Displays 17 (1997) 69-74

DISPLAYS

Visual processing of depth information in stereoscopic displays

Robert Patterson*

Received 15 December 1993; accepted 15 May 1996

Abstract

This paper discusses the perception of depth in stereoscopic displays, with an emphasis on the validity of depth perception. The paper presents the idea that stereoscopic depth perception involves a number of processing steps such as detecting disparity and perceptual resealing of disparity for different viewing distances to yield perceived depth. The paper concludes with several ideas relating to the design of stereoscopic displays.

Kr~~ords: Stereopsis; Depth constancy: Binocular disparity; Stereoscopic displays

1. Introduction

Stereopsis refers to depth perception based on retinal disparity information (interocular difference in the retinal position of images), which arises from binocular viewing with horizontally separated eyes [l]. In visual displays, representing depth among display elements by using stereopsis may provide certain advantages, such as enhanced perception of depth among objects which improves perceptual discrimination of figure and ground [2]. A number of applications of stereoscopic displays exist, including air traffic control, telerobotics, computer-aided design, and meteorology [3].

This paper discusses the validity of depth perception in stereoscopic displays. A concern that arises when stereo- scopic displays are viewed is whether the depth perceived is ‘correct’ or valid in that its magnitude is consistent with geometric predictions [4]. Valid depth perception, which requires perceptual integration of disparity and viewing distance information, should be important in many applied situations as, for example. runway scenes viewed with helmet-mounted displays [5,6].

We begin with coverage of background information relevant to depth perception in stereoscopic displays. This information will form the foundation for topics presented later.

* E-mail:rpatter:ir mail.wsu.edu

0141-9382:97’$17.00 (1, 1997 Elsevier Science B.V. All rights reserved PZI SOl41-9381(96)01072-O

2. Background

This section presents concepts relevant to a basic understanding of stereoscopic depth perception: the horopter, crossed versus uncrossed disparity, eye move- ments, binocular fusion and patent versus qualitative stereopsis.

Stereopsis is induced by horizontal disparity, as shown in Fig. 1 (top-down view of two eyes fixating point F). The curved line through F is the imaginary longitudinal horopter. Objects on the horopter give rise to images that stimulate corresponding retinal points in the two eyes. For example, an image from object A stimulates point a in the left eye and another image stimulates point a’ in the right eye. Because these points are equally distant from f and f’ (fovea), they are corresponding points; object A has zero disparity relative to F. The horopter defines the locus of points in space that give rise to images that stimulate corresponding retinal points for a given degree of convergence.

Object B, in front of the horopter, gives rise to images that stimulate point b in the left eye and point b’ in the right eye (Fig. 1). Because these points are not equally distant from f and f ’ (angle f ‘b’ in the right eye is larger than fh in the left eye), they are noncorresponding retinal points. and object B has a non-zero disparity. Objects

70

Left Eye Right Eye

Fig. I. Top-down view depicting left and right eyes fixating point F. the longitudinal horopter. stimuli A and B. and Panum’s fusional area. See text for details. Reprinted with permission from Human Factors. 34(6) (1992). Copyright i_‘ 1992 Human Factors and Ergonomics Society. All rights reserved.

positioned at greater depths in front of or behind the horopter have greater disparity.

The horopter defined by strict geometry (called Vieth- Muller circle) is different from the horopter defined empirically by perceptual measurements [7.8]. The empirical horopter is based on several different criteria, such as common perceived direction (nonius method) [8]. The radius of curvature of the empirical horopter. which is larger than that of the Vieth-Muller circle. varies as a function of viewing distance and gaze direction for reasons not well understood [7].

2.2. Crossed versus uncrossed disparity

Disparity in front of the horopter is called ‘crossed’. and disparity behind the horopter is called ‘uncrossed’, a distinction derived from the spatial relationships of images within each monocular view (for crossed dis- parity, the disparate image is right of fixation in the left eye’s view, and left of fixation in the right eye’s view; for uncrossed disparity, the disparate image is left of fixation in the left eye’s view, and right of fixation in the right eye’s view). Crossed and uncrossed disparity are defined by stimulation of disparate retinal points, corresponding to depth in front of or behind the horopter, respectively.

