Disparity Limit Research Articles

Match propagation for image-based modeling and rendering

This paper presents a quasi-dense matching algorithm between images based on the match propagation principle. The algorithm starts from a set of sparse seed matches, then propagates to the neighboring pixels by the best-first strategy, and produces a quasi-dense disparity map. The quasi-dense matching aims at broad modeling and visualization applications which rely heavily on matching information. Our algorithm is robust to initial sparse match outliers due to the best-first strategy. It is efficient in time and space as it is only output sensitive. It handles half-occluded areas because of the simultaneous enforcement of newly introduced discrete 2D gradient disparity limit and the uniqueness constraint. The properties of the algorithm are discussed and empirically demonstrated. The quality of quasi-dense matching are validated through intensive real examples.

The Limits of Transparent Depth Perception with Restricted Field of View: Application in an Augmented Reality Surgical Microscope

This paper describes an investigation into the effect of reduced field of view and target size in transparent stereo augmented reality systems. Six subjects were asked to identify the maximum disparity limit of correct 3D perception for a random dot target of different sizes, viewed through a transparent scene with a varying field of view (FOV). The results showed that the maximum disparity limit increased linearly up to 25 degrees FOV after which it showed no significant increase for increasing FOV. There was no significant difference in the maximum disparity values obtained using a 4, 8, or 10 degree target. The maximum disparity limit of 5.9 ±1 (mean ± SD) degrees visual angle was used in an equation to predict the range in which correct depth perception occurs for transparent AR in a binocular surgical microscope. We suggest that the optimum image position to give the greatest range for correct 3D depth perception is 25cm when viewing transparent targets behind a transparent real scene.

Stereo correspondence in one-dimensional Gabor stimuli

Previous data [Prince, S.J.D., & Eagle, R.A., (1999). Size-disparity correlation in human binocular depth perception. Proceedings of the Royal Society of London B, 266, 1361–1365] have demonstrated that the upper disparity limit for stereopsis (DMax) is considerably smaller in filtered noise stereograms than in isolated Gabor patches of the same spatial frequency. This discrepancy is not currently understood. Here, the solution of the correspondence problem for bandpass stereograms was further examined. On each trial observers were presented with two one-dimensional Gabor stimuli containing disparities of equal magnitude but opposite sign. Subjects were required to indicate which interval contained the crossed disparity stimulus. It was found that matching behaviour changed as a function of Gabor envelope size. As a function of disparity magnitude, performance cycled between mostly correct and mostly incorrect at large envelope sizes but was always correct at small envelope sizes. At intermediate envelope sizes performance was cyclical at small disparities but always correct at large disparities. The critical envelope size at which performance changed from mostly correct to mostly incorrect at 270° phase disparity was used as a measure of the matching performance as other parameters of the Gabor were varied. Both absolute and relative contrast were shown to influence the perceived sign of matches. Critical envelope size was also found to decrease as a function of spatial frequency, but more slowly than a phase-based limit would predict. These data cannot be predicted by current models of stereopsis, and can be used to constrain future models.

Relaxation labeling in stereo image matching

This paper outlines a method for solving the global stereovision matching problem using edge segments as the primitives. A relaxation scheme is the technique commonly used by existing methods to solve this problem. These techniques generally impose the following competing constraints: similarity, smoothness, ordering and uniqueness, and assume a bound on the disparity range. The smoothness constraint is basic in the relaxation process. We have verified that the smoothness and ordering constraints can be violated by objects close to the cameras and that the setting of the disparity limit is a serious problem. This problem also arises when repetitive structures appear in the scene (i.e. complex images), where the existing methods produce a high number of failures. We develop our approach from a relaxation labeling method ( [1] W.J. Christmas, J. Kittler, M. Petrou, Structural matching in computer vision using probabilistic relaxation, IEEE Trans. Pattern Anal. Mach. Intell. 17(8) (1995) 749–764), which allows us to map the above constraints. The main contribution is made, (1) by applying a learning strategy in the similarity constraint and (2) by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem produced by the required fixation of a disparity limit. Consequently, we improve the stereovision matching process. A better performance of the proposed method is illustrated by comparative analysis against some recent global matching methods.

