Visual Perception Lecture 5: Spatial Vision

What is spatial vision concerned with?

-concerned with variations in luminance across space

-assessed using VA and contrast sensitivity tests

Contrast Sensitivity

-provides a more comprehensive test of spatial vision

-measured by finding the lowest contrast needed to see light/dark gratings of varied fineness or spatial frequency

-VA is merely one point on the contrast sensitivity function (CSF)

Spatial Vision

the ability of visual system to detect (or discriminate) and resolve (luminance-defined) stimuli of various sizes and contrast

ex: VA measurement-determination of spatial resolution; a highly sensitive measure of visual function

Luminance

the physical amount of light emitted by a source or reflected from an illuminated object (candela per square meter, cd/m^2)

Brightness

the perception of a luminous object by the human visual system

What can brightness be affected by?

-adaptation

-aftereffects

-the presence or absence of other objects in the visual field

Contrast

-the difference in luminance between an object (Lmax) and its background (Lmin), where the object is brighter than the background

-the difference in brightness levels between light and dark elements of a pattern

What is the formula for contrast?

L difference/L(average)

L(average) = average of light peaks and dark troughs

Modulation

the contrast of a repeating pattern, commonly referred to as a grating, where it is not apparent which part of the pattern is the "object" and which is the "background"

What is the formula for modulation?

M = (Lmax - Lmin)/(Lmax + Lmin)

the ratio of the difference of the luminances to the sum of the luminances, where the luminance is measured across the spatial extent of each component part of the pattern

What is the formula for the mathematically equivalent ratio of modulation?

M = (Lmax - Lavg)/Lavg, where Lavg = (Lmax + Lmin)/2

Logarithm

represents that values as a power of 10, mathematically much easier to characterize the range

How is a contrast sensitivity function (CSF) plotted?

-because of the potentially large range of responses for both spatial frequency and sensitivity, the data is commonly plotted on logarithmic scales on both axes

-this results in the characteriztic inverted-U shape of the function

Contrast Threshold (CT)

the least amount of contrast that can be seen (or resolved by the patient) in a chart = Weber contrast in letter chart

Contrast Sensitivity (CS)

CS = 1/CT

the reciprocal of contrast threshold

Log Contrast Sensitivity (Log CS)

-converts the contrast sensitivity values to a linear scale

-suitable for comparisons between levels of contrast sensitivty

-smaller the Log CS values = poorer the patients CS

Spatial Frequency

the number of light/dark cycles per degree (c/deg) of visual angle on the retina

Gratings

defined by gradual sine-wave (i.e. sinusoidal) variations in luminance

What is contrast usually expressed as?

expressed as percent, then the ratio is multiplied by 100; ex: 10% Bailey-Lovie chart

What is the maximum contrast?

100% contrast, optotypes of VA charts are close to max contrast

Weber Contrast

-preferred for letter stimuli

-commonly used in cases where small features are present on a large uniform background

-aka Weber fraction

Michelson Contrast

-preferred for gratings

-aka visibility

-maximum and minimum luminance

RMS Contrast

-preferred for natural stimuli

-does not depend on the angular frequency content or the spatial distribution of contrast in the image

-the standard deviation of the pixel intensities

-not used clinically, but for image processing/analysis

What is the formula for Weber contrast?

Weber contrast = (Lb - Lt)/Lb

What is the formula for Michelson contrast?

Michelson contrast = (Lmax - Lmin)/(Lmax + Lmin)

What are the charts used for Weber contrast?

-Pelli-Robson

-MARS chart

What are the charts used for Michelson contrast?

sine wave gratings: VACT and VISTECH charts

What are some similarities of Weber and Michelson contrast?

-0% indicates the absence of contrast

-100% indicates the theoretical maximal contrast

-for values in between, the two scales differ

What is the difference between Weber contrast and Michelson contrast when the range is between 1% and 10% (normal range for clinical measurements)?

Weber contrast values are about twice the Michelson values; the log(CS) values differ by 0.3

Contrast Sensitivity Function (CSF)

depicts an observer's sensitivity (i.e. 1/contrast threshold) to sinusoidal bar gratings of widely varied spatial frequency

What is the peak contrast sensitivity in adults?

contrast sensitivity is greatest to intermediate spatial frequencies (about 2 to 4 cpd) - peak at 4 cpd

How do we study the complex processes of spatial vision?

choose a simple stimuli: sine wave gratings

Sine Wave or Sinusoid

a mathematical curve that described a smooth repetitive oscillation

How are sine waves characterized?

by their spatial frequency (dark/light stripes in a given distance @ cycles/deg), contrast and their phase

Why do we use sine wave in a CSF?

