THREE DIMENSIONS
INTRODUCTION
• Realism = philosophical position arguing that there is a real sense
• Positivism = philosophical position arguing that we all really have to go on is the evidence of the
senses, so the world might be nothing more than an elaborate hallucination
• The problem of the visual system: how to construct a 3D world based on the inverted images on the
retina of each eye
• The retinal area occupied by an object gets smaller as the object moves further away from the
eyeball
• Our visual experience is a reconstruction of the world based on 2 inputs: the 2 distinct retinal images
o They always differ because your eyeballs and their two retinas are in slightly different places
in your head
Our visual field restricted to 190 degrees from left to right, 110 degrees covered by both eyes
Restricted vertically; 140 degrees, 60 degrees up to a limit defined by eyebrows and 80 degrees down to
cheeks
• Probability summation = the increased detection probability based on the statistical advantage of
having two (or more) detectors rather than one
o Ex. 2 independent people with each 50% chance of missing a target, chance of both missing
is 50x50=25%. So the chance of at least one finding target is 100-25 =75%
• Binocular summation = combination / summation of signals from both eyes in ways that make
performance on many tasks better than with either eye alone
o Makes the probability to detect small / fast moving objects much higher
o may have provided the evolutionary pressure that first moved eyes toward the front of some
birds’ and mammals’ faces
o under most circumstances, we do not get complete probability summation
• Binocular disparity = differences between the two retinal images of the same scene. Disparity is the
basis for stereopsis; vivid perception of the three-dimensionality of theworld that is not available
with monocular vision
o Technical term for the binocular perception of depth is stereopsis
• Stereopsis = ability to use binocular disparity as a cue to depth
o Adds a richness to perception of the three-dimensional world
• Monocular depth cue = depth cue available even when the world is viewed with one eye alone
• Binocular depth cue = depth cue that relies on information from both eyes. Stereopsis is the
primary example in humans, but convergence and the ability of two eyes to see more of an object
than one eye are also binocular depth cues
,MONOCULAR CUES TO THREE-DIMENSIONAL SPACE
• Every view of the world provides multiple depth cues, which usually reinforce each other
PICTORIAL DEPTH CUES
• Pictorial depth cue = a cue to distance or depth used by artists to depict 3D depth in 2D pictures
• Natural consequence of the projection of the 3D world onto the 2D surface of the retina
• When an image is viewed in the right position, the retinal image formed by the 2D picture will be the
same as the retinal image that would have been formed by the 3D world and thus we can see depth
in pictures
OCCLUSION
Occlusion = a cue to relative depth order in which (for
example) one object obstructs the view of part of another
object
• Gives information about the relative position of
objects
• Present in almost every visual scene
• Occlusion is a nonmetrical depth cue ; just gives us the relative orderings of occluders and
occludes
• Non metrical depth cue = depth cue that provides information about the depth order (relative
depth) but not depth magnitude (ex. His nose is in front of his face)
• Metrical depth cue = provides quantitative information about distance in the third dimension
• Occlusion is nonmetrical, providing only depth ORDER
SIZE AND POSITION CUES
• The image on the retina formed by an object in real life gets smaller as the object gets further away
Projective geometry = the geometry that describes transformations that occur when the 3D world is
projected onto a 2D surface. For example, parallel lines do not converge in real life, but they do in the
2D projection of the world
o Describes how the world is projected onto a surface
§ Ex. A shadow is a projection of an object onto a surface
, Relative size = a comparison of size between items without knowing the absolute size of either one
• 1. Texture gradient = a depth cue based on the geometric fact that
items of the same size form smaller images when they are farther
away. An array of items that change in size smoothly across the image
will appear to form a surface tilted in depth
o Larger objects in one area and smaller objects in another
• 2. Relative height = depth cue, the observation that objects at
different distances from the viewer on the ground plane will form
images at different heights in the retinal image. Objects farther away will be seen as higher in the
image
•
• arranged in orderly texture but less sense of depth
• Includes another depth cue;
Relative height: the closer rabbit lies lower in the visual
field than the farther rabbit. The smaller image of a more
distant rabbit will be projected higher in your visual field.
