L2.1: size

SIZE PERCEPTION

Week 2 Textbook Readings

• STT 104-113

• STT 120-125

• STT 223-224

• STT 227-232

INTRODUCTION

What’s the Problem?

• The primary challenge in size perception is that humans seek to understand the actual size of objects in the world (distal stimulus) while the visual system only receives optical size information presented in the image (proximal stimulus). WE SEEK TO KNOW THE DISTAL STIMULUS BUT CAN ONLY KNOW THE PROXIMAL STIMULUS

• This issue is a general problem for vision, impacting our perception of various attributes, including shape, color, and motion.
      - As an example, two people of similar sizes can appear to differ in size due to their distance from the viewer; the person farther from the camera appears smaller.

• Size Constancy: Typically, our perceptual system maintains size constancy, allowing objects to appear the same size regardless of their distance from us.
      - This is crucial to how we interpret visual information and understand the world.

• Visual illusions highlight the extent of our visual processing, which often operates without conscious awareness.

RETINA AND VISUAL PERCEPTION

Retinal Image and Size Perception

• The only information available to the visual system is the retinal image, which is influenced by both the object's size and its distance from the observer.

SIZE ILLUSIONS

Examples of Size Illusions

• Illustrations of size illusions indicating how perception can be altered based on viewpoint.

VIEWING GEOMETRY

A. Viewing Geometry

• Discusses how the geometry of viewing affects perception.

B. Retinal Image

• Analysis of the retinal image and its implications on visual perception.

VISUAL ANGLES

• Visual Angle Definition: Refers to the angle formed by two lines extending from the observer’s eye to the edges of an object, which is crucial in determining size perception.
      - Formula: $ext{Visual Angle} (a) = 2 imes ext{arctan}\bigg( rac{h}{2d}\bigg)$ where:
          - $h$ = height of the object
          - $d$ = distance from the observer to the object.

PERCEIVING SIZE

Visual Angle Relationships

• The visual angle of an object significantly contributes to how its size is perceived:
     - An object's visual angle establishes a relationship between its image on the retina and its physical attributes.
     - Both the size of the object and its distance from the observer affect the visual angle.

• Visual Angle Dependency:
      - Two equally sized objects can display different visual angles when located at varying distances.
      - Conversely, two objects with different sizes can appear to have the same visual angle if they are placed at specific distances from the observer.

• Example: During an eclipse, both the sun and the moon subtend an equal visual angle of approximately $0.5$ degrees despite their vast difference in distance (the sun being approximately $93,000,000$ miles away compared to the moon's $245,000$ miles).

SIZE CONSTANCY

The Law of Size Constancy

• Law of Size Constancy: Individuals can correctly perceive an object’s physical size, regardless of its distance from the viewer or the size of its image on the retina.

HOLWAY AND BORING’S 1941 EXPERIMENT

Experiment Overview

• The experiment involved an observer positioned at the junction of two hallways examining luminous comparison circles positioned at various distances.
      - The luminous comparison circle was fixed at a distance of $10$ feet from the observer, subtending a visual angle of $1^ ext{o}$.
      - Test circles were presented at distances ranging from $10$ to $120$ feet, designed so that they consistently subtended a visual angle of $1^ ext{o}$ as well.

• Task: Adjust the diameter of the comparison circle to align its perceived size with the test circle.

Conditions of the Experiment

• The absolute distance of the test circles did not matter as they continuously subtened $1^ ext{o}$.

• Various conditions provided differing depth cues:
      - Initial conditions offered ample depth cues.
      - Subsequent conditions limited depth cues (e.g., viewing with one eye, using a peephole, etc.).

COMPETING PREDICTIONS

Analysis of Results

• Figure 1: Illustrates the laws of visual angle and size constancy for objects subtending $1^ ext{o}$.
      - Diagram demonstrates how perceived size (diameter $S$ in inches) of the comparison stimulus equates to that of a standard stimulus.
      - Loci of data conforming to size constancy and the law of visual angle diverge as distance from the observer changes.

FINDINGS OF HOLWAY AND BORING’S EXPERIMENT

Perception and Depth

• Observers' ability to determine the size of the test circles diminished when depth cues were less prominent.

• The study reinforces how depth information is critical for assessing sizes accurately, revealing a reliance on size-distance scaling.
      - This means we perceive an object's distance based on its perceived size and, conversely, an object's size based on its perceived distance.

Emmert’s Law

• Emmert’s Law: A statement that the farther away an afterimage appears, the larger it seems.
      - The mathematical representation is given by:
      - $SP = K imes (SR imes DP)$
          - $SP$ = perceived size of an afterimage;
          - $K$ = constant;
          - $SR$ = size of the retinal image;
          - $DP$ = perceived distance of the afterimage.

ILLUSIONS OF DEPTH AND SIZE

Perspective Cues

• Distinct perspective cues play an integral role in altering the perception of size and distance.
      - Example: Two lines of identical length appear differently sized based on the additional perspective cues in the background, which influences our judgment.

THE AMES ROOM

How the Ames Room Works

• The Ames Room provides a distorted perspective when viewed from a single eye, giving an impression of cubic dimensions despite being geometrically flawed.

• In reality, one corner of the room’s back wall is closer to the observer than the other.

• The perceived height and size of objects differ based on their position due to misinterpreted depth cues.
      - A person standing in the nearer corner is interpreted as being the same distance away as someone positioned further away, skewing the perceived visual angles considerably.

THE MOON ILLUSION

The Moon Illusion Phenomenon

• Observations reveal that the moon appears larger when positioned on the horizon compared to when it's high in the sky.
      - This phenomenon is termed the 'Moon Illusion'.

Theories of the Moon Illusion

1. Apparent Distance Theory: Proposes that the moon seems larger on the horizon because it is perceived to be further away due to the presence of environmental objects (e.g., trees, buildings) that aid in depth perception.
       - The theory asserts that since the horizon moon is perceived as farther away while subtending the same visual angle as the moon in the sky, it seems bigger.
       - Supporting Evidence: Kaufman and Rock's experiment showed the moon appeared $1.3$ times larger over terrain versus a masked horizon.

2. Angular-Size Contrast Theory: Suggests that the moon appears smaller when isolated against the vast background of the sky because the sky seems infinitely larger; conversely, the horizon moon appears larger due to the contrast with nearby smaller objects.