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Space Perception and Binocular Vision
-Realism – a philosophical position arguing that there is a real world to sense
-Positivism – a philosophical position arguing that all we really have to go on is the
evidence of the senses, the world may be nothing more than an elaborate
The geology of the world, so named in honor of Euclid, the ancient Greek geometer
of the third century BC E. in Euclidean geometry, parallel lines remain parallel as they
are extended into space, objects maintain the same size and shape as they move
around in space, the internal angles of a triangle always add to the 180° and so forth
-The geometry of retinal images of the world is decidedly non-Euclidean
We construct the world from two non-Euclidean inputs: the two distinct retinal
-Advantages to having two eyeballs: you can lose one eye and still be able to see,
and they enable you to see more of the world
Our visual field is limited to about 190° from left to right, 110° of which is
covered by both eyes; 60° up from the center of gaze and 80° down
Binocular visual fields just a better chance to spot small, fast-moving objects
-Binocular summation – the combination (or “summation”) of signals from each eye in
ways that make performance on many tasks better with both sides with either eye
They have provided evolutionary pressure that first moved eyes to the front of
some birds’ and mammals’ face
-Binocular disparity – the differences between the two retinal images of the same
Disparity – a basis for vivid perception of the three dimensionality of the world
that is not available with purely monocular (one-eyed) vision.
-Stereopsis – the ability to use binocular disparity as a cue to depth.
Not a necessary condition for depth perception or space perception
-Depth cues – information about the third dimension (depth) of visual space. Depth
cues may be monocular or binocular.
-Monocular depth cue – a depth cue that is available even when the world is viewed
with one eye alone.
-Binocular depth cue – a depth cue that relies on information from both eyes.
Stereopsis is the primary example in humans, but convergence and he ability of
two eyes to see more of an object than one eye sees are also binocular depth
When Ocular Cues to Three-Dimensional Space
-Occlusion gives information about the relative positions of objects (makes it easy to
infer relative position in depth.)
Present in almost every visual scene
Most reliable of all depth cues
-Researchers argue that it is the most reliable of all the depth cues.
-Non-metrical depth cue – provides information about the depth order (relative depth)
but not depth magnitude (e.g. his nose is in front of his face) Example: Occlusion
-Metrical depth cue – provides quantitative information about distance in the third
Size and Position Cues
-Projected geometry - the geometry that describes the transformations that occur
when a three-dimensional world is projected onto a two-dimensional surface – for
example parallel lines do not converge in the world, but they do in the two-
Smaller things are farther away
Relative size - the comparison of size between items without knowing the
absolute size of either one
-Texture gradient – a depth cue based on the geometric fact that items of the same
size form smaller images when they are farther away.
-Relative height – as a 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 way will be seen as higher in the image.
For objects on the ground plane, objects that are more distant are higher in the
Texture fields that provide an impression of three-dimensionality are really combinations
of relative size and relative height cues provide metrical information
Do not tell the exact distance to an object or between objects
-Familiar size – a depth cue based on knowledge of the typical size of objects like
humans or pennies.
-Occlusion is a non-metrical cue, providing only depth order.
-Relative metrical depth cue – a depth cue that could specify that object 1 was twice
as far away as object 2 without providing information about the absolute distance
-Absolute metrical depth cue – a depth cue that provides absolute information about
the distance in the third dimension (e.g. object 1 is 4cms in front of object 2)
Haze / Aerial Perspective
-Relies on an implicit understanding that light is scattered by the atmosphere, and
that more light is scattered when we look through more atmosphere.
-More distant objects are subject to more scatter and appear fainter and less distinct
-Short wavelength (blue) are scattered more than medium and long wavelength
-Based on the fact that lines that are parallel in the three-dimensional world will
appear to converge in a two-dimensional image
-When the parallel lines lie in a plane that is parallel to the plane of the two-
dimensional image, the parallel lines will not appear to converge.
-Linear perspective provides relative metrical depth information.
-Vanishing point - apparent point at which parallel lines receding in depth converge
Pictorial Depth Cues and Pictures
-Pictorial depth cue – cue to distance or depth used by artists to depict three-
dimensional depth in two-dimensional pictures.
-When image is viewed from the correct 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 hence we see depth in the picture.
-To correctly interpret the shape of three-dimensional objects from two-dimensional
pictures, people take the orientation of the flat surface of the image into account so
that they can understand both that the picture is, in fact, a picture and at the same
time, calculate an accurate impression of the thing that is portrayed
-Our visual system compensates for the perceptual distortion in the first picture, or
the context enables us to take the orientation of the surface and account page
-Anamorphosis (Anamorphic projection) – use of the rule of linear perspective to
create a two-dimensional image so distorted that it looks correct only when viewed
from a special angle or with a mirror that counters the distortion.
-Motion parallax – an important depth cue that is based on head movement. The
geometric information obtained from an eye in two different positions at two different
times is similar to the information from two eyes in different positions in the head at
the same time.
Parallax geometric relationship: when your eyes move, objects closer to you
shift position more than objects farther away when you change your viewpoint
-The geometric information obtained from an eye in two different positions at two
different times (motion parallax) is similar to the information by two eyes in different
positions in the head at the same time (stereopsis).
relative metrical information of how far away objects are
-The downside of motion parallax is that it works only if the head moves
Accommodation and Convergence
-The human eye focuses via a process called accommodation, in which the lens gets
fatter as we direct our gaze toward nearer objects; and convergence, refocusing by