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Sensation & Perception V3: Chapter 9: Depth Perception

Sensation & Perception V3
Chapter 9: Depth Perception
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Notes

table of contents
  1. Front Matter
  2. Preface
  3. Acknowledgements
  4. Chapter 1: Introduction to the Study of Sensation and Perception
  5. Chapter 2: Approaches to Studying Sensation and Perception
  6. Chapter 3: Receptors and Neural Processing
  7. Chapter 4: The Lateral Geniculate Nucleus (LGN) and Primary Visual Cortex (V1)
  8. Chapter 5: Higher-Level Visual Processing: Beyond V1
  9. Chapter 6: Attention and Visual Perception
  10. Chapter 7: Object Recognition
  11. Chapter 8: Color Vision
  12. Chapter 9: Depth Perception
  13. Chapter 10: Motion
  14. Chapter 11: Audition
  15. Chapter 12: Cutaneous Senses
  16. Chapter 13: Gustatory Senses
  17. Chapter 14: Olfaction
  18. Version History

Chapter 9: Depth Perception

Depth perception enables us to perceive the world in three dimensions. In this chapter, we will explore the mechanisms and cues that our visual system employs to determine the relative distances of objects in our environment.

Ocular Motor Depth Cues

Convergence: The Dance of the Eyes

One depth cue that is used when viewing objects that are close to the face is convergence. Convergence occurs when we focus on objects within arm's length (Howard & Rogers, 2012). When an object is very close to us, our eyes naturally converge or move toward each other. This causes changes in the eye muscles and provides a clear signal to our brain that the object is nearby. Conversely, if an object is far away, our eyes remain parallel.

A cartoon otter looks cross-eyed at a small ladybug perched on the tip of its nose. The eyes are turned inward to focus on the nearby object, illustrating the depth cue of convergence, in which the eyes rotate inward when viewing something at close range.

Figure 9.1

Illustration of the depth cue of convergence. The cartoon otter crosses its eyes slightly to focus on a ladybug resting on its nose. As objects move closer to the observer, the eyes rotate inward to maintain fixation. The brain can use the degree of this inward eye movement as a cue to estimate the distance of nearby objects.

"Convergence." by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

Accommodation: Adjusting the Lens

Accommodation is another ocular motor depth cue that comes into play when objects are nearby. Our eye lenses change shape to focus on object on the retina (Mon-Williams & Tresilian, 1999). This too informs us that an object is in close proximity.

Monocular Depth Cues

Occlusion: Objects in the Foreground

Occlusion occurs when one object partially blocks our view of another object. This cue allows us to perceive which object is closer to us (Nakayama et al., 1989). For example, if a triangle partially obscures a square in an image, we perceive the triangle as closer even though this did not need to be the case (e.g., perhaps the square was closer but had a cutout which allowed the triangle to be fully visible).

Figure 9.2

A visual diagram on a teal background showing a white triangle overlapping a red square on the left, and the two shapes separated on the right to reveal the red shape's actual notched, L-like outline.

People have a bias to see near objects as occluding more distant objects but illusions can occur if the nearby object has a cutout.

"Cutouts." by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

Relative Height and the Horizon

Objects' positions relative to the horizon also provide depth information. Objects below the horizon that appear higher in the visual field are perceived as farther away. Conversely, objects above the horizon that appear lower are perceived as more distant (Sedgwick, 1986).

Shadows: Clues Cast by Light

Shadows provide important depth cues. Changes in the direction and length of shadows can alter our perception of an object's location (Mamassian et al., 1998). In addition, the movement of a shadow can make objects seem closer or farther away.

Relative Size: A Matter of Perspective

When objects of the same size appear smaller on our retinas, we interpret them as being farther away (Epstein, 1965). This cue is especially useful for gauging distances when there are familiar objects of known size in the scene.

Familiar Size: Context Matters

Our knowledge of the typical size of familiar objects, such as boats or rocks, helps us gauge their distance (Epstein, 1965). If an object appears smaller than expected, we assume it's farther away; if it appears larger, it seems closer.