However, another definition of disparity may be encountered in certain applied situations. The baseline of zero depth is taken to be the display screen, and dis- parity corresponding to depth in front of the screen is crossed and disparity corresponding to depth behind the screen is uncrossed [9,10,2]. This definition of disparity is equivalent to that based on corresponding retinal points as long as the operator fixates the display screen. But if the operator converges to a depth plane different from

that of the screen, the visually-relevant disparities are inaccurately specified.

In addition to positional disparity between luminance- defined images as a basis for stereopsis, other kinds of disparity may induce depth, such as orientation disparity [ 1 l] or disparity of motion-defined contours [ 121, thus the visual system may be quite adept at detecting differences in image properties between the eyes.

2.3. Eye movements

Vergence eye movements change the magnitude and possibly the direction of visually-relevant disparities of objects by changing the position of the horopter relative to the depth position of those objects. For example, changing fixation from object A to object B eliminates object B’s previous disparity, thus placing object B on the horopter, and object A presents a non-zero disparity to the visual system. Signals which control vergence eye movements seem to be derived from the same processing of binocular disparity information as that for stereo- scopic depth perception [ 131.

Vergence eye movements may be beneficial because a greater range of disparities may be visually processed by shifting the horopter to different positions in the visual field. Voluntary eye movements have been known to increase the range of disparities over which depth can be perceived [14.2] and to improve stereoscopic depth discrimination [15]. On the other hand, vergence eye movements may create a number of problems. For instance. the stimulus for accommodation (display screen) may be at one distance while vergence angle is appropriate for another distance (disparate stimulus), thereby producing a mismatch between accommodation and vergence, which could produce discomfort for the operator.

2.4. Binocular ,&ion

Objects slightly in front of or behind the horopter give rise to small disparities. Objects on or near the horopter are within a region surrounding the horopter called Panum’s fusional area (Fig. 1, dotted area). Fusion is the sensory process of blending together two correspond- ing monocular images into one perceived image. Objects farther away from the horopter, outside Panum’s area, give rise to large disparities and images that are not fus- able (i.e. double images or diplopia). The range of fusable disparities depends upon a number of factors (e.g. stimulus type or size); representative values are 20 arcmin for simple isolated stimuli [7] and up to over 1 arcdeg for complex multi-element stimuli [ 161.

When objects are positioned at large distances from the horopter. images from the same object stimulate dis- parate retinal points in the two eyes whereas images from different objects stimulate corresponding retinal points.

R. Parterson:Displays 17 ( 1997) 69- 74 71

Stimulating corresponding points in the two eyes with different images provokes binocular rivalry, a process in which the visibility of the images fluctuates every few seconds: first the left eye’s image is visible (right eye perceptually suppressed), then the right eye’s image is visible (left eye suppressed). The characteristics of the suppressed image are almost completely eliminated from perceptual awareness during suppression. Rivalry occurs because the visual system cannot fuse dissimilar images [17,18].

images in the two eyes’ views which come from the same distal or simulated object. Perceptual matching of images between eyes is necessary so that the magnitude of posi- tional disparity can be computed by the visual system. The establishment of binocular correspondence is a com- plex process and is influenced by vergence [23], color [24], and geometric form information [25].

Rivalry may create problems in stereoscopic displays if knowledge of image characteristics (e.g. object identity) is important for an operator to perform certain tasks or functions. Because rivalry may be encountered when objects with large disparities (e.g. 1 arc deg) are viewed, attempts should be made to avoid presenting stimuli with large crossed or uncrossed disparities.

2.5. Patent versus qualitative stereopsis

Stereoscopic depth perception may be classified into two types, patent and qualitative stereopsis, depending upon the magnitude of disparity [19-21,7]. Patent stereopsis refers to depth perception that increases monotonically with increases in disparity; it involves per- ceived depth from small disparities and, in most cases, fused images [7]. Near its disparity limit (e.g. 1 arc deg), patent stereopsis may occur with diplopia. Qualitative stereopsis refers to depth perception that does not bear a one-to-one relationship with disparity (e.g. depth may decline toward the horopter with increases in disparity); it involves perceived depth from large disparities and diplopic images. Bishop and Henry [ 191 offered a similar classification scheme of fine and coarse stereopsis.

