Visual computation of lightness in simple and complex images Alan Gilchrist National Science Foundation: BCS-9906747 Public Health Service: GM 60826-02

Perceived white, gray, or black shade of a surface. What is Lightness? Perceived white, gray, or black shade of a surface.

The problem of lightness constancy: Adelson’s checkered shadow These two squares are identical

Luminance is ambiguous Any absolute luminance can appear as any shade of gray

1948 - Wallach’s solution: Relative luminance

1948 - Wallach’s solution: 1 5 50 10 Relative luminance Disks appear equal when luminance ratios are equal

Near condition Far condition

without an anchoring rule, But, without an anchoring rule, luminance ratios are also ambiguous 1 5 This local luminance ratio. . . . . . is consistent with any of these:

THE ANCHORING PROBLEM Given: the scale of A range of luminances WHITE GRAY BLACK SELF- LUMINOUS the scale of perceived gray shades Given: A range of luminances in the image How to map these onto….

Two proposed anchoring rules Wallach, Land & McCann SELF- LUMINOUS WHITE Highest luminance Rule Average luminance Rule GRAY Helson, Buchsbaum Gray world assumption BLACK

Which rule is correct? Another rule Bipolar anchoring Koffka,Rock SELF- LUMINOUS Koffka,Rock WHITE Bipolar anchoring GRAY BLACK Which rule is correct?

Challenge: pit these rules against each other in the simplest possible image

Two surfaces of different gray that fill the entire visual field. What is a simple image? Heinemann: Disk/annulus in a dark room Gilchrist: Disk/annulus is too complex Simplest image: Two surfaces of different gray that fill the entire visual field. Wallach: "Opaque colors which deserve to be called white or gray, in other words ‘surface colors,’ will make their appearance only when two regions of different light intensity are in contact with each other..."

1 2 3

Highest Luminance Rule wins Anchoring under minimal conditions: Two surfaces fill entire visual field Physical Stimulus 5.5 2.5 4.5 9.5 Li & Gilchrist, 1999 Appearance Highest Luminance Rule wins

Highest luminance rule: The highest luminance within a framework appears white and darker regions are computed relative to this value.

Three rules of anchoring in simple images: Physical Stimulus Appearance 1. Highest Luminance Rule Highest luminance appears white Physical Stimulus Appearance 2. Area Rule. The larger the lighter 3. Scale Normalization Rule. The perceived range of grays tends toward that between black and white. (30:1) Physical Stimulus Appearance

Two problems for the highest luminance rule Self-luminosity perception Upward induction/downward induction problem

What color is the ceiling? Highest luminance rule fails

When the luminance difference between two adjacent regions increases: Upward induction/downward induction problem When the luminance difference between two adjacent regions increases: Does the darker one appear to get darker? Or does the lighter one appear to get lighter still? Downward induction Upward induction

Downward induction Upward induction

The answer lies in relative area

Method Nine stimulus domes: Each viewed by a different group of 15 subjects Matches made from immediate memory using a Munsell chart

Standard Deviations Perceived Log reflectance White Gray Black 1.89 1.69 1.49 Gray 1.29 1.09 0.89 0.69 Black 0.49

Degrees of dark gray Perceived Log reflectance White Gray Black 1.85 1.65 1.45 Gray 1.25 1.05 0.85 0.65 Black 0.45 50 100 150 200 250 300 350 Degrees of dark gray

lightens as it gets larger The area rule: The darker region lightens as it gets larger As the darker region becomes very large, the lighter region appears first super-white, and then self-luminous..

2 degree square 7 x 9 degree rectangle

WHITE GRAY BLACK 1 8 6 4 2 3 9 1 3 2 TARGET LUMINANCE (cd /m ) 2 4 6 8 1 3 TARGET LUMINANCE (cd /m ) % LUMINOSITY REPORTS 50% BACKGROUND LIGHTNESS 3 1 9 2 TARGET LUMINANCE (cd /m ) WHITE GRAY BLACK

Theoretical significance: Inconsistent with inverse optics Neurally plausible

Scale normalization rule: The perceived range of grays within a framework tends toward that between black and white If the range is truncated (less than 30:1), expansion occurs. Coefficient of expansion proportional to the degree of truncation. The expansion shows up at the bottom of the range, not the top, which is anchored at white. Similar to MacLeod and Brown’s gamut expansion

EXPANSION COMPRESSION Disk/Ganzfeld Percentage Rescaling 160 140 120 100 4.8 80 60 40 1 10 40 Stimulus: Disk/Ganzfeld Range full Gilchrist & Bonato (1995)

Three rules of anchoring in simple images: Physical Stimulus Appearance 1. Highest Luminance Rule Highest luminance appears white Physical Stimulus Appearance 2. Area Rule. The larger the lighter 3. Scale Normalization Rule. The perceived range of grays tends toward that between black and white. (30:1) Physical Stimulus Appearance

What about complex images?

What is the relationship between simple and complex images? Contrast era: Findings from simple images can be directly applied to complex images Arend (1994): Disk/annulus displays are too simple to tell us anything useful about lightness perception. Gilchrist: Simple and complex images are related in a systematic way. Applicability assumption Co-determination principle

The applicability assumption: Rules of lightness computation in simple images can be applied to frameworks embedded within complex images

The co-determination principle Lightness is determined by computations both in the relevant framework and in adjacent and/or superordinate frameworks Lajos Kardos ... brilliant but largely-unknown Gestalt psychologist.

Applicability assumption: Highest luminance rule 2. Area function 3. Scale normalization

A B Corrugated Mondrian (Adelson)

Now for a Live Demo!

LOG T/H LOG PERCEIVED REFLECTANCE WHITE WHITE GRAY BLACK GLOBAL LOCAL 2 WHITE WHITE GLOBAL 1.8 1.6 1.4 GRAY 1.2 1 LOCAL 0.8 BLACK 0.6 0.4 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 LOG T/H

Applicability assumption: Highest luminance rule 2. Area function 3. Scale normalization

Applicability assumption: Highest luminance rule 2. Area function 3. Scale normalization

Frameworks of illumination exist in the visual environment Photo: Cartier-Bresson

Cartier-Bresson

Cartier-Bresson

We can explore frameworks using a probe disk of constant luminance:

Conclusions: Lightness computation in simple images described by three rules: 3. Scale Normalization Rule. 2. Area Rule. Physical Stimulus Appearance 1. Highest Luminance Rule

Conclusions: These rules can be applied to frameworks embedded with complex images (the applicability assumption) GLOBAL LOCAL Lightness is co-determined by computations in multiple frameworks.

Thank You

Standard Deviations Perceived Log reflectance White Gray Black 1.89 PR=(100-Ad)/50 x (Lt/Lh x 90%)+(Ad-50)/50 x 90% Ad - Area of darker region Lt - Luminance of target Lh - Highest luminance 1.69 1.49 Gray 1.29 1.09 0.89 0.69 Black 0.49

Visual Field