Chapter 6: 3D Perception Flashcards
- How do we understand the SPATIAL extent of the world?
What’s in front/behind?
How close/far is that predator/prey?
What shape is an object?
What is the size of something?
How do we go from
2-dimensional stimulation
to
3-dimensional experience?
??
The world is 3D and follows the rules of Euclidian geometry:
Parallel lines remain parallel as they are extended in space
Objects maintain the same size & shape as they move around in space.
Internal angles of a triangle always add up to 180 degrees, etc.
Euclidean geometry is just the fancy term for the geometry you learned in high school…
Notice that images projected onto the retina are NOT Euclidean!
Projective geometry
Investigates the mathematical relationships between objects in the environment and their optical projections on the retina or on a picture.
- Euclidean geometry of the 3-dimensional world turns into something quite different on the curved, 2-dimensional retina
Re-construct a Euclidean world from non-Euclidean stimulation.
The optical projections of objects are inherently ambiguous:
For example, all of the black lines shown below (straight, swigly, short, crooked) would produce exactly the same image on the observer’s retina. One of the great mysteries of perception is how the visual system is able to resolve this ambiguity to accurately perceive the 3D structure of the environment.
Shading information is inherently ambiguous up to a stretching or shearing transformation in depth.
It is not yet known how a single perceived surface is selected for the set of possible alternatives.
extreme accidental animated image from Web Activity 4.3, Object Ambiguity. See next slide for animation
even in 3D space, we can suffer from Accidental views of objects that lead us to the wrong interpretations of objects.
Depth cue
Information about the 3rd dimension (depth) of visual space.
Monocular depth cue
A depth cue or perceptual bias that is available even when the world is viewed with one eye alone.
Pictorial depth cue
A cue to distance or depth used by artists to depict 3-dimensional depth in 2-dimensional pictures. (Basically a monocular cue in a picture.)\
Binocular depth cue
A depth cue that relies on information from both eyes.
Primarily stereopsis in humans.
Stereopsis
From the Greek ‘stereo,’ meaning “solid”, and opsis, “appearance, sight”
A term that is most often used to refer to the perception of depth and 3-dimensional structure obtained on the basis of visual information deriving from two eyes by individuals with normally developed binocular vision.
Monocular Depth Cues / Perceptual Biases
Occlusion
Familiar Size
Resting on ground bias
Linear Perspective:
- Foreshortening
- Relative Size
- Relative Height
Shape from Texture
Ground plane Bias
Shape from Shading
Convexity Bias
Aerial Perspective
Depth of Field
Motion Parallax
Ocular-Motor Cues
Accommodation (Monocular)
Convergence & Divergence (Binocular)
Binocular Depth Cues Include…
Binocular Disparity
Stereopsis
Occlusion
A monocular cue to relative depth order in which, for example, one object obstructs the view of part of another object
Shapes overlapping each other
Familiar size
A monocular cue based on knowledge of the typical size of objects
Overriding familiar size is the basis of many “B” science fiction movies…
…
Godzilla
Three of the infinite number of scenes that could generate the retinal image in Figure 6.42
pennies
Resting on the ground bias
Unless there is information to the contrary, objects will be perceived as resting on the ground.
Information from shadows or indirect illumination can override the bias to perceive objects to be in contact with the ground.
Linear perspective
Monocular Cue to 3-Dimensional Space
Lines that are parallel in the 3-dimensional world will appear to converge in a 2-dimensional image as they extend into the distance.
This is a result of projective geometry.
Vanishing point
The apparent point at which parallel lines receding in depth converge.
The vanishing point below is on a horizon line.
Relative size & Foreshortening
Changes in shape due to linear perspective.
Foreshortening
Changes in surface orientation causes projected shape to change.
Monocular Bias
Relative Size:
Changes in surface depth causes projected size to change.
Monocular Bias
Closed, Open Door to Hallway picture.
Parallel lines in the image plane, such as those defining the door in (a), remain parallel in the image
Train tracks picture:
The two people lying across these train tracks are the same size in the image
Relative height
Below the horizon, objects higher in the visual field appear to be farther away.
The ratio of an object’s projected height relative to the height of the horizon specifies physical size in units of eye height.
Taller than eye height
vs.
Shorter than eye height
The height of an object’s base with respect to the horizon specifies its distance in depth.
This assumes that objects are in contact with the ground
Apparent distance can have a strong effect on apparent size.
The projected sizes of all 3 cylinders are the same, yet their apparent sizes are quite different.
The perception of 3D shape from texture (gradients)
OP Art (Optical Art)
In the 60s, an art style known as Optical Art emerged that made use of optical illusions.
Pieces by Bridget Riley that depict surfaces with contour textures.
As you can see, 2D images give rise to 3D perceptions.
The goal of Eric’s Master’s research was to model how the visual system interprets these images.
(Cartography, mechanical drawings, & computer graphics)
Eric Egan’s Study on Planar Cut Contours.
Imagine taking an object and slicing it up with a knife.
Those cut lines create planar cut contours.
Now lets take the simplest case where these cut lines are getting farther away from you.
When this is the case we can easily determine the relative distance between any 2 points by just counting the contours between them.
For example, this point is 4 contours from this point.
All we have to do is add a scaling parameter and we know the distance in depth z.
The problem with this simple model is that contour textures are rarely oriented to that we are looking directly at them.
We therefore improved our model to take into account the orientation of the planar cut contours.
It is very important that we take the orientation of the contours into account because it has a dramatic effect on our perceptions.
These 2 (black & white wavy blanket) images are of the same surface, the only thing that has changed is the orientation of the planar cut contours.
Psychophysics:
The Depth Profile Task
How to we measure people’s perceptions?
We use a depth profile task where we ask people to recreate the depth they see by moving these dots up and down.
Data with more complex object:
The red lines denote where we asked people to judge depth.
Down here, these black lines are show what the actual shape of the object is.
The red dots are people’s judgments.
The red lines are the model fits.
People’s judgments are most accurate when the planar cuts are not slanted.
When the planar cuts are slanted to the side, this effects peoples judgments of the horizontal lines.
When the planar cuts are slanted down, this effects peoples vertical judgments.
And the model is able to capture both of these distortions.