-when passed through an optical system, they maintain shape even after degradation (defocus, aberration, diffraction), and only change in contrast (amplitude) and phase (luminance remains sinusoidal)

-sine wave gratings constitute the building blocks of complex periodic waveforms

Sine Wave Grating

alternating bright and dark bars, transition from bright to dark is gradual

What do we use to describe sine wave gratings?

-frequency

-contrast

-phase

-orientation

What are the different wave cycles in frequency of sine wave gratings?

-low spatial frequency

-high spatial frequency

-same contrast

How can spatial frequency of a grating be specified?

by giving the number of cycles/degree of visual angle

ex: 30 cycles/degree

Low and High Contrast Grating

-same spatial frequency

-dashed lines: luminance profiles represent the average luminances of the gratings (average of peaks and troughs)

-average luminance is same for both gratings

Phase

the position of a sine wave grating with respect to another sine wave grating

In Phase

peaks and troughs of the luminance profiles are in alignment

180 degrees Out of Phase

peaks of one luminance profile aligns with troughs of other profile

Orientation

describes the angle made by a grating with respect to a reference (such as the horizontal)

Fourier Transformation

-mathematical process that transforms a signal (function) from the spatial domain to frequency domain

-image processing, signal detection

-sine waves of the proper frequency, contrast, phase, and orientation can be used to construct complex stimuli

-ex: black and white photo

Square Wave Grating

luminance profiles show abrupt changes between bright and dark bars "step" changes in luminance

How can square waves be constructed?

by adding together appropriate sine waves

Fundamental

sine wave that is of same frequency as square wave

Harmonics

-higher frequency sine waves

-3rd harmonics have 3 times the frequency of the fundamental and 1/3 of its contrast

-5th harmonics have 5 times the frequency of the fundamental and 1/5 of its contrast

What produces a square wave?

addition of the fundamental sine wave and the odd numbered harmonics (3rd and 5th)

What produces a perfect square wave?

adding all the odd numbered harmonics (up to infinity) to the fundamental

Modulation Transfer Function (MTF) - Image Quality

the ability of an optical system to produce accurately an image of an object

What is the formula for MTF?

MTF = image modulation (contrast)/object modulation (contrast)

calculated as the ratio of the image modulation to the object modulation for a given spatial frequency

Why is MTF calculated the way it is?

-diffraction

-chromatic and monochromatic aberrations

-focus and power errors

-the image will never be a perfect representation of the object

What is the MTF like for low spatial frequencies?

image blur is hardly noticeable

What is the MTF like for high spatial frequencies?

image is almost fully obscured

Optical System (SMTF = Image Quality)

simple lenses (e.g. spectacles) or complex lens systems (e.g. telescopes and cameras), the modulation transfer function (MTF) gives the modulation transfer for all possible spatial frequencies

What is the CSF like in the human visual system?

-CSF is the MTF of the visual system

-neural and cortical processing and the optics of the eye contribute to the final outcome of the CSF

How can we quantify the precision with which an optical lens (system) transfers information?

-grating of specific spatial frequency and contrast (as object)

-image contrast is measured

-the ratio = image quality (MTF)

-this procedure is repeated for a spectrum of spatial frequencies ranging from low to high to get SMTF

-MTF = 0 to 1 (1 --> best image quality)

Spatial Modulation Transfer Function (SMTF)

shows the image quality as a function of spatial frequency

What is the SMTF like for a lens in focus?

low and moderate frequencies, the image is transferred with good fidelity as aberrations (in the optical system) have very little effect in lower spatial frequencies and typically affect higher spatial frequencies

What is the SMTF like for a lens system in defocus?

reduction in image quality in higher spatial frequencies

What is the SMTF like for translucent lens?

equal degradation at all spatial frequencies

Spatial Contrast Sensitivity Function (sCSF)

-ability to differentiate stimuli (target) that vary in luminance across space

-ex: most contrast sensitivity eye charts/tests

Temporal Contrast Sensitivity Function (tCSF)

-ability to differentiate stimuli (target) that vary in luminance across time

-temporal (time varying, flickering)

Human Contrast Sensitivity Function

contrast sensitivity function (CSF) where sensitivity (not image contrast) is measured

How is CSF measured?

spatial grating is presented at varying levels of contrast (low to high) starting below threshold until its seen (values are plotted)

What is the reciprocal of threshold contrast?

contrast sensitivity of the grating

What is the human CSF peak sensitivity?

4 cpd

What is the shape of the human contrast sensitivity function?

-inverted U-shaped function

-contrast sensitivity is highest at mid-spatial frequencies

What are the important landmarks of CSF?