Atmospheric Perspective: The Influence of the Air

The atmosphere can affect our perception of depth. Objects farther away often appear hazier or less distinct due to atmospheric effects (like fog) (Palmer, 1999). Sharper images typically signal closeness, while blurrier images suggest greater distance.

Linear Perspective: Parallel Lines Converge

Parallel lines in a scene (e.g, a roadway) appear to converge as they extend into the distance. This linear perspective cue helps us perceive depth and distance, as illustrated in artworks and photographs (Sedgwick, 1986).

Texture Gradient:

Equally spaced elements (e.g., telephone poles or bricks in a wall), appear more closely packed when they are distant. Texture gradient is a crucial cue for perceiving depth in scenes with repetitive patterns (Gibson, 1950).

A scenic Maine coastal highway illustrates several monocular depth cues. Cars of the same general size appear at different distances along a winding road, with nearby vehicles partially blocking more distant ones. The road, lane markings, utility poles, and stone wall converge toward the horizon, creating linear perspective. A stone wall on the right shows a texture gradient, with large, detailed stones in the foreground and smaller, less distinct stones farther away. A bald eagle flies overhead, and its shadow on the road provides a shadow cue for judging its height. A lighthouse sits on a distant headland, and hazy blue mountains fade into the background, demonstrating atmospheric perspective. Labels identify the depth cues throughout the scene.

Figure 9.3

Illustration of monocular depth cues in an AI-generated scene. The image depicts occlusion (near cars partially block farther cars), relative size and familiar size (identical-sized cars appear smaller with increasing distance and we are familiar with the size of cars), relative height (for objects below the horizon more distant objects appear higher in the visual field), linear perspective (the lane markings converge toward a vanishing point), texture gradient (stones in the wall become more packed in the distance), atmospheric perspective (distant mountains appear lighter and bluer), and shadow cues (the eagle's shadow on the roadway indicates its height above the ground).

"Maine Depth Cues." by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

Binocular Depth Cues

Binocular Disparity

Perhaps the most powerful depth cue comes from having two eyes spaced approximately 6 centimeters apart. Because our eyes view the world from slightly different positions, each eye receives a slightly different image. Binocular disparity refers to these small differences between the images seen by the left and right eyes (Howard & Rogers, 2012). Your brain compares these two images and uses the differences to calculate how far away objects are and where they are located in three-dimensional space.

To understand binocular disparity, it is helpful to introduce the concept of the horopter. Imagine that you are looking directly at a coffee mug on a table. The horopter is an imaginary curved line that passes through the point you are fixating on and includes all other points in space that project onto corresponding retinal points in the two eyes (Ogle, 1950). Corresponding retinal points are locations on the left and right retinas that send matching information to the brain.

When light comes from objects that lie on the horopter, it falls on corresponding retinal points, so the brain receives nearly identical information from each eye. In Figure 9.4, points A and A′ and points B and B′ represent corresponding retinal points. These are locations on the left and right retinas that occupy the same relative position. If you could imagine placing one retina directly on top of the other, points A and A′ would line up, as would points B and B′. When light from objects stimulate corresponding retinal points, the brain recognizes that these objects are equally distant. Objects that are closer to you than the point of fixation or farther away from it do not stimulate corresponding retinal points. Instead, their images fall on different locations on the two retinas, creating binocular disparity. Specifically, for objects that are closer than the fixation point, the image falls farther toward the temporal side of each retina, whereas for objects that are farther away, the image falls farther toward the nasal side of each retina. The brain uses these differences in retinal position to determine whether an object is in front of or behind the point you are looking at and to estimate its distance(Howard & Rogers, 2012).

Figure 9.4

Diagram illustrating the horopter and corresponding retinal points. Two eyes are shown at the bottom, with green dots representing the pupils. Two objects positioned on an arc above the eyes (the horopter) project light rays into both eyes. The rays from each object land on matching locations in the left and right retinas, labeled A and A′ and B and B′, demonstrating corresponding retinal points.

Light from objects on the horopter stimulates corresponding retinal points. The two circles at the bottom represent the eyes; green dots indicate the pupils. Light rays from objects located on the horopter (top) enter each eye and are focused on corresponding retinal points (A and A′, B and B′).