Unconstrained stereoscopic matching of lines

The computation of horizontal binocular disparities used in stereoscopic depth perception depends upon the identification of corresponding features in the two retinal images. In principle, binocular matching is a two-dimensional problem that considers matches in all possible meridians. Normally, constraints such as end points or crossing points limit the direction and magnitude of matches. If matching is unconstrained, such as is the case with long lines, it is completely ambiguous. Under these conditions the default match will be determined by the operating range, or upper disparity limit, of matchable vertical and horizontal disparities. We computed the operating range of vertical matches for stereoscopic depth as a function of line orientation. Our results suggest that the two-dimensional operating range is anisotropic for vertical and horizontal disparity and that unconstrained matches are not based upon either epipolar geometry or nearest neighbor constraints, but rather the mean of disparity estimates within the operating range for binocular matches. This operating range can be extended vertically when matches are constrained by image primitives.

RECIPROCAL-WEDGE TRANSFORM IN ACTIVE STEREO

The Reciprocal-Wedge Transform (RWT) facilitates space-variant image representation. In this paper a V-plane projection method is presented as a model for imaging using the RWT. It is then shown that space-variant sensing with this new RWT imaging model is suitable for fixation control in active stereo that exhibits vergence and versional eye movements and scanpath behaviors. A computational interpretation of stereo fusion in relation to disparity limit in space-variant imagery leads to the development of a computational model for binocular fixation. The vergence-version movement sequence is implemented as an effective fixation mechanism using the RWT imaging. A fixation system is presented to show the various modules of camera control, vergence and version.

Dmax for stereopsis and motion in random dot displays.

The upper displacement limit for motion was compared with the upper disparity limit for stereopsis using two-frame random dot kinematograms or briefly presented stereograms. dmax (the disparity/displacement at which subjects make 20% errors in a forced-choice paradigm) was found to be very similar for motion and stereo at all dot densities, and to fall with increasing dot density (0.006% or two dots to 50%) according to a power law (exponent -0.2). If dmax is limited by the spacing of false targets, this pattern of results suggests that the spatial primitives in the input to the correspondence process may be derived from multiple spatial scales. A model using MIRAGE centroids provides a good fit to the data.

Relaxation by Hopfield network in stereo image matching

This paper outlines a relaxation approach using the Hopfield neural network for solving the global stereovision matching problem. The primitives used are edge segments. The similarity, smoothness and uniqueness constraints are transformed into the form of an energy function whose minimum value corresponds to the best solution of the problem. We combine two methods: (a) optimization/relaxation [1]and (b) relaxation merit [2]with the above three constraints mapped in an energy function. The main contribution is made (1) by applying a learning strategy in the similarity constraint and (2) by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem arising from the required fixation of a disparity limit. So, we improve the stereovision matching process. A better performance of the proposed method is illustrated with a comparative analysis against a classical relaxation method.

Decreases in the critical disparity gradient with eccentricity may reflect the size-disparity correlation.

The interaction between dot separation and fusible disparity limits (critical disparity gradient) was assessed at 0, 2, 4, and 8 deg eccentricity by 19 subjects. The critical disparity gradient showed a significant decrease with eccentricity such that larger separations were required for fusion of a given disparity as eccentricity increased. An argument is put forth that this relationship supports a size-disparity correlation. The significant disparity-eccentricity interaction may be explained by both the progressive loss of higher-spatial-frequency channels with eccentricity and a reduction in the range of disparities processed by a channel as eccentricity is increased. Individual differences in the trend across eccentricity are noted and discussed.

New Data on Chelidonura Amoena Bergh, 1905 (Opisthobranchia: Cephalaspidea: Aglajidae)

Chelidonura amoena Bergh, 1905 is redescribed, principally on material from Australia. The single extant type specimen is designated as lectotype. Considerable intraspecific colour variation is evident, with that relating to the caudal lobes being greatest. The variation in coloration and shape observed in one specimen from Belau lies outside those described for C. amoena and we believe it could be explained as the product of hybridisation with C. electra Rudman, 1970. Aggregation for the purpose of breeding is shown to be normal for C. amoena. The collection data and observations indicate C. amoena is widely distributed in the tropical western Pacific and eastern Indian Oceans with disparate limits on the eastern and western coasts of the Australian continent.