Two basic approaches have been developed to explain how the visual system performs such matching [26]. One approach, based on multi-element displays, assumes that the establishment of binocular correspondence involves activation of a binocular neural network [27-301. This idea is relevant for display design in so far as such activa- tion takes a certain amount of time to occur (e.g. tens of msec), which could retard the latency for stereopsis in multi-element displays. A second approach assumes that the establishment of binocular correspondence involves activation of size-selective spatial channels in the visual system [3 l-341. This idea is relevant for display design in so far as large disparities are processed by mechanisms activated by large stimuli (low spatial frequencies) while small disparities are processed by mechanisms activated by small stimuli (high spatial frequencies). This means that, for good stereopsis, target size has to match in the two eyes and that the selected disparity range has to be appropriate for the size of the targets carrying the disparity.

To sum up, stereoscopic depth is induced by retinal disparity information, which is a difference in the retinal position of images in the two eyes. Crossed disparity corresponds to depth in front of fixation while uncrossed disparity corresponds to depth behind fixation. Visual processing of crossed and uncrossed disparity likely involves two stages, discussed next.

Once binocular correspondence is established, the visual system computes disparity magnitude which involves the metrical encoding of signals from disparate retinal points in the two eyes. The visual system may compute disparity from edge or boundary segments (i.e. zero crossings) in the two eyes’ views. Such compu- tations may be performed across different spatial scales or channels to yield a net disparity estimate. See Blake and Wilson [26] for further discussion.

3.2. Perceiving depth from disparity

3. Perceiving depth from disparity information

Visual processing of disparity information likely involves at least two stages: (1) establishing binocular correspondence/detecting disparity and (2) disparity scaling to yield perceived depth [22].

3.1. Binocular correspondence/disparity detection

Once disparity is computed, an estimate of perceived depth must be obtained by the visual system. Note that disparity, by itself, is an ambiguous depth cue. Changes in viewing distance between observer and stimuli pro- duce changes in disparity even when depth among objects remains constant. The perception of constant and valid depth despite changes in disparity is called depth constancy [4,35,36]. Depth constancy requires that the visual system rescale disparity for different view- ing distances. In stereoscopic displays, the visual system rescales disparity (half-image separation) for viewing distance in order for depth to be valid and consistent with the geometry of binocular vision [4,37].

The first stage of depth perception involves the estab- There are a number of viewing distance cues for lishment of binocular correspondence and disparity scaling disparity. Two cues are accommodation and detection. In establishing binocular correspondence, the vergence, which would be valid for close distances (up visual system establishes a match between corresponding to about 2 meters) [35,38]. Such oculomotor cues would

72 R. Putterson~Displu~s 17 ( 1997) 6Y- 74

provide invalid distance information for longer distances because perceived distance would be biased towards closer distances, especially under degraded conditions [39-421. Errors of accommodation and vergence may underlie reports of misperceived depth in head-up dis- plays [43-461. Other distance cues are perspective and texture gradient, which would be valid for short or long distances [37]. Depth information from disparity is integrated with depth information from other sources (e.g. motion parallax) to yield an overall visual estimate of perceived depth [47].

Recent studies have revealed interesting aspects of stereoscopic depth perception. Stereopsis is good for very fast image motion, implying that the computation of depth involves a rapid visual process [48]. In addition, perceived depth from disparity may be influenced by non-disparity factors such as stimulus shape [49]. Finally, note that depth perception can occur without disparity information for unpaired image points stemming from occlusion [50].

3.3. Geometry qf stereoscopic displays

Depth perception can be simulated in stereoscopic dis- plays by presenting a pair of two-dimensional views, one view to each eye of an observer, with a lateral shift (half- image separation) between the position of corresponding images. Consider Fig. 2, which presents a top-down view of two eyes. One of two drawings is presented to each eye: the drawings depict half-images of stimuli A and B. The half-images of stimulus A (A and A’) are presented to corresponding retinal points a and a’, while the half- images of stimulus B (B and B’) are presented to disparate retinal points (b and b’). Upon binocular

ba Left Eye

b’ a’ Right Eye

Fig. 2. Top-down view depicting two drawings (‘half-images’), one drawing presented to the left eye. the other drawing presented to the right eye. See text for details. Reprinted with permission from Human Factors. 34(6) (1992). Copyright ‘(‘ 1992 Human Factors and Ergonomics Society. All rights reserved.

fusion, an observer perceives stimulus B in depth behind stimulus A.