"Light from objects on the horopter." by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

The Correspondence Problem

Although binocular disparity provides powerful information about depth, the brain first faces an important challenge known as the correspondence problem (Marr & Poggio, 1976). Before it can calculate depth, the visual system must determine which parts of the image seen by the left eye correspond to the same objects in the image seen by the right eye. This is far from a simple task because every scene contains countless edges, textures, and patterns that could potentially match one another. Yet our brains solve this problem almost instantly, allowing us to experience a stable three-dimensional world.

Figure 9.5

Two side-by-side square panels filled with dense, randomly distributed black and white dots are separated by a vertical black divider. At first glance the two dot patterns appear identical and contain no visible object. When viewed using a wall-eyed (parallel viewing) technique or with a stereoscope, a square region in the center appears to float in front of the background. The square is created solely by a slight horizontal displacement of corresponding dots between the left and right images, illustrating how the visual system solves the binocular correspondence problem by matching individual dots across the two retinal images to recover depth from binocular disparity.

The left and right panels consist of nearly identical fields of randomly distributed black and white dots. A small central region is horizontally displaced between the two images while preserving the local dot pattern. When the two panels are viewed using a wall-eyed (parallel viewing where the left image goes to the left eye and the right image goes to the right eye) technique or with a stereoscope, the displaced region is perceived as a square floating in front of the surrounding dot field. Because the image contains no monocular cues to the square's location, the percept of depth depends entirely on establishing correct correspondences between matching dots in the left and right images. This demonstrates the correspondence problem in stereopsis: the visual system must determine which features in one retinal image correspond to the same physical features in the other before binocular disparity can be used to compute depth.

"Random-dot stereogram illustrating the binocular correspondence problem." by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

One of the best demonstrations of the correspondence problem comes from random-dot stereograms (Julesz, 1960; Julesz, 1971). These images consist of two patterns of randomly arranged dots that appear almost identical. When viewed with only one eye, neither image contains any recognizable object or depth information. However, when one pattern is presented to the left eye and the other to the right eye, the brain identifies the matching dots between the two images. Once these correspondences are established, a hidden three-dimensional shape suddenly appears to "pop out" from the background. This remarkable illusion demonstrates that depth perception does not come from either image alone but from the brain's ability to correctly match corresponding features across the two eyes. Although researchers understand many of the neural mechanisms involved in stereoscopic vision, exactly how the brain solves the correspondence problem so quickly and accurately remains unclear.

In summary, stereoscopic depth perception depends on two key steps: first, the brain determines which parts of the two retinal images correspond to one another (the correspondence problem), and second, it uses the binocular disparity between those matched points to calculate depth.

Motion-Based Depth Cues

Motion Parallax: Objects on the Move

As we move, nearby objects appear to glide rapidly past us, while distant objects seem to move more slowly across our retinas (Gibson et al., 1959). This motion-based cue provides valuable information about an object's proximity.

Deletion and Accretion: The Dance of Occlusion

Deletion and accretion are dynamic depth cues that occur when moving objects gradually hide or reveal parts of other objects (Gibson et al., 1969). Deletion refers to portions of a stationary object disappearing from view as they become blocked (or occluded) by a moving object. Accretion is the opposite process: previously hidden portions of the stationary object gradually reappear as the moving object passes by. Because the visual system assumes that objects usually continue to exist even when they are temporarily hidden, these changes provide important information about the relative positions of objects in space. For example, if a person walks in front of a parked car, parts of the car are progressively deleted from view as the person passes, and then progressively accreted as the person moves away. From this pattern, the brain concludes that the person is closer than the car. Thus, deletion and accretion are dynamic forms of occlusion that help us perceive depth and determine which objects are in front of others while they are in motion.

Three-Dimensional Imagery

3D Glasses: Tricks of Perception

Red-blue 3D glasses, also known as anaglyph glasses, demonstrate how the brain uses binocular disparity to perceive depth. Because the eyes are approximately 6 cm (2.5 inches) apart, each eye naturally views the world from a slightly different angle. The small difference between the images received by the left and right eyes is called binocular disparity (Howard & Rogers, 2012). The visual cortex compares these two images and uses the amount of disparity to judge how far away objects are.

