Space Perception and Binocular Vision

Introduction

• Realism vs. Positivism:

  • Realism: The external world exists independently.
  • Positivism: The world's existence depends on sensory evidence; it could be a hallucination.

• Euclidean Geometry:

  • Parallel lines remain parallel.
  • Objects maintain size/shape in space.
  • Triangle internal angles sum to 180 degrees.

• Retinal images are non-Euclidean.

  • Brains process non-Euclidean geometry constantly.

• Probability Summation:

  • Increased likelihood of stimulus detection with multiple samples (e.g., two eyes).

• Binocular Summation:

  • Combination of signals from each eye improves performance on tasks.

• Binocular Disparity:

  • Differences between the two retinal images of the same scene.
  • Basis for stereopsis: vivid 3D perception not available with one eye.

• Depth Cues:

  • Information about the third dimension (depth).
  • Monocular: Available with one eye.
  • Binocular: Relies on information from both eyes.

Monocular Cues to Three-Dimensional Space

• Occlusion:

  • One object partially blocking another indicates relative depth order.

• Metrical vs. Nonmetrical Depth Cues:

  • Metrical: Provides quantitative distance information.
  • Nonmetrical: Provides depth order (relative depth) but not magnitude.

• Relative Size:

  • Smaller objects assumed to be farther away if all else is equal.

• Relative Height:

  • Objects touching the ground, higher in the visual field appear farther.
  • In the sky, objects lower in the visual field appear farther.

• Texture Gradient:

  • Items of the same size form smaller, closer-spaced images with distance.
  • Combines relative size and relative height cues.

• Familiar Size:

  • Knowledge of typical object size allows distance estimation based on apparent size.
  • Works with relative size cue.

• Relative Metrical Depth Cue:

  • Specifies relative distances (e.g., object A is twice as far as object B) without absolute distances.

• Absolute Metrical Depth Cue:

  • Provides quantifiable distance information.

• Aerial Perspective:

  • Light scattered by the atmosphere.
  • Distant objects appear fainter, bluer, and less distinct.

• Linear Perspective:

  • Parallel lines converge in a 2D image as they recede into the distance.
  • Vanishing Point: Point where parallel lines converge.

• Pictorial Depth Cue:

  • Used by artists to depict 3D depth in 2D pictures.

• Anamorphosis (Anamorphic Projection):

  • Distorted 2D image appears correct only from a specific viewpoint or with a corrective mirror.

Triangulation Cues to Three-Dimensional Space

• Motion Parallax:

  • Closer images move faster across the visual field than farther images.
  • Brain calculates distances based on this information.
  • Head/relative movements reveal these cues.

• Accommodation:

  • Eye changes focus; lens gets fatter for nearer objects.

• Convergence:

  • Eyes turn inward to focus on nearer objects.

• Divergence:

  • Eyes turn outward to focus on farther objects.

Binocular Vision and Stereopsis

• Corresponding Retinal Points:

  • Points on each retina where monocular images of a single object are formed, equidistant from the fovea.

• Horopter:

  • Location of objects whose images lie on corresponding points (surface of zero disparity).

• Vieth-Müller Circle:

  • Location of objects whose images fall on geometrically corresponding points in the two retinas (often considered the same as the horopter).

• Panum’s Fusional Area:

  • Region in front of and behind the horopter where single binocular vision is possible.

• Diplopia:

  • Double vision.
  • Stimuli outside Panum’s fusional area appear diplopic.

• Crossed Disparity:

  • Disparity created by objects in front of the horopter.
  • Images displaced left in the right eye, right in the left eye.

• Uncrossed Disparity:

  • Disparity created by objects behind the horopter.
  • Images displaced right in the right eye, left in the left eye.

• Stereoscope:

  • Device presenting one image to each eye.

• Free Fusion:

  • Converging/diverging eyes to view a stereogram without a stereoscope.
  • "Magic Eye" pictures rely on this.

• Stereoblindness:

  • Inability to use binocular disparity as a depth cue.
  • Often from childhood visual disorders (e.g., strabismus).

• Random Dot Stereogram (RDS):

  • Stereogram of randomly placed dots with no monocular depth cues.
  • Stimuli visible stereoscopically in RDSs are cyclopean.

• Cyclopean:

  • Stimuli defined by binocular disparity alone.

• 3D Movies:

  • Each eye receives a slightly different view.
  • Early methods used anaglyphic glasses (red/blue lenses).
  • Current methods use polarized light and polarizing glasses.

• Correspondence Problem:

  • Determining which part of the left eye image matches which part of the right eye image.

• Solutions to the Correspondence Problem:

  • Blurring the image (low-spatial frequency information).
  • Uniqueness Constraint: A feature is represented once in each retinal image.
  • Continuity Constraint: Neighboring points are at similar distances (except at object edges).

• Stereopsis in the Brain:

  • Input from two eyes converges onto the same cell.
  • Binocular neurons respond to corresponding points (neural basis for the horopter).
  • Other binocular neurons respond to slightly different positions on the two retinas (tuned to binocular disparity).

• Stereopsis as Metrical and Nonmetrical Depth Cue:

  • Some cells code whether a feature is in front of or behind the fixation plane (nonmetrical).
  • Other cells code precise distance (metrical).

• Stereopsis in a Hunting Insect (Praying Mantis):

  • Mantises catch bugs using stereoscopic depth perception.
  • Experiment: Mantises with anaglyphic glasses reacted to 3D movies of bugs at the correct striking distance.
  • Conclusion: Praying mantises have stereoscopic vision and respond to depth defined by disparity.

Combining Depth Cues

• Bayesian Approach:

  • Depth perception combines multiple cues.
  • Perception is a combination of the current stimulus and prior knowledge.
  • Prior knowledge influences the probability estimates of an event.

• Illusions and Space Construction:

  • Visual systems consider depth cues when interpreting object size.

• Binocular Rivalry:

  • Competition between the two eyes when different stimuli are presented to each.

• Stereoacuity:

  • Measure of the smallest binocular disparity that generates depth sensation.
  • Often tested using dichoptic stimuli (different stimuli to each eye).

Development of Binocular Vision and Stereopsis

• Critical Period:

  • Time when an organism is susceptible to developmental change.

• Strabismus:

  • Misalignment of the two eyes where a single object is imaged on the fovea of one eye and a nonfoveal area of the other.

• Suppression:

  • Inhibition of an unwanted image in vision.

• Esotropia:

  • Strabismus where one eye deviates inward.

• Exotropia:

  • Strabismus where one eye deviates outward.