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. 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.

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. 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. 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 9.1

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.

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. 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. This cue is especially useful for gauging distances when there are familiar objects of known size in the scene.

Figure 9.2

Familiar Size: Context Matters

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

Figure 9.3

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). 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.

Texture Gradient: The Art of Crowding

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.

Figure 9.4

Binocular Depth Cues

Binocular Disparity: The Magic of Stereopsis

Figure 9.5

Perhaps the most powerful depth cue comes from having two eyes spaced approximately 6 centimeters apart. Binocular disparity refers to the slight differences in the images received by each eye. These differences allow our brains to calculate the depth of objects and their positions in space. The horopter, an imaginary arc passing through objects, is a key concept in understanding binocular disparity. Light from objects that fall on the horopter will stimulate corresponding retinal points in each eye, while light from objects that are nearer or further to you than the object you are looking at will not stimulate corresponding retinal points. Instead, for objects that are closer the light will fall toward the temporal portion of the retina and for objects that are further the light will fall toward the nasal portion of the retina. By matching the two eyes your brain is provided with information about an objects is located in space.

The Correspondence Problem: Stitching It All Together

While binocular disparity is a powerful cue, the correspondence problem highlights the complexity of our visual system. We don't fully understand how our brains effortlessly match up corresponding retinal points to create a coherent perception of depth. To illustrate the Correspondence Problem, let's consider random dot stereograms. Random dot stereograms consist of two seemingly identical patterns of randomly arranged dots. These patterns are nearly identical but have subtle differences. When viewed by each eye individually, these patterns do not convey any 3D information or meaningful shapes. However, when you view them stereoscopically (with one image presented to each eye), your brain can perceive a three-dimensional image or structure.To perceive depth, the brain needs to figure out which dots or features in the left-eye image correspond to those in the right-eye image. In other words, it must find matching points between the two images. Somehow our visual system is able to do this amazingly complex matching quickly and effortlessly.

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. This motion-based cue provides valuable information about an object's proximity.

Deletion and Accretion: The Dance of Occlusion

Deletion and accretion occur when moving objects obscure or reveal parts of stationary objects. These cues, related to occlusion, help us perceive the relative distances of objects in motion.

Three-Dimensional Imagery

3D Glasses: Tricks of Perception

Red-blue 3D glasses, also known as anaglyph glasses, demonstrate how the brain processes visual information from each eye differently. By tinting images differently for each eye, two images taken from slightly different perspectives can be directly input into either the left or right eye. The red lens (over the left eye) will filter the image tinted red while the blue lens (over the right eye) will filter the image tinted blue. When the same object in each eye stimulates the temporal portions of each retina (known as crossed perception) it is perceived as being nearer and when the same object in each eye stimulates nasal portions of each retina (known as uncrossed) it is perceived as further away.

Figure 9.6

Pulfrich's Pendulum: A Visual Illusion

Pulfrich's Pendulum is a fascinating example of how motion and depth perception can create optical illusions. By swinging a pendulum while one eye is shaded (e.g., covering the left eye with sunglasses), we can observe how depth cues affect our perception of the pendulum's movement. Here, when the pendulum moves from the right to the left the signal sent from the left eye is slightly delayed (because of the sunglasses) and the object is perceived as being closer than it is in reality. Then, when the object moves from the left to the right the left eye continues to have a delay, which now causes the object to appear further away than it is in reality. Together, this creates the illusion that the moving object is traveling in an ellipse rather than moving straight back and forth.

Figure 9.7

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.

Figure 9.8

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: Objects in Motion

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.

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.

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).

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. It is typically constructed with trapezoidal walls and floor, making one corner of the room appear much closer than the other. When viewed from a specific angle through a peephole or camera, it gives the illusion that people or objects standing in the far corner are very short and people in the near corner are very tall, even though they are of the same size in reality. This fascinating visual trick plays on providing poor depth information which causes us to interpret the differences in the visual angle as differences in size.

Figure 9.9

2. Plank Illusion: Similar to the Ames Room, the Plank Illusion occurs outdoors. It exploits perspective and depth to make two individuals, even if they're of the same size, appear vastly different in height.

3. Hering-Helmholtz and Wundt Illusions: These illusions involve parallel lines that appear to bow outward or inward, respectively. The background provides depth cues that create the illusion that the lines are not parallel when, in fact, they are. Specifically, the apparent size of the space between two parallel lines may seem to vary from the center to the edges of these illusions due to the influence of the background. This happens because, although the actual angle of the gap between the parallel lines remains unchanged (since the lines are parallel), our perception of the size of the gap is affected by the background. In essence, the background of these illusions can create a sense of depth, leading us to perceive the parallel lines as if they are not parallel.

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.