Perceiving Depth

Question 1

Sources of depth information that would be available in a 2D picture (cues that rely on only one eye)

Answer 1

Pictorial (monocular)

Question 2

– Information obtained from/relating to motion

Answer 2

Kinematic Cues

Question 3

– Cues based on sensing the position of the eyes and muscle tension

Answer 3

Oculomotor

Question 4

– Information obtained by comparing input from the left and right eyes (binocular)

Answer 4

Stereoscopic

Question 5

Pretend this puppy is driving this car… Objects nearer to him appear to move

Answer 5

Faster

Question 6

Motion Parallax/Motion Perspective

Answer 6

• when observer moved, displacement of an object’s image on the eye depends on its distance
• closer objects move more than farther objects
• Optic flow: when the whole visual field is considered,

Question 7

Expansion/Contraction

Answer 7

• when an object approaches, its image expands

- if on a hit path the expansion is symmetric

Question 8

Accretion/Deletion of Texture

Answer 8

when a surface moves relative to another, the nearer surface progressively occludes background texture on the farther surface

Question 9

Kinetic Information

Answer 9

• means relating to motion
• • motion perspective/motion parallax
• • optical expansion/contraction
• • accretion/deletion of texture

Question 10

Stereoscopic: Binocular Disparity

Answer 10

• differences in the two eyes’ views of an object
• amount of disparity depends on the distance of an object from the observer
• the two images of a three-dimensional world are not the same

Question 11

Stereoscopic: Horopter

Answer 11

• refers to sets of points in the world having identical binocular disparities.
• crossed disparity indicates that a point is nearer to the observer than the point being fixated.
• uncrossed disparity indicates that a point is farther from the observer than the point being fixated

Question 12

Oculomotor: Accommodation

Answer 12

• refers to changes in the shape of the lens to achieve focused images at varying distances
• may provide distance info via unconscious sensing of the muscular movements (in the ciliary muscles) that produce the lens changes

Question 13

Oculomotor: Convergence/Divergence

Answer 13

• refers to the turning of the two eye to get a particular point in the center of fixation (fovea) of each eye
• provides depth info via unconscious sensing of the muscular movements used to turn the eyes

Divergence: when the eye moves to see something further away

• doesn’t work past 2 meters (near space)

Question 14

Oculomotor provide ______

Answer 14

metric: absolute distance information

* limitation not useful past 2 meters, lens (accommodation) is at thin as it gets

Question 15

Pictorial Information (monocular)

Answer 15

• monocular cues (can operate with only one eye)
• mostly relates to rules of optics and geometry that governs the projection of the world onto the retina
• involves using rules of projection (inverse optics) in reverse
• laws of optics: scene → retina
• inverse optics: retina → scene

Question 16

What are some results of the laws of optics that the brain might use to infer depth of objects in a 2D image?

Answer 16

• Nearer objects take up more of the visual field

- further away an object is, the nearer it appears to the vertical horizon (vanishing point)

Question 17

Perception as an inference:

Answer 17

brain infers scene due to its probability

the nervous system calculates the probability of each scene given the sensory evidence, and prior knowledge, and chooses the scene that has the highest probability

• • unnoticed judgement: Al-Haytham/Alhazen
• • unconscious inference: von Helmholtz
• Bayes rule

Question 18

Bayes Rule

Answer 18

• probability of a specific scene given an image is proportional to the probability that, that scene can give rise to that image times the probability of the likelihood of that retinal image in general
• *P(Sx | I) [posterior]: P(I | Sx)[likelihood]P(Sx)[prior]

Question 19

Combining depth cues

Answer 19

• P(depth | cue1, c2, c3, …) : P(c1 | d)P(c2 | d)…P(d)
• the nervous system follows an optimal statistical rule of combination in combining different cues (weighted average if P(d) is uniform)

Question 20

Which cue(s) provide non-metric information?

Answer 20

Occlusion

Question 21

Which cue(s) provide metric information?

Answer 21

Convergence, Accommodation, and Familiar Size

Question 22

Which cue(s) provide relative metric information?

Answer 22

Motion Parallax
Relative Size
Relative Height
Binocular Disparity

Question 23

Pictorial Depth cues

Answer 23

Relative Size
Familiar Size
Texture Gradient 
Relative Height
Linear Perspective
Occlusion 
Aerial Perspective

Question 24

Bayesian Inference

Answer 24

Combining multiple sources of information to arrive at a final percept of the depth to an object or a final interpretation of a 2D image

The final percept will be some combination of prior beliefs and the evidence at hand

Question 25

Priors

Answer 25

Before even looking at an image, we have an a priori belief about how likely it is that the world is in a given state

• The evidence we obtain from the image is combined with the sea priori beliefs

Question 26

Bayesian Inference: The Basic Idea

Answer 26

• Multiple kinds of information are taken into account to arrive at a final decision or percept
• A priori, humans have some belief about the likelihood of the world being in a given state (PRIOR)
• The retinal image could have been produced by many possible states of the world. However, assuming a given state of the world, that state has a likelihood of producing the retinal image supposing an image of the scene were taken from a random viewpoint (LIKELIHOOD)

Question 27

Likelihood:

Answer 27

Assuming a given state of the world is true, the likelihood of that state producing the 2D image shown

Question 28

Posterior:

Answer 28

Probability that the reality is a given state of the world given that we observed image I

Question 29

Generic viewpoint:

Answer 29

The vast majority of random viewpoints of a scene will fall into this category; these viewpoints provide similar information about the scene and suggest roughly the same surfaces

Question 30

Accidental viewpoint:

Answer 30

A kind of “freak accident” viewpoint. The 3D surfaces suggested at this viewpoint are very unlike those existing in the real world.