-dimensional display systems, binocular disparities must be limited within a certain fusional area, called as “Panum's fusional area”, otherwise too large disparity could cause double view or serious eye tiresome. In this study, a three-dimensional display device was employed with a constant stimuli method to measure the disparity limits of the Panum's fusional area in sixteen different directions from 0 degree to 360 degrees by a step of 22.5 degrees in the retinal fovea. The following results were obtained: (1) the horizontal disparity limit of binocular fusional area is about 32-40min of arc and the vertical limit is about 19.2-25.6min of arc. (2) The disparity limits of binocular fusional area are approximatively symmetrical about horizontal meridian. (3) The disparity limits are not symmetrical about vertical meridian, and the nasalward disparity limits are obviously larger than the temporalward disparity limits. (4) In the nasal side of retina, the disparity limits decrease in a monotonic fashion and in the temporal side, however, the disparity limits have no obvious difference.

論文取消：全立位におけるパナマの融合領域測定に関する研究

論文取消：全立位におけるパナマの融合領域測定に関する研究

Measurement for the Panum's Fusional Area in Retinal Fovea Using a Three-Dimension Display Device

The limits of Panum’s fusional area have been studied by many research groups. Those studies, however, focused only on the measuring direction of horizontal and vertical meridian. In this study, a new experimental method was employed by using a three-dimension display device to fully measure the limits of Panum’s fusional area in eight different directions from 0 degree to 360 degrees with a step of 45 degrees in the retinal fovea. The following results were obtained: (1) the horizontal limit of Panum’s fusional area in fovea is larger than the vertical limit; (2) the limits of Panum’s fusional area are almost symmetrical about the horizontal meridian; (3) the limits of Panum’s fusional area are not symmetrical about the vertical meridian; the nasalward limits are obviously larger than the temporalward limits; (4) the form of Panum’s fusional area in retinal fovea is suggested to be an off-centered ellipse instead of a standard ellipse reported in previous works.

Fully Measuring the Panum's Fusional Area in Retinal Fovea

Fully Measuring the Panum's Fusional Area in Retinal Fovea

The ellipse of vision

The contention of this article is that the horopter, as well as the Panum fusional area, is more precisely explained as an ellipse that employs corresponding points on each retina as geometric foci. This analysis, using principles of physics and euclidean geometry, produces the theory of the “ellipse of vision.”

Quantitative analysis of the accommodative convergence to accommodation ratio: linear and nonlinear static models.

Ogle and his colleagues proposed two measures of oculomotor linkage called the accommodative convergence to accommodation (AC/A) ratio. This ratio provided a clinically useful assessment of the drive of accommodation, or focusing system, on vergence, or binocular fixation system. The phoria method measured the relatively large deviation in eye alignment under the monocular condition, whereas the fixation disparity method measured the relatively small misalignment of the eyes under the binocular condition to obtain the AC/A ratio. Ogle et al. indicated that these two measures should be equal. However, experimental results showed a substantial difference between the AC/A ratios obtained by the two methods. To quantitatively assess the difference between the two methods, a linear static model was first evaluated. This model was based on an earlier successful model of the accommodation and vergence system. The linear-model solution showed that these two methods were equivalent and thus could not account for the differences found. Then, a nonlinear static model, containing the deadspace operators depth of field and Panum's fusional area (PFA), was evaluated. Since two solutions were possible for each deadspace operator, there were four basic solutions. However, there were two binocular-viewing paradigms. This resulted in four prism-viewing and four lens-viewing solutions. Finally, a difference was taken between the prism- and lens-viewing measures, giving a total combination of 16 solutions. Only four of these solutions were equal to that using the phoria method. Some of the other solution lines were widely separated, thus providing a range of possible data values across different solution lines. Calculations showed that the variation in AC/A ratio values for data across difference solution lines was comparable to that found experimentally. Thus, the deadspace operators in the nonlinear model were able to account for the discrepancy between the AC/A ratio determined by the phoria and fixation disparity methods.