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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
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