Chapter 6 –Space Perception and Binocular vision
The ability to perceive and interact with the structure of space is one of the fundamental goals of the
Realism: A philosophical position that there is a real world to sense.
Positivism : a philosophical position that all we have to go on is the evidence of our senses, so the world
might be nothing more than an elaborate hallucination .
Euclidean: named in honor of Euclid
The geometry of real world is Euclidean.
Parallel lines remain parallel as they are extended in space, objects maintain their size and shape in the
BUT, Euclidean geometry is not the only geometry, the geometry of retinal images of that world is
The geometry becomes non-Euclidean when the D world is projected onto the curved 2D surface fo teh
retina. Parallel lines in the world donot remain parallel in the retinal iamge.teh retinal area occupied by
an object gets smaller as the object moves further away---- if we want to appreciate the Euclidean
world, we have to reconstruct it from non-Euclidean input.
We reconstruct teh world from 2 non-Euc inputs: teh two distinct retinal images.
Teh two retinal images always differ. They differ because the retinas are in different places.i.e just as u
and the person next to u sees different views of the world.
Why have two eyes?
-same evolutionary advantage as having two kidneys, lungs etc you can lose one eye and still be able
-doubling the number of eyes is that they enable u to see more of the world.
Our visual field is limited to 190 deg from L to R. 110 is covered by both eyes.
Field is more restricted vertically: 60 deg up an d 80 deg down.
Overlapping binocular visual field give predators a better chance to spot small, fast-moving objects.
Binocular summation: the combination of signals from each eye in ways that make performance on
many tasks better with both eyes than with one
-may have caused the evolution of eyes infront of faces.
Another benefit for overlapping binocular fields : Binocular disparity
b. disparity :
-the differences between the two retinal images of the same scenes.
-is the basis for vivid perception of 3 dimensionality of the world , which is not available with purely
Stereopsis – binocular perception of depth
Monocular = one-eyed vision -Loss of stereopsis
But stereopsis is not necessary for depth perception but it does add a richness to teh perception of 3D
Monocular Cues to 3D space
M.C Escher- Relativity picture
Each bit of stairway uses cues that allow us to infer 3D from 2 but when we follow the stairs,
the drawings cleverly fails to form a coherent representation.
Even when no one is trying to fool us, its hard to reconstruct faithfully the Euclidean image
from non-Euc input. we must use depth cues!
Every view of the world provides multiple depth cues. The cues may reinforce each other or be
1. Occlusion-gives information about the relative position of objects
- Present in almost every scene
- Most reliable as some argue
- Wrong only in accidental viewpoints
- Is a nonmetrical depth cue: just gives us the relative orderings of occluders and
metrical depth cue- provides information about distance in 3D.
2. Size and position cues- the image on the retina formed by an object out in the world
gets smaller as the object gets further away. projective geometry
- The visual system knows projective geometry implicitly
- Describes how teh world is projected on to a surface.
- All else being equal, smaller things are farther away.
- Relative size: a comparison of size between items without knowing teh absolute
size of either one.
- Texture gradient: a depth cue based on the geometric fact that items of same
size form smaller images when they are farther away. An array of items that
change in size across the image will appear to form a surface in depth.
- Relative height: depth cue that objects with different heights will form images
at different heights in the retinal image. Objects farther away will be seen higher
in the retinal image
- Texture fields : are combinations of relative size and height cues
- Familiar size : Knowledge of how something ought to be ca be a depth cue in its
own right.a depth cue based on knowledge of teh typical size of objects.
While occlusion is a nonmetrical depth cue, providing only depth order. The relative size and
height cues provide some metrical info.
Relative size and height do not tell us the exact distance to an object or between objects they
are relative metrical depth cues. Familiar size could be an absolute metrical depth cue. 3. Aerial Perspective :
- The visual system knows about the properties of the atmosphere: that light is
scattered by the atmosphere and that more light is scattered when we look
through more atmosphere-> therefore, more distant objects are subject to
more scatter and appear fainter and less distinct haze or aerial perspective
4. Linear Perspective:
- Based on the rules that determine how lines in D space are projected onto 2D
- Lines that are parallel in the 3D world will appear to converge in the 2D image at
the vanishing point.
- Provides relative metrical depth cues
5. Pictorial depth cues and pictures
- So far pictorial cues: cues produced by the projection of the 3D world on to 2D
surface of the retina.
- A realistic picture or painting is the result of projecting the 3D world on to 2D
canvas or film.
- To correctly interpret the shape of 3D objects from 2D pictures, people take the
orientation of the flat surface of the image into account so that they can
understand both that the picture is a picture and not a real thing and yet
accurately get a impression of the thing that is portrayed.
- “ the pic in the pic” is actually distorted when the picture in this pic is isolated
but the visual system compensates for the perceptual distortion in the “pic in
the pic” image
- Anamorphosis or anamorphic projection: the projection of 3D into two creates
a picture that is recognizable only from an unusual vantage pointanamorphic
- i.e Kurt Wenner creates anamorphic images that look real from one vantage
point and distorted from elsewhere.
6. Motion Cues
- Nonpictorial depth cue real world scenes that cannot be reproduced in a
static 2D pic.
- Motion parallax: depth cue. Based on head movement. i.e staring at the
branches of a tree with one eye vs two eyes. motion parallax restores the sense
of depth. The geometric info obtained from an eye in 2 diff positions at two diff
times is similar to info from two eyes in diff positions (motion parallax) in the
head at the same time (stereopsis)
- How does motion provide a cue for depth?
When your eyes move, objects closer to you shift position more
than objects farther away when you change your viewpoint. Not
just on train but even moving your head.
Parallex refers to this geometric relationship indicated above
- Motion parallax provides relative metrical info about how far objects are - Disadvantage? Works only if the head moves.
7. Accomodation and Convergence
- The eyes need to be focused to see objects at different distances clearly
- Accommodation-process of eye focusing.lens gets fatter as we focus our eyes on
- We also have to point our eyes to focus on objects at diff distances.
- What about focusing on distance?-converge vs divergence
- Convergence – rotate inwards
- Divergence – rotation outward
- The more we have to converge and the more the lens has to bulge inorder to
focus on the object, the closer it is.
- When we focus on objects,, the lens is as thin as it can get and the eyes are
- Convergence is used more than accommodation