Chapter 10: Perceiving Depth and Size

Overview of Questions

• How can we see far into the distance based on the flat image of the retina?

• Why do we see depth better with two eyes than with one eye?

• Why don’t people appear to shrink in size when they walk away?

Figure 10.1 (a) The house is farther away than the tree, but (b) the images of points F on the house and N on the tree both fall on the two-dimensional surface of the retina, so (c) these two points, considered by themselves, do not tell us the distances of the house and the tree.

Cue Approach to Depth Perception

• This approach focuses on information in the retinal image that is correlated with depth in the scene.

• We learn the connection between the cue and depth.

• The association becomes automatic through repeat exposure.

Cue Approach to Depth Perception - continued

• Oculomotor cues are based on sensing the position of the eyes and muscle tension

– Convergence - inward movement of the eyes when we focus on nearby objects

– Accommodation - change in the shape of the lens when we focus on objects at different distances

Figure 10.2 (a) Convergence of the eyes occurs when a person looks at something that is very close. (b) The eyes look straight ahead when the person observes something that is far away.

Cue Approach to Depth Perception - continued

• Monocular cues come from one eye

– Pictorial cues - sources of depth information that come from 2-D images, such as pictures

• Occlusion - when one object partially covers another

• Relative height - objects below the horizon that are higher in the field of vision are more distant

–Objects above the horizon lower in the visual field are more distant

Pictorial Cues

• Relative size - when objects are equal size, the closer one will take up more of your visual field

• Perspective convergence - parallel lines appear to come together in the distance

• Familiar size - distance information based on our knowledge of object size

Figure 10.4 Drawings of the stimuli used in Epstein’s (1965) familiar-size experiment. The actual stimuli were photographs that were all the same size as the real quarter.

Pictorial Cues - continued

• Atmospheric perspective - distance objects are fuzzy and have a blue tint

• Texture gradient - equally spaced elements are more closely packed as distance increases

• Shadows - indicate where objects are located

– Enhance 3-D of objects

Figure 10.1 Range of effectiveness of different depth cues

Motion-Produced Cues

• Motion parallax - close objects in direction of movement glide rapidly past but objects in the distance appear to move slowly

• Deletion and accretion - objects are covered or uncovered as we move relative to them

– Covering an object is deletion

– Uncovering an object is accretion

VIDEO: Motion Parallax

Figure 10.8 Eye moving past (a) a nearby tree; (b) a far-away house. Notice how the image of the tree moves farther on the retina than the image of the house.

Binocular Depth Information

• Binocular disparity - difference in images from two eyes

– Difference can be described by examining corresponding points on the two retinas

• The horopter - imaginary sphere that passes through the point of focus

– Objects on the horopter fall on corresponding points on the two retinas

Binocular Depth Information - continued

• Objects that do not fall on the horopter fall on noncorresponding points

– These points make disparate images.

– The angle between these points is the absolute disparity.

– The amount of disparity indicates how far an object is from the horopter.

– Relative disparity is the difference between the absolute disparity of two objects.

Figure 10.11 Location of images on the retina for the “Two Eyes: Two Viewpoints” demonstration. See text for explanation.

Figure 10.12 Corresponding points on the two retinas. To determine corresponding points, imagine that one eye is slid on top of the other one.

Figure 10.13 (a) When the lifeguard looks at Frieda, the images of Frieda, Susan, and Harry fall on corresponding points on the lifeguard’s retinas, and the images of the other swimmers fall on noncorresponding points. (b) The locations of the images of Susan, Frieda, and Harry on the lifeguard’s retina.

Figure 10.14 The location of the images of Frieda and Carole in the lifeguard’s eyes, when the lifeguard is looking at Frieda. Because Carole is not located on the horopter, her images fall on noncorresponding points. The absolute angle of disparity is the angle between the point on the right eye that corresponds to Carole’s image on the left eye (CL), and the point where the image actually falls (CR).

Figure 10.15 The location of the images of Frieda and Carole in the lifeguard’s eyes, when the lifeguard is looking at Carole. Because Frieda is not located on the horopter, her images fall on noncorresponding points. The absolute angle of disparity is the angle between the point on the right eye that corresponds to Frieda’s image on the left eye (FL) , and the point where the image actually falls (FR).

Binocular Depth Information - continued

• Stereopsis - depth information provided by binocular disparity

– Stereoscope uses two pictures from slightly different viewpoints.

– 3-D movies use the same principle and viewers wear special glasses to see the effect.

– Random-dot stereogram has two identical patterns with one shifted in position.

Figure 10.19 (a) A random-dot stereogram. (b)The principle for constructing the stereogram. See text for explanation.

Correspondence Problem

• How does the visual system match images from the two eyes?

– Matches may be made by specific features of objects.

– This may not work for objects like random-dot stereograms.

– A satisfactory answer has not yet been proposed.

Depth Perception in Other Species

• Animals use the range of cues that humans use.

• Frontal eyes, which result in overlapping fields of view, are necessary for binocular disparity.

• Lateral eyes, which do not result in overlapping fields of view, provide a wider view.

– This is important for watching for predators.