Anaglyph images recreate this process by presenting each eye with a slightly different version of the same image. Two images taken from slightly different perspectives are superimposed, with one tinted red and the other tinted blue. The red lens (placed over the left eye) allows the blue image to pass while blocking most of the red image. Likewise, the blue lens (placed over the right eye) allows the red image to pass while blocking most of the blue image. Think of it this way: through the red lens, red images blend into the reddish background and become difficult to distinguish, while blue images stand out clearly. Through the blue lens, blue images blend into the bluish background, while red images stand out. As a result, each eye receives only the image intended for it. The brain then combines the two images into a single three-dimensional percept, just as it does during normal binocular vision.

Figure 9.6 illustrates how red/blue (anaglyph) glasses create the perception of depth by presenting a different image to each eye. The red lens allows the left eye to see the blue triangle, while the blue lens allows the right eye to see the red triangle. Because each eye receives a slightly different image, the visual cortex combines the two images into a single three-dimensional percept using binocular disparity. Whether the object appears closer to or farther from the viewer depends on the relative horizontal positions of the two images.

In the left panel, the rays of light from the two images remain uncrossed as they travel to the eyes. The image intended for the left eye is shifted to the left of the image intended for the right eye, producing uncrossed disparity. To fuse these images, the eyes would need to converge less than they would for an object on the screen, so the brain interprets the triangle as being farther away, behind the plane of the page. In retinal terms, the corresponding images fall on the nasal halves of the retinas.

Figure 9.6

Two side-by-side diagrams illustrate how red/blue anaglyph glasses create depth perception. Each panel shows a pair of eyes wearing colored glasses, with a red and a blue triangle positioned above them. In the left panel, light rays from the triangles travel to the eyes without crossing, producing uncrossed binocular disparity and causing the fused triangle to be perceived behind the page. In the right panel, the light rays cross before reaching the eyes, producing crossed binocular disparity and causing the fused triangle to be perceived in front of the page.

Red/blue (anaglyph) glasses present a different image to each eye. In the left panel, the image produces uncrossed disparity, so the brain perceives the object as being farther away than the page. In the right panel, the image produces crossed disparity, so the brain perceives the object as being closer than the page.

“Binocular disparity and anaglyph images”  by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

In the right panel, the rays of light cross before reaching the eyes. The image intended for the left eye is shifted to the right of the image intended for the right eye, producing crossed disparity. To fuse these images, the eyes must converge more than they would for an object on the screen, so the brain interprets the triangle as being closer, appearing to float in front of the page. In retinal terms, the corresponding images fall on the temporal halves of the retinas.

For example, in Figure 9.7, the word crossed is presented with crossed binocular disparity and therefore appears to float in front of the page. The word uncrossed is presented with uncrossed binocular disparity and appears to recede behind the page. Although both words are printed on a flat surface, the different images presented to each eye allow the brain to reconstruct the illusion of depth, demonstrating how binocular disparity is one of the most important cues for three-dimensional perception.

3D text graphic featuring the word "HOROPTOR" in sharp gray font in the foreground, with double-image offset text reading "UNCROSSED" above and "CROSSED" below in overlapping cyan and magenta colors.

Figure 9.7

When viewed with red/blue glasses this word crossed will appear close and the word uncrossed will appear far away.

"Red/blue glasses." by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

3D photograph taken with a fisheye lens looking up at tall, bare trees in a forest, rendered with red and cyan stereoscopic color fringes.

Figure 9.8

When viewed with red/blue glasses this anaglyph picture will appear in 3D.