Predictions of perceived depth in stereoscopic displays may be derived from geometry [4]: d = S x D/(Z + S), for crossed half-image separations (crossed disparity), and d = S x D/(Z - S), for uncrossed separations (uncrossed disparity), where d = predicted depth between object and fixation, S = separation between half-images of the disparate stimulus, D = viewing dis- tance from observer to fixation. and I = interpupillary distance. For crossed and uncrossed separations, per- ceived depth should increase linearly with half-image separation and with viewing distance, with a greater increase occurring for uncrossed separation. Perceived depth varies inversely with interpupillary distance, but overall this effect is small.

4. Results from recent studies

Recent research from our laboratory [51] has examined several factors affecting patent stereopsis in stereoscopic displays: half-image separation magnitude, separation direction (crossed versus uncrossed), viewing distance, stimulus size, and exposure duration. The stereoscopic stimuli were isolated bright geometric forms seen against a dark background, created from pairs of images rear-projected onto a display screen (disparity ranged from 6.9 to 32.1 arcmin). Perceived depth was estimated using a depth matching task and compared to geometric predictions.

The results showed that perceived depth was generally consistent with geometric prediction: increases in separa- tion and distance produced increases in depth, especially for uncrossed separations (crossed depth was equal to or slightly less than prediction; uncrossed depth was equal to or slightly greater than prediction). There was no effect of size. Depth with brief exposure (eliminating vergence eye movements) was similar to depth with unlimited exposure (allowing vergence eye movements), with a tendency for brief exposure to increase depth with uncrossed separations [9].

The effects of half-image onset asynchrony (delaying onset of one eye’s image relative to partner eye’s image) on depth perception was also studied [51]. One method for implementing stereopsis in visual displays is to pre- sent each eye’s view on alternate frames (field-sequential or time-multiplexing method). Successful induction of stereopsis implies that visual persistence exists in each monocular pathway which overlaps temporally with the other eye’s information. This persistence was examined by investigating depth perception with half- image onset asynchrony. The results showed that, for both crossed and uncrossed separations, perceived depth was on average consistent with geometric predic- tion up to quite long asynchronies, although asynchrony

produced small to moderate increases in the variability (decreases in reliability) of perceived depth.

Other research from our laboratory, using high- density multi-element displays, found that crossed depth was similar to geometric prediction across condi- tions but that uncrossed depth was significantly less than prediction when the stimulus was small and exposed briefly [52]. Also, depth discrimination was good in the crossed direction but depth discrimination was poor in the uncrossed direction [53]. This pattern of results was interpreted as evidence for the existence of separate crossed versus uncrossed stereoscopic mechanisms underlying the disparity scaling/depth constancy process [541.

Recent research [55,56], however, has called into ques- tion this idea of separate classes of crossed versus uncrossed stereoscopic processes. In our previous studies involving multi-element displays, less uncrossed depth [52] and poor uncrossed depth discrimination [53] may have been related to occlusion. The background elements of the stereogram appeared as an occluding surface behind which the uncrossed stimuli were seen. These occlusion cues made the boundaries of the uncrossed stimuli appear as if they belonged to the background, thus stimulus boundaries were perceptually undefined and depth information was weak [57]. Such occlusion cues would not occur in low element density displays. Uttal and colleagues [58] have shown that good stereop- sis can occur with very brief exposure durations with low density displays and good binocular registration.

5. Concluding remarks

Stereoscopic depth perception involves two processing stages: the establishment of binocular correspondence/ disparity detection and disparity scaling for different viewing distances. Factors that disrupt these stages may degrade stereopsis. For example. displays with large disparities may disrupt binocular correspondence and provoke binocular rivalry, or misregistration of viewing distance may render perceived depth invalid.

In stereoscopic displays involving moderate disparity values, a small number of stimulus elements, and multi- ple distance cues, perceived depth follows geometric predictions quite closely. Perceived depth increases with half-image separation and with viewing distance, sug- gesting that large separations or long distances may be used when large depth intervals are needed. Large view- ing distances may be particularly advantageous because disparity magnitude decreases with increases in distance, thus the fusional limits of the operator should not be exceeded in an effort to gain greater depth [9]. Perceived depth is generally consistent with geometric predictions with quite long half-image asynchronies, thus time- multiplexed displays may be used when a high degree

of reliability of perceived depth is not required [51]. The idea of monocular visual persistence feeding into the stereoscopic process is interesting [59].

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