W9 - Spatial Frequency Analysis

Question 1

What does spatial frequency analysis seek to ask?

Answer 1

what are the building blocks used by the visual system to reconstruct the outside world?

Question 2

What are the 2 hypotheses of potential building blocks of the visual system?

Answer 2

1. 1st hypothesis = the cells are processing bars and edges
2. 2nd hypothesis = V1 simple cells collect spatial frequency components (sine wave variations in luminance in different spatial scales), then reconstruct sine waves in later visual processing stage, V2, V3, V4, V5

Question 3

What’s a sinewave?

Answer 3

Sine wave variation = gradual changes in luminance

Graph shows the graphical output of how luminance changes, from light to grey to dark and repeats in a periodical order

Question 4

Why do we chose sinewaves over polymers?

Answer 4

V1 cells appear to extract spatial frequency components

Question 5

EVIDENCE - Why do we think that the visual system uses sine wave modulations in luminance?

Answer 5

1. Its mathematically possible from Fourier’s theorem (every image can be represented/broken down by a series of sine waves (could also be represented in polynomials)
2. Receptive-field profiles / tuning properties of V1 simple cells can be modelled as sensitive to different SF components at particular locations)

Question 6

What are the 2 two potential uses of SFA?

Answer 6

1. Description/model of what the visual system actually does
2. It’s a way to determine what any observe should see when presented with any stimulus, using SFA on ANY ORGANISM would see when shown ANYTHING (after tests you can predict what someone will see after been presented with any stimulus, eg. vision impaired, animals, infants

Question 7

What are the 2 implications for using SFA?

Answer 7

1. Determining how different people/organisms might see, eg. infants, visually impaired, animals
2. Can also account for particular/specific percepts appear
   eg. Einstein-Marilyn Monroe illusion, Mona Lisa smile

Question 8

What are the building blocks of SFA?

Answer 8

The building blocks of SFA are sinewave modulations in luminance

Luminance = brightness, sinewave modulation = brightness varies as a sine wave function, eg.

Question 9

What 3 things do you need to define to specify sine waves?

Answer 9

1. Contrast © = how big are the sine waves? / how much energy you have at the spatial frequency
   The difference between peak and trough compared to a background, the higher the contrast, the bigger the waves, eg. black/white = big waves, grey = minimal tiny waves -
2. Spatial frequency (SF = 1/wavelength) = how many peak-to-peaks/cycles do we have in a certain distance?
   Top of the wave to the next top of the wave = wavelength
   One cycle of the sinewave = from one peak to another peak
3. Phase (position 0) = what point does the sinewave start, midpoint, peak or trough?
   Increasing or decreasing? A full cycle =360 degrees in the sinewave of phase angle, for a single sine wave, changing the phase merely changes where the location of the sine wave

Question 10

What happens when you change the phase by 180 degrees?

Answer 10

the peak will move to where the trough was and vise were, location of peaks and troughs will change

= can produce different looking images

Question 11

When the wavelengths are further apart…

Answer 11

…there are less cycles per degree (cpd) in a given distance

Question 12

Smaller SINEwavelengths tend to have =

Answer 12

more cycles per degree

Question 13

How is spatial frequency the inverse of a wavelength? (1/wavelength)

Answer 13

because the shorter the wavelength, the higher the spatial frequency

the longer the wavelength, the lower the spatial frequency

Question 14

How do we quantify spatial frequency (SF) sine waves?

Answer 14

visual angle
1. accounts for distance
2. asks how many cycles do you have in a degree of visual angle?
the same visual angle can have different cpd depending on the number of SFs in an angle

Question 15

What is visual angle important for?

Answer 15

1. Important for our ability to RESOLVE the object, need to factor in the SIZE of the object and how FAR AWAY the object is

Question 16

What happens to the spatial frequency content as the object gets further away?

Answer 16

a higher spatial frequency / more wavelength cycles per degree
is produced upon the same visual angle

Question 17

What does the Spatial-frequency Spectrum plot?