"3D anaglyph" by zkj102 is licensed under CC BY-NC-ND 2.0

Pulfrich's Pendulum: A Visual Illusion

Pulfrich's Pendulum is a fascinating demonstration of how motion and binocular depth perception can combine to create an optical illusion (Pulfrich, 1922). In this demonstration, a pendulum swings back and forth in a straight line while one eye is covered with a dark filter, such as a pair of sunglasses over only the left eye. Because less light reaches the shaded eye, the visual signal from that eye is processed slightly more slowly than the signal from the unshaded eye. As the pendulum moves, this small timing difference causes each eye to register the pendulum in slightly different positions. The brain interprets this positional difference as binocular disparity—the same cue it normally uses to judge depth. When the pendulum moves from right to left, the delayed signal from the left eye causes the pendulum to appear closer than it really is. As the pendulum reverses direction and moves from left to right, the delay remains, but now the disparity is reversed, making the pendulum appear farther away than it actually is. Instead of perceiving the pendulum as moving in a straight line, the brain combines these changing depth signals into the perception of an elliptical or circular path through space. If you have a pair of sunglasses I recommend trying this demonstration with a friend. The Pulfrich Pendulum illustrates that the brain uses not only the images received by the two eyes but also the timing of those signals when constructing our perception of three-dimensional motion.

A two-panel scientific diagram illustrating the Pulfrich effect, showing how a filter over the left eye creates a visual processing delay that causes a side-to-side moving object to appear perceived closer (when moving left) or farther away (when moving right).

Figure 9.9

A pendulum that is actually swinging back and forth in a straight line is perceived as moving in an elliptical path when one eye views the pendulum through a dark filter (shown as a gray rectangle in the figure above). The gray circles show the pendulum's actual and delayed positions as it swings horizontally. Because the brain combines these mismatched images from the two eyes, it calculates an incorrect binocular disparity and perceives the pendulum at a point in front of or behind its actual location (shown here as a circle marked with an X). When the pendulum moves in one direction, it appears closer; when it reverses direction, it appears farther away. The continuous change in perceived depth as the pendulum swings makes it appear to travel in an ellipse instead of a straight line.

"Pulfrich’s Pendulum." by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

Depth Perception in Art and Media

Visual media, including video games and movies, often use various depth cues to enhance the viewer's experience. Motion parallax, relative size, linear perspective, and other cues create a more immersive and realistic environment.

Size Perception and Depth

The Influence of Depth Information

Size perception is intimately linked to depth information. How we perceive the size of an object in the world is greatly influenced by our brain's interpretation of its distance from us. To illustrate this relationship, we can examine a few key principles.

Size Constancy

One critical aspect of size perception is size constancy. When an object moves further away from us, we don't perceive it as getting smaller. For instance, as someone walks away from us down a path, we don't believe they are shrinking. This phenomenon is due to the brain's ability to factor in depth information when interpreting size (Holway & Boring, 1941).

The Role of Retinal Angle and Distance

The Retinal Angle

To understand how we perceive size based on depth, we must consider the concept of retinal angle. The retinal angle is the angle formed from the top to the bottom of an object on our retina. It represents how much space the object occupies on our retina. Larger objects create larger retinal angles, and smaller objects create smaller angles (if you keep the distance of the object from the person the same).

Distance and Its Impact

In addition to the retinal angle, distance plays a pivotal role in size perception. The distance from an object to our eyes affects how we perceive its size. An object farther away will appear smaller on our retinas compared to the same object up close but it will have a larger distance (D) than the near object.

Formula for Size Perception

Our brain accounts for changes in retinal angle and distance by consider a simple formula:

S=r*D

  • S: Perceived size of an object.
  • r: The retinal angle, representing how the object appears on the retina.
  • D: The distance of the object from the eye.

This formula illustrates that our perception of an object's size (S) depends on both the retinal angle (r) and the object's perceived distance from our eyes (D) (Kilpatrick & Ittelson, 1953).

Diagram illustrating the principle of size constancy. An eye on the left views two identical-height people standing at different distances. The nearer person is connected to the eye by blue lines, forming a larger retinal angle (rₙₑₐᵣ), while the farther person is connected by orange lines, forming a smaller retinal angle (rfₐᵣ). Vertical arrows next to both people indicate that their actual heights are the same. Horizontal arrows along the ground show that the farther person is at a greater distance from the observer (Dfₐᵣ > Dₙₑₐᵣ). The figure demonstrates that although retinal angle decreases with distance, perceived size remains constant because the visual system takes viewing distance into account.