Analysis of stereothresholds for stimuli below 2.5 c/deg

We analyze published data on disparity detection thresholds for a wide range of conditions. This type of detection changes behavior dramatically at the spatial frequency of 2.5 c/deg; above this frequency threshold remains constant while below it threshold grows at a uniform rate. Many other types of threshold, such as upper disparity limits for depth perception and threshold amplitudes for stereo and monocular motion, show similar behavior. These data lead to the postulate that there are no foveal stereo channels peaking below 2.5 c/deg, so that foveal stimuli in the whole range below 2.5 c/deg are processed by a single channel tuned to this frequency. Consequently, disparity detection thresholds at frequencies below this frequency are controlled by the single parameter of effective contrast in the 2.5 c/deg channel, whose output depends jointly on the contrast and spatial frequency of the stimuli. We develop this idea to explain the relations between spatial and contrast tuning functions for disparity thresholds. To validate our conclusions, we describe an experiment with difference-of-Gaussian stimuli over a range of interocular widths and contrast differences. For a dichoptic width ratio of 2:1, the dichoptic contrast ratio required to minimize disparity detection thresholds was 1:4, just as predicted by the model.

Coarse spatial scales constrain the range of binocular fusion on fine scales

To examine interactions among spatial scales in disparity processing, we have measured the upper disparity limit for binocular single vision (the diplopia threshold) for high-spatial-frequency test stimuli in the presence of cosine gratings of lower spatial frequency that defined a surface in depth. When the frequency of this grating surface was 2.0 octaves below that of the test, the test fusion range was reduced by a factor of 3-4 relative to the condition in which no grating surface was present. However, gratings 4.0 octaves below the test frequency had no effect, and the test and grating were seen transparently at different depths. Further experiments indicate that the effect is orientation specific and that high-frequency gratings do not affect low-frequency tests. Finally, experiments using grating surfaces tilted in depth indicate that fusion at high spatial frequencies is constrained to a range centered on the local disparity of the surface defined by the lower frequency. These results are important for computational models for stereopsis that are based on coarse-to-fine matching strategies.

Panum's fusional area estimated with a criterion-free technique.

It has been reported that criterion-free estimates of the upper disparity limits for fusion of line targets are small enough to be accounted for by monocular vernier sensitivity. However, targets such as lines, which contain high spatial frequencies, may ensure small fusion limits, since fusion limits obtained with criterion-dependent methods for narrow-band targets, such as sinusoids or difference-of-Gaussian luminance profiles, are proportional to target spatial periods. Experiment 1 therefore explored whether criterion-free methods give fusion limits for narrow-band targets that can be accounted for by vernier sensitivity. Vertical fusion limits were estimated by a method that forced observers to discriminate a disparate sinusoidal grating from an immediately adjacent zero-disparity grating. Fusion limits were too large to be explained by monocular vernier thresholds obtained for the same targets. In addition, fusion limits were not affected by large changes in target contrast, whereas vernier thresholds increased as contrast was decreased. The results of Experiment 1 also argued against interocular suppression as the cause of single vision, since vernier offsets that were visible when viewed monocularly were invisible under binocular viewing conditions. In Experiment 2, manual adjustment of disparities yielded fusion limits little different from those obtained with the forced-choice method of Experiment 1, demonstrating that it is possible to design adjustment methods for assessing fusion limits that are as sensitive as forced-choice methods. In Experiment 3, large reductions in target contrast, which have the effect of decreasing disparity sensitivity, did not alter fusion limits, disconfirming the idea that fusion limits estimated with discriminative procedures represent disparity-detection thresholds. In Experiment 4, disparities were adjusted until a just noticeable difference in grating contrast appeared. These disparities were larger than fusion limits, indicating that fusion limits did not represent a change in apparent contrast arising from disparity limitations of binocular summation. Together, the four experiments support the existence of binocular fusion as a unique category of sensory performance, disconfirm several nonfusional explanations of single vision, and support the use of criterion-free as well as adjustment methods in measuring fusion limits.

Binocular fusion limits are independent of contrast, luminance gradient and component phases

Panum's binocular fusion limit has been shown to increase with the size of graded contrast targets ( Schor, Wood & Ogawa, 1984). This suggests the hypothesis that the fusion limit may be controlled by the maximum luminance gradients present in the stimuli. The luminance gradient is reciprocally related to image contrast, so the hypothesis predicts that the fusion limits should also decrease with increasing contrast. To investigate this luminance gradient hypothesis we designed stimuli in which the contrast and phase of the spatial frequency components could be varied independently of the luminance gradients. Disparity limits for fusion were unaffected by variations of as much as a log unit in contrast, luminance gradient or phase of the frequency components, disconfirming the luminance gradient hypothesis. Instead, fusion limits for various compound frequency targets were well predicted by the smallest fusion range for any spatial frequency component in the image that was above its contrast detection threshold.