Depth Perception in Other Species - continued

• Locusts use motion parallax to judge distance.

• Bats use echolocation to judge the distance of objects in the dark.

– They emit sounds and note the interval between when they send them and when they receive the echo.

Figure 10.22 When a bat sends out its pulses, it receives echoes from a number of objects in the environment. This figure shows the echoes received by the bat from (a) a moth located about half a meter away; (b) a tree, located about 2 meters away; and (c) a house, located about 4 meters away. The echoes from each object return to the bat at different times, with echoes from more distant objects taking longer to return. The bat locates the positions of objects in the environment by sensing how long it takes the echoes to return.

Physiology of Depth Perception

• Experiment by Tsutsui et al.

– Monkeys matched texture gradients that were 2-D pictures and 3-D stereograms.

– Recordings from a neuron in the parietal lobe showed:

• Cell responded to pictorial cues

• Cell also responded to binocular disparity

Figure 10.23 Top: gradient stimuli. Bottom: response of neurons in the parietal cortex to each gradient. From Tsutsui, K. I., Sakata, H., Naganuma, T., & Taira, M. (2002). Neural correlates for perception of 3D surface orientation from texture gradient. Science, 298, 402-412; Tsutsui, K. I., Tiara, M., & Sakata, H. (2005). Neural mechanisms of three-dimensional vision. Neuroscience Research, 51, 221-229.

Physiology of Depth Perception - continued

• Neurons have been found that respond best to binocular disparity.

– These are called binocular depth cells or disparity selective cells.

• These cells respond best to a specific degree of absolute disparity between images on the right and left retinas.

Figure 10.24 Disparity tuning curve for a neuron sensitive to absolute disparity. This curve indicates the neural response that occurs when stimuli presented the left and right eyes create different amounts of disparity. From Uka, T., & DeAngelis, G. C. (2003). Contribution of middle temporal area to coarse depth discrimination: Comparison of neuronal and psychophysical sensitivity. Journal of Neuroscience, 23, 3515-3530.

Connecting Binocular Disparity and Depth Perception

• Experiment by Blake and Hirsch

– Cats were reared by alternating vision between two eyes.

– Results showed that they:

• had few binocular neurons.

• were unable to use binocular disparity to perceive depth.

Connecting Binocular Disparity and Depth Perception - continued

• Experiment by DeAngelis et al.

– Monkey trained to indicate depth from disparate images.

– Disparity-selective neurons were activated by this process.

– Experimenter used microstimulation to activate different disparity-selective neurons.

– Monkey shifted judgment to the artificially stimulated disparity.

Size Perception

• Distance and size perception are interrelated

• Experiment by Holway and Boring

– Observer was at the intersection of two hallways.

– A luminous test circle was in the right hallway placed from 10 to 120 feet away.

– A luminous comparison circle was in the left hallway at 10 feet away.

Figure 10.27 Setup of Holway and Boring’s (1941) experiment. The observer changes the diameter of the comparison circle in the left corridor to match his or her perception of the size of the test circles in the right corridor. Each test circle has a visual angle of 1 degree and is presented separately. This diagram is not drawn to scale. The actual distance of the far test circle was 100 feet.

Experiment by Holway and Boring

• On each trial the observer was to adjust the diameter of the test circle to match the comparison.

• Test stimuli all had same visual angle (angle of object relative to the observer’s eye).

– Visual angle depends on both the size of the object and the distance from the observer.

Figure 10.28 (a) The visual angle depends on the size of the stimulus (the woman in this example) and its distance from the observer. (b) When the woman moves closer to the observer, the visual angle and the size of the image on the retina increase. This example shows how halving the distance between the stimulus and observer doubles the size of the image on the retina.

Figure 10.29 The “thumb” method of determining the visual angle of an object. When the thumb is at arm’s length, whatever it covers has a visual angle of about 2 degrees. The woman’s thumb covers the width of her iPod, so the visual angle, from the woman’s view, is 2 degrees. Note that the visual angle will change as the distance between the woman and the iPod changes.

Experiment by Holway and Boring - continued

• Part 1 of the experiment provided observers with depth cues.

– Judgments of size were based on physical size.

• Part 2 of the experiment provided no depth information.

– Judgments of size were based on size of the retinal images.

Figure 10.31 Results of Holway and Boring’s (1941) experiment. The dashed line marked “Physical size” is the result that would be expected if the observers adjusted the diameter of the comparison circle to match the actual diameter of each test circle. The line marked “Visual angle” is the result that would be expected if the observers adjusted the diameter of the comparison circle to match the visual angle of each test circle.

Figure 10.32 The moon’s disk almost exactly covers the sun during an eclipse because the sun and the moon have the same visual angle.

Size Constancy

• Perception of an object’s size remains relatively constant.

• This effect remains even if the size of the retinal image changes.

• Size-distance scaling equation

– S = K (R X D)

– The changes in distance and retinal size balance each other

Size-Distance Scaling

• Emmert’s law:

– Retinal size of an afterimage remains constant.

– Perceived size will change depending on distance of projection.

– This follows the size-distance scaling equation.

Figure 10.33 The principle behind the observation that the size of an afterimage increases as the afterimage is viewed against more distant surfaces.