Answer 17

SF spectrum shows the energy in the stimulus (sinewave variation) in each spatial frequency

shows how much CONTRAST at different spatial frequencies

Question 18

Imagine 2 Spatial-frequency Spectrums, (SFSs) with different heights, what would this mean?

Answer 18

The left figure A has HIGHER CONTRAST (BIGGER SINE WAVES, peaks/troughs are further away from the midpoint) and lower spatial frequency compared to figure B

Question 19

What happens to the SF spectra in going from a) to f)?

SFS spectra decreasing from A-F, turning to grey

Answer 19

1. TO THE RIGHT OF THE X-AXIS = HIGHER SPATIAL FREQUENCIES
2. LOWER ON THE Y-ASIS = LOWER CONTRASTS

GRAPH SHOWS DECREASING CONTRASTS WITH INCREASING SPATIAL FREQUENCIES

2. F (NO LINE SHOWN) would have no contrast as it is the same colour

Question 20

What would happen to the SF spectra if the phase of the sine wave was changed?

Answer 20

Phase doesn’t change anything on spectra

Question 21

How are square waves constructed?

Answer 21

an image constructed by adding different sine waves together (eg. Fourier’s theorem) -by summing the fundamental + odd harmonic components

Question 21

What is phase used for?

Answer 21

Make an image by adding different sinewaves together by changing the relative phase of some sinewave components relative to others (phase of SFs)
Cosine waves have different location of phase compared to sinewaves

Question 22

How are sine and square waves different in apppearence?

Answer 22

Square wave modulation of luminance comes in from a mean luminance background from dark to light to dark very sharply

while sine waves show gradual changes in luminance from light to dark in periodical order

Question 23

Sine waves needed to make a squarewave include fundamental and odd harmonics:
`
What is a fundamental?
What are odd harmonics?

Answer 23

Fundamental (1st sine wave) = start off with a sine wave with the same spatial scale as the square wave same spatial scale, has the same distance between peaks to peaks

Odd Harmonics = are integer multiples of the fundamental = with a higher spatial frequency compared to the fundamental such that the 3rd harmonic has a spatial frequency 3 times greater than the fundamental sine wave, but the contrast is a third of the fundemental

Question 24

What is unique about the fundamental in a square wave?

Answer 24

The fundamental is the lowest spatial frequency sine wave in the image

Question 25

What would first odd harmonic be for for a fundamental with 2 cycles per degree?

Answer 25

the 3rd harmonic would have 6 cycles per degree, as 2 * 3 = 6

Question 26

What are the characteristics of the 5th harmonic? (assuming the fundamental only had 1 cycle per degree)

Answer 26

Then add the next odd number 5th harmonic, 5x spatial frequency of the fundamental, ⅕ of the wavelength in size, even lower contrast

Question 27

What happens to the CONTRAST and the APPEARANCE of the squarewave you add more harmonics?

Answer 27

1. The contrast DECREASES, eg. the 5th harmonic only has a 1/5 of the contrast of the fundamental As you add more harmonics, the sinewave looks more sharper edged

Question 28

At what contrast level would you be able to discriminate a square wave from a sine wave?

Answer 28

When the third harmonic is visible

Question 29

What experiment would test the detectability of a sinewave from a squarewave? How much contrast do we need to tell them apart?

Answer 29

1. Use an experimental procedure - have 2 computer screens, one has the square wave and the other has a sinewave 2. Start at 0% contrast = both grey screens 3. Slowly increase the contrast, reach a point that the contrast of the sinewave becomes detectable at threshold 4. At threshold, you can detect the fundamental, but all other contrasts are subthreshold/undetectable, and both sinewave and square wave look identical 5. You can predict the contrast level at which you can discriminate a sinewave from a square wave when the third harmonic becomes visible - when the square wave looks different to the sine wave

Question 30

Could you detect a squarewave from a sinewave at the precise contrast that a sinewave becomes detectable at threshold?