Energetic Contributions to the Two-Electron Bond: A Simplified Group Function (SGF) Analysis

The group function (GF) formalism coupled with the limit in which intergroup electron interchange symmetry is rigorously neglected (the simplified group function (SGF) approach) is shown to lead to a resolution of intergroup bonding as an effective power series in overlap density. The successive orders are shown to correspond to a concomitant resolution into traditional bonding contributions: zeroth order leads to the conventional excitonic description (no electron transfer or interchange); first-order terms may be interpreted as dative bonding, in which electron transfer configurations mix with the excitonic states; and finally, second-order terms correspond directly to the incorporation of electron interchange symmetry and hence to pure covalent bonding. A conceptual parallelism of the division of long range (static, inductive and dispersive) interactions with short range (ionic, dative and covalent) interactions is drawn to emphasize the unity of these apparently disparate limits in the SGF/GF analysis. Explicit application to the archetypical two-electron bond highlights the conceptual simplicity of the approach, and is compared to a commensurate MO and VB analysis expressed in terms of the same integrals. The results show clearly why such a simple resolution is difficult to extract from MO and VB approaches, which are philosophically biased towards the strong bonding limit.

Binocular sensory fusion is limited by spatial resolution

Binocular sensory fusion which was previously thought to have a maximum spatial extent at the fovea of 1 deg is at least 600% larger when stimulated by low spatial frequency (coarse) detail. This upper limit for sensory fusion has a constant phase disparity limit of 90 deg which corresponds to the monocular Rayleigh criterion for spatial resolution of two diffraction patterns. At low spatial frequencies the sensory fusion limit equals the upper disparity limit for stereoscopic depth perception which suggests that a common mechanism underlies these two phenomena.

Disparity range for local stereopsis as a function of luminance spatial frequency

The disparity range for stereo sensitivity was investigated with spatially filtered bars, tuned narrowly over a broad range of spatial frequencies. When measured with narrow (high spatial frequency) bars the disparity range for stereopsis exceeded two orders of magnitude. The range was reduced with broad (low spatial frequency) bars by an elevation of stereothreshold that increased according to a constant 6deg phase disparity. The upper disparity limit also increased at broad spatial periods but at a lower rate. These size disparity correlations illustrate quantitative stereopsis along a continuum from fine to coarse disparities ( ± 2deg). A disparity matching task revealed that greater amounts of uncrossed than crossed disparity were required to match suprathreshold disparities. The ratio of standard/matched disparity was lower in both directions for small suprathreshold disparities subtended by broad than by narrow spatial periods. This selective reduction of stereo-efficiency ratio illustrates tuning to coarse disparities subtended by broad (low spatial frequency) stimuli and accounts for the marked reduction of stereoacuity caused by spectacle blur.

The Disparity Gradient Limit for Binocular Fusion: An Answer to J D Krol and W A Van de Grind

The observations reported earlier by the authors are shown to support the view that the constraints for fusion are stimulus-centered and not observer-centered, thus justifying the reformulation of the disparity limits for binocular fusion in terms of a gradient limit which is disputed by Krol and van de Grind.

Spatio-temporal properties of Panum's fusional area

Horizontal and vertical disparity limits of binocular fusion were examined with temporal or with spatio-temporal modulation of binocular disparity for two lines at 0.5 deg retinal eccentricity. For both horizontal and vertical disparity, Panum's fusional areas became extended by low spatial frequency variation in disparity. The horizontal extent of Panum's area also varied with temporal frequency of disparity variation. Under low spatial frequency conditions, Panum's area increased horizontally by as much as a factor of 10 (but vertically by less than a factor of 2) when temporal frequency decreased from 5.0 Hz to 0.1 Hz. At high spatial frequencies the horizontal and vertical extents of Panum's area remained almost constant (within a factor of 1.5) over the entire range of temporal frequencies. These results illustrated that Panum's area is the combination of a constant minimum area with an extended area that responds to low frequency time-varying disparities.

Modifications of the classical notion of Panum's fusional area.

It is generally believed that there is an absolute disparity limit for binocular fusion; objects with disparities within this limit, known as Panum's fusional area, will appear fused and single, while objects with disparities outside the limit appear double. It is demonstrated, however, that the disparity gradient, rather than the disparity magnitude, dictates binocular fusion when several objects occur near one another in the visual field. The disparity gradient is defined as the difference between the disparities of neighboring objects divided by their angular separation. If this ratio exceeds a critical value (approximately 1) then fusion does not occur, even though the absolute disparities of the individual objects may be well within the classical Panum's area. This discovery leads to the reinterpretation of several enigmatic phenomena in stereopsis, including Panum's limiting case.