-provides and evaluation of real-world vision

-everything under the CSF is visible

-everything above the CSF is invisible

-it's a window of visibility

What does a high spatial frequency cut-off (x-axis) correspond to in CSF?

best VA

What does peak contrast sensitivty 4 cpd (2-5 cps) correspond to in CSF?

average receptive field size of retinal ganglion cells

What does a low spatial frequency cut-off correspond to in CSF?

due to lateral inhibition throughout the visual system

What may appear in the CSF if a single spatial frequency channel is affected?

notches

What do lower and higher spatial frequencies require in order to be detected?

require more contrast, resulting in an inverted -U function (graph)

What kind of contrast can the highest spatial frequency be resolved?

at very high contrast, and corresponds to the observer's acuity level

What does the shape of the CSF reflect?

-underlying spatial frequency channels

-evidence comes from selective adaptation experiments

CSF High Frequency Cutoff

-refers to visual system's limited ability to resolve detail when the contrast is 100%

-as the spatial frequency of 100% contrast is increased, a point is reached where the grating is no longer resolved

What is the high-frequency cut off for healthy adults?

~60 cpd

What is the VA of high-frequency cutoff determined with?

optotypes rather than gratings

VA is recognition acuity

What is the relationship between VA and the CSF?

-bottom row (100% contrast) represent VA chart optotypes

-the smallest high contrast optotype (under the curve) represents threshold acuity

-vertically contrast diminish

-low contrast VA not measured routinely in clinical care

High Spatial Frequency Cutoff

regular VA measurement measures only limited aspect of patient's spatial vision

Why does the visual system show reduction in sensitivity for high spatial frequencies?

-optical limitations: high spatial frequency limitations due to aberrations

-packing density of photoreceptors

How does the packing density of photoreceptors reduce the sensitivity for high spatial frequencies in the visual system?

-limits high spatial frequency

-consider low vs high densities of photoreceptors

-if each receptor sums up the light that falls on it

-high density can resolve

-foveal cones 0.5 min arc

-if each cycle subtends 1 min arc, then spatial frequency is 60 cpd - this corresponds to high spatial frequency cutoff for the CSF (60 cpd = 20/10 Snellen acuity)

What happens to the high frequency cutoff if the eye is out of focus, such as uncorrected refractive errors (myopia)?

out of focus = reduction in high spatial frequency cutoff

CSF Low Frequency Cutoff

-consider the response of a ganglion cell to light that falls on its receptive field

-center, sound

-excitation: increase in the frequency of action potentials

-inhibition: decrease in the frequency of action potentials

-high spatial frequency strongly activated

-low spatial frequency has smaller response

What is the CSF in infants?

-at birth, infants' sensitivity to fine, high spatial frequency gratings, like their acuity, is very poor, but improves steadily with age

-newborns can't resolve targets above 2-3 cpd

the improving contrast sensitivity can be seen in the CSFs at birth, 3 months and 6 months

How does the CSF of an infant differ from that of an adult?

-peak is lower

-function is shifted to the left

-shape is a "low pass" rather than a "band pass" function

What can infants begin to see with increasing age?

fine detail and low contrast elements in their environment

What are some examples of diseases that have a loss at low spatial frequencies?

-optic neuritis

-multiple sclerosis

-glaucoma - POAG

-papilledema

-visual pathway lesions

-diabetes

-Parkinson's disease

-Alzheimer's disease

-diseases that affect all or part of the visual pathway

How is the visual system considered to be a Fourier Analyzer?

-thought to deconstruct the retinal image into its spatial frequency components

-several narrow CSF channels (4-6)

-prior adaptation to specific frequency, discrete reduction in sensitivity to that specific frequency

-although there is evidence, it actually isn't a Fourier Analyzer

MACH Bands

-non-existent perceptual bands (seeing a gradual transition between white to black, but is not perceived that way)

-caused by the relative enhancement of high spatial frequencies, resulting in perception of enhanced boundaries

Numerator of Snellen Fraction

distance at which measurement is taken

Denominator of Snellen Fraction

-foot-size of the smallest optotype patient can resolve

-optotype detail subtends 1/5 (1 min of arc)

Foot-Size

the distance at which an optotype subtends 5 min of arc

What is the advantage of using Snellen charts?

easy calculation of MAR

How do you convert Snellen to spatial frequency (CPD)?

-for 20-ft Snellen demand, use 600 = (spatial frequency) x (Snellen denominator)

-for 6-m Snellen demands, use 180 = (spatial frequency) x (Snellen denominator)

ex: 20/20 = 30 cpd, 20/10 = 60 cpd

What charts are used for contrast sensitivity for fixed size, variable contrast?

-Pelli-Robson

-MARS CS (near)

-Rabin

What charts are used for contrast sensitivity for fixed contrast (low), variable size?

EDTRS