Kees van Overveld

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

-1-

The sampling layer•sampling – background of spatial vision and color-vision (and the perception of dynamical phenomena)

•isotropic and anisotropic detectors

•sampling and color

•sampling and meaning

Kees van Overveld

sampling of the light field

sea combat: a metafor for sampling-as-reconstruction

-2-

the enemy playfield (reality) …

… containing the enemy fleet (things from reality)

my representation of the enemy playfield (the HVS)

results of my measurements (sampling) the enemy playfield (measurements in the HVS)…

the (sometimes: wrong) hypotheses on the enemy fleet based on my measurements (the mental reconstruction of things in reality)

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld -3-

finitely many samples to represent infinitely much information: errors (aliasing)

remedy: low-pass filtering (make sure no small-scale details are present)

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

sampling of the light field

Kees van Overveld

what constitutes visual sampling?

In the image plane (retina, ...) , light intensity is a function of

•location (x,y),

•time (t), and

•wavelength ()

being measured with detectors, each with their own footprint, both for x,y,t, and .

domain of the detector

sensitivity

not sensitive

sensitive

not sensitive

not sensitive

sensitive

not sensitive

inverted sensitivity

-4-

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

sampling of the light field

Kees van Overveld -5-

… furthermore: detectors with a footprint in sombrero-shape

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

sampling of the light field

Kees van Overveld -6-

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

sampling of the light field

Kees van Overveld -7-

Anisotropic filters are only sensitive for intensity-transitions aligned with their own orientation

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

sampling of the light field

Kees van Overveld

Properties of various types of detectors

-8-

two slightly different signals …

…sampled with a single broad footprint can not be distinguished

signal present

no signal

no signal

signal present

small signal

small signal

…sampled with multiple narrow footprints can be distinguished

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

sampling of the light field

What is 'seen' by which detector?

various footprints measure various aspects of a distribution of color or brightness:

Kees van Overveld

“as long as there is energy (light), it is seen”

“as long as there is an oriented transition, it is seen”

“as long as there is a difference from a background, it is seen”

-9-

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld -10-

The size of the footprint – perspective, distance and scale

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld -11-

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

The size of the footprint – perspective, distance and scale

Kees van Overveld

isotropic and anisotropic detectors

-12-

these are no 'mental images'

– rather, they are outcomes of measurements in the sampling layer,

imposing constraints on a (re)constructed mental image.

brightness and en color brightness and en color distributionsdistributions

vertical transitionsvertical transitions

horizontal transitionshorizontal transitions

borders in arbitrary directionborders in arbitrary direction

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld -13-

visual aquity, contrast, and seeing details

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld

From physical spectra to the subjective sensation of color

-14-

400 nm 800 nm

wavelength

energy per w

avelength interval

relative sensitivity per w

avelength interval

sampling a spectrum with 'short wavelength' detectors

sampling a spectrum with 'medium wavelength' detectors

sampling a spectrum with 'long wavelength' detectors

… yields a representation of any spectrum in precisely 3 'numbers' (measurements) – let's say X,Y,Z.

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

http://www.artelista.com/en/artwork/2566943631689989-colourful-fruit-com

position-ii.html

http://www.artelista.com/en/artwork/2566943631689989-colourful-fruit-com

position-ii.html

Kees van Overveld

Color space: sampling spectra with three different footprints

-17-

So: any spectrum is interpreted as a collection of three measured values

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld

Color space: mixing (altering) colors by adding or filtering

-18-

Mixing of light colors: spectra are perceived simulatenously.

The resulting spectrum is the sum of the spectra.

The measured (perceived) values are the sums of the individual measured values in each of the three channels.

Hence: linear color space-behavior of subjective color.

light

light

light

Mixing of colored paint or by colored filters.

The resulting spectrum is, for each wavelength, the product of the light spectrum and the filter 'spectrum'.

Perceived values are NOT the product of the individula measured values in each of the three channels.

light

light

filter / reflector

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld -19-

Color matching: assigning intersubjective coordinates to subjective color

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld

Make X,Y,Z independent of intensity by normalizing:•x=X/(X+Y+Z)•y=Y/(X+Y+Z)•z=Z/(X+Y+Z)

•consider a plane in x-y-z- space for z=constant:

x: 0…1

y: 0…1

•a straight line in XYZ maps to a straight line in xy (where did we see that before ...? Perspective!)

•adding colors additively = adding spectra = in xy space: linear interpolation

•monochrome colors (rainbow colors) are on the border of a diagram; you cannot go beyond since additon coefficients cannot be <0

•The red/violet line contains colors, not in the rainbow. These are mixed from two extreme rainbow colors

-20-

CIE-diagram

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

From physical spectra to the subjective sensation of color

Kees van Overveld

Color space - an intersubjective 3D representation of subjective colors

-21-

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld

3D color space – alternative geometric representations

-22-

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld

Consequences of CIE diagram

-23-

Each color (such as X) can be reproduced by additive mixing of no more than two well-chosen monochrome spectra (e.g. A and B or C and D) with appropriate

mixing ratios.

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld -24-

Complementary colors are colors that, additively mixed together, form white or grey.

After images are complementary: there are neural correlates for

differences of primary colors

Complementary colors give maximal hue contrast.

Distance to white point: saturation. Rainbow colors hence are maximally saturated.

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Consequences of CIE diagram

Kees van Overveld

Color illusions: do we actually see colors or do we estimate ? (Retinex theory – 1970-ies)

-25-

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld

Georges Seurat (1859-1891; pointillism)

•painting on the 'sampling layer'

•paradox: approximate additive color mixing with colored paint-26-

From color spectra to subjective color sensation

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld -27-

Meaning at the sampling layer

Differences in locations: above - below

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Kees van Overveld -28-

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Meaning at the sampling layer

Differences in locations: above - below

Kees van Overveld -29-

Colors and their connotation in nature and culture

From Light to Enlightenment – From Light to Enlightenment – samplingsampling

Meaning at the sampling layer