Answer 30

NO = At threshold, you can detect the fundamental, but all other contrasts are subthreshold/undetectable, and both sinewave and square wave look identical

Question 31

How could you predict when a participant could discriminate between a sinewave and a squarewave?

Answer 31

1. Work out CONTRAST DETECTION THRESHOLDS to predict when a participant can discriminate between the two waves when the harmonic component of the image becomes detectable 2. IMPLICATIONS = You could PREDICT PERFORMANCE performance of the task by knowing the the components in the two images and the sensitivity of the participant’s contrast threshold

Question 32

What is the difference between the square wave and the peaks add wave? (Peaks add wave have little sharp light and dark bars in appearance around a grey background)

Answer 32

1. The spectrum, the contrast and the spatial frequency doesn’t change… only the RELATIVE PHASE of the waves change 2. The 3rd and 7th harmonics have a NEGATIVE NUMBER, so the phase angle has been shifted by 180 degrees (Relative phase dramatically changes the image appearance and luminance)

Question 33

What specific cells are tuned to specific spatial frequencies? / How are spatial frequencies processed at a cellular level?

Answer 33

V1 cells are tuned to particular oriented tuned columns at a particular orientation and cells within different spatial frequency components: 1. Parvo cells are tuned to HIGH spatial frequencies, encode fine detail 2. Magno cells are tuned to LOW spatial frequencies, encode course detail

Question 34

What are the visual differences in transitions to light to dark between low and high SFs?

Answer 34

1. LOW SFs have a gradual transition from light to dark and encode course information 2. HIGH SFs have a rapid transition from light to dark and encode fine detail

Question 35

What are the 2 methods used in SFA to predict visual performance?

Answer 35

Compare a generic lens system vs. visual system: 1. MTF (Modulation Transfer Function), lens 2. CSF (Contrast Sensitivity Function), human sensitivity

Question 36

How is the MTF plotted?

Answer 36

the plot of the sensitivity of the system to different spatial frequencies (how does the system transfer/modify information that goes through it) MTF = Percent transmission of a function of spatial frequency Response of the system = stimulus spectrum * MTF

Question 37

What 2 things is the MTF used for?

Answer 37

1. Can break down a stimulus into its sinewave components 2. Can predict the visibility of the stimulus based upon the visibility of sinewave components

Question 38

How does SFs cycles per degree change percent transmission in a MTF?

Answer 38

1. Any spatial frequencies with 0-10 cycles per degree (cpd) - percent transmission/100% of the contrast is transmitted At a spatial frequency of 20 cycles of degree, only 50% of energy/contrast is transmitted At a spatial frequency of 30 cycles of degree, sinewave contrast is reduced to 0%, any sinewave over 30 cycles per degree, none of energy gets through, contrast is reduced to 0%

Question 39

If MTF is essentially the output image spectra, how does contrast change of the image at different cpd?

Answer 39

At 10 cpd there is 100% transmission - so the contrast of the sinewave is the same as the input image At 20 cpd there is a 50% transmission - so the contrast of the sinewave will be a half of the input image

Question 40

What happens if the lens gets degraded? (Fingerprints on the lens)

Answer 40

the MTF graph line changes (goes down quicker, closer to the left, takes less cpd to result in a loss of percent transmission

Question 41

Imagine speakers but couldn’t listen to them before, but could see the MTF of 2 speakers:. The MTF would be percent transmission as a function of temporal frequency with sound waves Blue = low pass filter, transmits low temporal frequencies Red = high pass filter, transmits high temporal frequencies All other things being equal, what do you do to determine speakers would you buy to listen to for Heavy metal?

Answer 41

1. Break the music down into temporal frequency spectra (what sinewaves is the music composed off) 2. heavy metal temporal frequency spectra has many low frequencies, eg. bass so better suited to headphones with lower temporal frequencies (blue)

Question 42

What are Sound waves as a function of SFA?

Answer 42

sinewave variations of air density, (pressure waves)

Question 43

How does hertz correlate to cpd?