Figure 9.10

Size constancy depends on both retinal angle and perceived distance. Two people of identical physical height are viewed at different distances from the observer. The nearer object subtends a larger retinal angle (rₙₑₐᵣ), whereas the farther object subtends a smaller retinal angle (rfₐᵣ). At the same time, the farther object has a greater perceived viewing distance (Dfₐᵣ > Dₙₑₐᵣ). The visual system combines retinal angle (r) with perceived distance (D) to estimate object size (S ≈ r × D), allowing both people to be perceived as having the same physical size despite the smaller retinal image of the more distant object.

"Size constancy." by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

Distorted Size Perception

The Effect of Depth Information

When we have accurate depth information, our size perception is generally reliable. However, problems arise when depth information is distorted or misleading, such as in optical illusions or unusual scenarios.

Illusions of Size

  1. Ames Room

The Ames room is an optical illusion that creates a distorted perception of size (Ittelson, 1952). Although it appears to be a normal rectangular room when viewed from one specific position, the room is actually highly distorted. It is built with trapezoidal walls, a slanted floor and ceiling, and one corner is much farther from the viewer than the other. Viewing the room from a single fixed angle removes many of the depth cues that would normally reveal its true shape, causing the brain to interpret it as a regular rectangular room.

As a result, people or objects standing in the two corners appear dramatically different in size. The person standing in the farther corner appears unusually small, while the person standing in the nearer corner appears unusually large, even though they are actually the same size. This occurs because the distorted shape of the room makes both corners appear to be the same distance from the observer. Since the brain assumes the two people are equally far away, it interprets differences in their retinal image size as differences in their actual size rather than differences in distance.

Figure 9.11

Two side-by-side photographs of Todd Kahan and Kathy Mathis standing in an Ames room at the Museum of Illusions. The room is painted with an orange-and-black geometric cube pattern and appears to be an ordinary rectangular room, although it is actually distorted. In the left photograph, Todd stands in the left corner and appears much taller than Kathy, who stands in the right corner. In the right photograph, after the two people switch corners, Kathy now appears much taller than Todd. The apparent size difference is an optical illusion caused by the room's distorted shape: the two individuals are standing at different physical distances from the camera, but the room's forced perspective makes them appear to occupy the same depth, leading the visual system to interpret the difference in retinal image size as a difference in height.

Two photographs show the same people standing in an Ames room, a specially constructed room with a trapezoidal shape that appears rectangular when viewed from a fixed vantage point. In the left photograph, Todd Kahan appears much taller than Kathy Mathis. In the right photograph, after the two individuals switch corners, Kathy appears much taller than Todd. Although their apparent heights change dramatically, neither person's height changes. Instead, each person moves to a different physical distance from the camera while the room's distorted geometry creates the illusion that both individuals are standing at the same depth. Because the visual system assumes the room is rectangular, differences in retinal image size are interpreted as differences in height rather than differences in viewing distance.

"Ames room." by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

This illusion can be explained by the size–distance relationship, where perceived size depends on both the size of the image projected onto the retina and the perceived distance of the object. Because the observer incorrectly perceives both people as being the same distance away, the person with the smaller retinal image is judged to be physically smaller, even though they are simply farther away. The Ames room demonstrates how the visual system relies on assumptions about perspective and distance to judge the size of objects, and how those assumptions can be manipulated to produce striking perceptual illusions.

In terms of the size–distance relationship, perceived size (S) = retinal image size (R) × perceived distance (D). Because the brain incorrectly assumes the perceived distance (D) is the same for both people, the smaller retinal image is interpreted as a smaller person rather than as someone standing farther away.

  1. Plank Illusion

The Plank Illusion is an outdoor version of the famous Ames Room illusion that demonstrates how our perception of size depends on assumptions about distance. Instead of using a specially constructed room, the illusion takes advantage of a sloping hillside and a long wooden plank. In a typical demonstration, a plank is placed on a hill so that one end is physically much farther from the observer than the other. From a carefully chosen viewing position, however, the plank appears to be level, making it seem as though the two people standing on it are the same distance away. Because the brain assumes they are equally distant, it interprets differences in the size of their retinal images as differences in their actual heights. As a result, the person standing at the farther end of the plank appears unusually tall, while the person at the nearer end appears unusually short. If the two people switch places, their apparent heights reverse instantly.