Objects that are more distant will be higher in the visual field
Texture fields that provide an impression of 3dimensionality are combinations of relative size & relative
height cues
INTRODUCTION
• Realism = philosophical position arguing that there is a real sense
• Positivism = philosophical position arguing that we all really have to go on is the evidence of the
senses, so the world might be nothing more than an elaborate hallucination
• The problem of the visual system: how to construct a 3D world based on the inverted images on the
retina of each eye
• The retinal area occupied by an object gets smaller as the object moves further away from the
eyeball
• Our visual experience is a reconstruction of the world based on 2 inputs: the 2 distinct retinal images
o They always differ because your eyeballs and their two retinas are in slightly different places
in your head
Our visual field restricted to 190 degrees from left to right, 110 degrees covered by both eyes
Restricted vertically; 140 degrees, 60 degrees up to a limit defined by eyebrows and 80 degrees down to
cheeks
• Probability summation = the increased detection probability based on the statistical advantage of
having two (or more) detectors rather than one
o Ex. 2 independent people with each 50% chance of missing a target, chance of both missing
is 50x50=25%. So the chance of at least one finding target is 100-25 =75%
• Binocular summation = combination / summation of signals from both eyes in ways that make
performance on many tasks better than with either eye alone
o Makes the probability to detect small / fast moving objects much higher
o may have provided the evolutionary pressure that first moved eyes toward the front of some
birds’ and mammals’ faces
o under most circumstances, we do not get complete probability summation
• Binocular disparity = differences between the two retinal images of the same scene. Disparity is the
basis for stereopsis; vivid perception of the three-dimensionality of theworld that is not available
with monocular vision
o Technical term for the binocular perception of depth is stereopsis
• Stereopsis = ability to use binocular disparity as a cue to depth
o Adds a richness to perception of the three-dimensional world
• Monocular depth cue = depth cue available even when the world is viewed with one eye alone
• Binocular depth cue = depth cue that relies on information from both eyes. Stereopsis is the
primary example in humans, but convergence and the ability of two eyes to see more of an object
than one eye are also binocular depth cues
,MONOCULAR CUES TO THREE-DIMENSIONAL SPACE
• Every view of the world provides multiple depth cues, which usually reinforce each other
PICTORIAL DEPTH CUES
• Pictorial depth cue = a cue to distance or depth used by artists to depict 3D depth in 2D pictures
• Natural consequence of the projection of the 3D world onto the 2D surface of the retina
• When an image is viewed in the right position, the retinal image formed by the 2D picture will be the
same as the retinal image that would have been formed by the 3D world and thus we can see depth
in pictures
OCCLUSION
Occlusion = a cue to relative depth order in which (for
example) one object obstructs the view of part of another
object
• Gives information about the relative position of
objects
• Present in almost every visual scene
• Occlusion is a nonmetrical depth cue ; just gives us the relative orderings of occluders and
occludes
• Non metrical depth cue = depth cue that provides information about the depth order (relative
depth) but not depth magnitude (ex. His nose is in front of his face)
• Metrical depth cue = provides quantitative information about distance in the third dimension
• Occlusion is nonmetrical, providing only depth ORDER
SIZE AND POSITION CUES
• The image on the retina formed by an object in real life gets smaller as the object gets further away
Projective geometry = the geometry that describes transformations that occur when the 3D world is
projected onto a 2D surface. For example, parallel lines do not converge in real life, but they do in the
2D projection of the world
o Describes how the world is projected onto a surface
§ Ex. A shadow is a projection of an object onto a surface
, Relative size = a comparison of size between items without knowing the absolute size of either one
• 1. Texture gradient = a depth cue based on the geometric fact that
items of the same size form smaller images when they are farther
away. An array of items that change in size smoothly across the image
will appear to form a surface tilted in depth
o Larger objects in one area and smaller objects in another
• 2. Relative height = depth cue, the observation that objects at
different distances from the viewer on the ground plane will form
images at different heights in the retinal image. Objects farther away will be seen as higher in the
image
•
• arranged in orderly texture but less sense of depth
• Includes another depth cue;
Relative height: the closer rabbit lies lower in the visual
field than the farther rabbit. The smaller image of a more
distant rabbit will be projected higher in your visual field.
Objects that are more distant will be higher in the visual field
Texture fields that provide an impression of 3dimensionality are combinations of relative size & relative
height cues