Figure 10.35 Two cylinders resting on a texture gradient. According to Gibson (1950), the fact that the bases of both cylinders cover the same number of units on the gradient indicates that the bases of the two cylinders are the same size.

Visual Illusions

• Nonveridical perception occurs during visual illusions.

• Müller-Lyer illusion:

– Straight lines with inward fins appear shorter than straight lines with outward fins.

– Lines are actually the same length.

Figure 10.36 The Müller-Lyer illusion. Both lines are actually the same length.

Müller-Lyer Illusion

• Why does this illusion occur?

– Misapplied size-constancy scaling:

• Size constancy scaling that works in 3-D is misapplied for 2-D objects.

• Observers unconsciously perceive the fins as belonging to outside and inside corners.

• Outside corners would be closer and inside corners would be further away.

Müller-Lyer Illusion - continued

– Since the retinal images are the same, the lines must be different sizes.

• Problems with this explanation:

– The “dumbbell” version shows the same perception even though there are no “corners.”

– The illusion also occurs for some 3-D displays.

Figure 10.38 The “dumbbell” version of the Müller-Lyer illusion. As in the original Müller-Lyer illusion, the two lines are actually the same length.

Figure 10.39 A three-dimensional Müller-Lyer illusion.The 2-foot-high wooden “fins” stand on the floor. Although the distances x and y are the same, distance y appears larger, just as in the two-dimensional Müller-Lyer illusion.

Müller-Lyer Illusion - continued

• Another possible explanation:

– Conflicting cues theory - our perception of line length depends on:

• The actual length of the vertical lines

• The overall length of the figure

– The conflicting cues are integrated into a compromise perception of the length.

Ponzo Illusion

• Horizontal rectangular objects are placed over railroad tracks in a picture.

• The far rectangle appears larger than the closer rectangle but both are the same size.

• One possible explanation is misapplied size-constancy scaling.

VIDEO: Size Constancy and Visual Illusions, Part 2

The Ames Room

• Two people of equal size appear very different in size in this room.

• The room is constructed so that:

– The shape looks like a normal room when viewed with one eye.

– The actual shape has the left corner twice as far away as the right corner.

Figure 10.42 The Ames room. Both women are actually the same height, but the woman on the right appears taller because of the distorted shape of the room.

VIDEO: The Ames Room

Figure 10.43 The Ames room, showing its true shape. The woman on the left is actually almost twice as far away from the observer as the one on the right; however, when the room is viewed through the peephole, this difference in distance is not seen. In order for the room to look normal when viewed through the peephole, it is necessary to enlarge the left side of the room.

The Ames Room - continued

• One possible explanation - size-distance scaling

– Observer thinks the room is normal.

– Women would be at same distance.

– Woman on the left has smaller visual angle (R).

– Due to the perceived distance (D) being the same her perceived size (S) is smaller

The Ames Room - continued

• Another possible explanation - relative size

– Perception of size depends on size relative to other objects.

– One woman fills the distance between the top and bottom of the room.

– The other woman only fills part of the distance

– Thus, the woman on the right appears taller

Moon Illusion

• The moon appears larger on the horizon than when it is higher in the sky.

• One possible explanation:

– Apparent-distance theory - horizon moon is surrounded by depth cues while moon higher in the sky has none.

– Horizon is perceived as further away than the sky - called “flattened heavens”.

Moon Illusion - continued

– Since the moon in both cases has the same visual angle, it must appear larger at the horizon.

• Another possible explanation:

– Angular size-contrast theory - the moon appears smaller when surrounded by larger objects

– Thus, the large expanse of the sky makes it appear smaller

• Actual explanation may be a combination of a number of cues.

Figure 10.44 An artist’s conception of how the moon is perceived when it is on the horizon and when it is high in the sky. Note that the visual angle of the horizon moon is depicted as larger than the visual angle of the moon high in the sky. This is because the picture is simulating the illusion. In the environment, the visual angle of the two moons are the same.

Figure 10.45 When observers are asked to consider that the sky is a surface and to compare the distance to the horizon (H) and the distance to the top of the sky on a clear moonless night, they usually say that the horizon appears farther away. This results in the “flattened heavens” shown above.

Effects of Person’s Ability to Take Action on Distance Perception

• Distance perception can also be affected by the perception of ability to take action.

• Experiment by Proffitt et al.

– Participants made distance judgments with or without a backpack.

– Those with the backpack increased their estimates, even though they did not have to walk the distance.

Effects of Person’s Ability to Take Action on Distance Perception - continued

• Experiment by Witt et al.

• Phase 1:

– Participants threw balls to targets four to ten meters away.

– They used either a light or heavy ball.

– Distance estimates were larger after throwing the heavy ball.

Effects of Person’s Ability to Take Action on Distance Perception - continued

• Phase 2:

– Participants were divided into two groups:

• One group was told they would have to throw the balls while blindfolded.

• The other group was told they would have to walk to targets while blindfolded.

• The group that was told they would be throwing balls increased their estimates.

Figure 10.47 Results of Witt et al.’s (2004) experiment. See text for explanation.