  1. Hering-Helmholtz and Wundt Illusions

These geometric illusions demonstrate how the visual context surrounding an object can influence our perception of shape and spatial relationships (Hering, 1861/1964; Helmholtz, 1867/1962). In the Hering illusion, two physically straight and parallel lines appear to bow outward because they are superimposed on a background of radiating lines. In the closely related Wundt illusion, the arrangement of the background lines produces the opposite effect, causing the parallel lines to appear to bow inward. These illusions are thought to arise because the radiating background provides powerful perspective and depth cues that the visual system interprets as information about three-dimensional space. Rather than processing the parallel lines in isolation, the brain combines information from the lines and their surrounding context. As a result, the spacing between the parallel lines may appear to change across their length, even though the distance between them is constant. For example, the gap between the lines may seem wider in the Hering–Helmholtz illusion near the center of the figure (which looks further away) and narrower toward the edges (which look closer), despite the fact that the lines remain perfectly parallel and the angle between them does not change.

Side-by-side black-and-white diagrams comparing the Hering–Helmholtz and Wundt illusions. The left panel shows two thick, straight horizontal lines; the background shows a central point from which many thin lines radiate outward in all directions, causing the horizontal lines to appear slightly bowed outward. The right panel shows two thick, horizontal lines overlaid on radial line patterns with an angular diamond-shaped background, making the horizontal lines appear to bow inward.

Figure 9.12

The left panel illustrates the Hering–Helmholtz illusion, in which two physically straight, parallel horizontal lines appear to bow outward when viewed against a field of radiating lines. The right panel illustrates the Wundt illusion, in which straight, parallel horizontal lines appear to bow inward when viewed against contextual elements. In both cases, the horizontal lines are perfectly straight; the apparent curvature arises from the influence of the surrounding visual context.

"Hering-Helmhotz and Wundt illusions.” by Kahan, T.A. is licensed under CC BY-NC-SA 4.0

Conclusion:

In this chapter on depth perception, we have investigated the intricate factors that shape our perception of the three- dimensional world. We explored the critical role of oculomotor cues, monocular depth cues, and binocular disparity in our ability to gauge depth and spatial relationships. Additionally, we investigated the mechanisms through which 3D images are constructed and how depth information fundamentally influences our perception of object sizes. This knowledge is not only influential in the realms of television and media, where it enhances the creation of immersive visual experiences, but it also provides invaluable insights into the underlying reasons for the occurrence of various size illusions, shedding light on the fascinating intricacies of human vision and perception.

References:

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Gibson, J. J. (1950). The perception of the visual world. Houghton Mifflin.

Gibson, E. J., Gibson, J. J., Smith, O. W., & Flock, H. (1959). Motion parallax as a determinant of perceived depth. Journal of Experimental Psychology, 58(1), 40–51. https://doi.org/10.1037/h0043883

Gibson, J. J., Kaplan, G. A., Reynolds, H. N., Jr., & Wheeler, K. (1969). The change from visible to invisible: A study of optical transitions. Perception & Psychophysics, 5(2), 113–116. https://doi.org/10.3758/BF03210533

Helmholtz, H. von. (1962). Treatise on physiological optics (J. P. C. Southall, Trans.). Dover. (Original work published 1867.)

Hering, E. (1964). Outlines of a theory of the light sense (L. M. Hurvich & D. Jameson, Trans.). Harvard University Press. (Original work published 1861.) (No DOI.)

Holway, A. H., & Boring, E. G. (1941). Determinants of apparent visual size with distance variant. American Journal of Psychology, 54(1), 21–37. https://doi.org/10.2307/1417790

Howard, I. P., & Rogers, B. J. (2012). Perceiving in depth (Vol. 1: Basic mechanisms). Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199764143.001.0001

Ittelson, W. H. (1952). The Ames demonstrations in perception; a guide to their construction and use. Princeton University Press.

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