Answer 43

Human auditory system goes from 20 herz-20 kilohertz (on the x-axis) One hertz = one cycle per second, ie. temporary frequency = sinewave variations in air pressure per second

Question 44

All other things being equal, what do you do to determine speakers would you buy to listen to for String quartets?

Answer 44

1. Break the music down into temporal frequency spectra (what sinewaves is the music composed off) 2. strings have higher delicate string work vibration will have higher temporal frequencies)

Question 45

How would strings sound at lower temporal frequencies?

Answer 45

The strings would sound dampens/loss of detail on the lower temporal frequency headphones

Question 46

How would heavy metal sound at higher temporal frequencies?

Answer 46

it would sound tinny

Question 47

What is the human/VS equivalent of the MTF?

Answer 47

contrast sensitivity function (CSF)

Question 48

How do we plot CSF?

Answer 48

plot of 1/threshold for sinewaves at each spatial frequency, giving sensitivity to different sinewaves at different SFs “window of visibility”

Question 49

How does CSF differ to MTF?

Answer 49

the CSF can’t measure the input/output, must equate to how sensitive we are to different sinewaves

Question 50

What are the 3 steps to construct the human CSF?

Answer 50

1. Get sinewave components and then determine the human contrast detection threshold for sinewaves at different spatial frequencies (multiply together) 2. Plot the contrast threshold for different spatial frequencies 3. Make the CSF the inverse of the threshold for different spatial frequencies, it is reversed as it is more intuitive to think HIGHER scores mean BETTER performance

Question 51

How do we interpret the curve in the CSF?

Answer 51

Anything beneath the curve is visible, anything above the curve is invisible

Question 52

Campbell & Robson = What 2 things are needed to calculate CSF?

Answer 52

1. how much contrast do you need for different spatial frequencies 2. how much contrast a person needs to see the sinewaves (threshold), then plot 1/threshold

Question 53

Why do we plot sensitivity over participant’s threshold? / What causes the shape of the CSF?

Answer 53

it's more intuitive that it is inverted, more intuitive to think of the bigger the number the better the performance

Question 54

What causes the loss of sensitivity at LOW SFs?

Answer 54

Loss of sensitivity at LOW SFS occurs as the tuning properties of simple cells in V1 are NOT TUNED TO REALLY LOW SPATIAL FREQUENCIES (uniform luminance) as it would mean equal amount of excitation AND inhibition (They are only sensitive to changes in luminance of light OR dark that activate periods of (excitation or inhibition) Once you get to 0cpd, the visual system cannot detect changes from light to dark, and the luminance appears uniform with 0 contrast (grey)

Question 55

What causes the loss of sensitivity at HIGH SFs?

Answer 55

Loss of sensitivity at HIGH spatial frequencies is due to the sampling density and size of the receptive fields of the visual system, which is limited by how many visual cells are present, how tightly packed they are and how many feed into retinal ganglion cells The optics of the brain blurs how high spatial frequencies to avoid issues of aliasing from high SFs

Question 56

How do we design psychophysical studies to tap magno cells and parvo cells?

Answer 56

1. Produce an image of a number with different spatial frequencies by convolving the original image with a spatial frequency filter (grey pictures) - (not assessed, spatial filter put on every location of the image and combining images to create new image) Shows the animal represented at different spatial frequencies - taps different cells

Question 57

Infants can’t process high spatial frequencies, while older people also begin to lose the ability to make out finer spatial frequencies How would you determine the CSF of an infant?

Answer 57

1. Preferential Looking/eye tracking: Present with 2 screens one with mean luminance/grey screen and 2nd with sinewave/lines * if they can detect the sinewaves, they will preferentially look at a stimulus over a blank screen *If they cannot make out the sinewave, they would have no preferential look to either one and look at both blank screens equally 2. plot the infant's contrast sensitivity by comparing preferential looking at grey screen to stimulus with different sinewave SFs

Question 58

Campbell & Robson = Given the differences in the CSF, what would an infant not see when looking at a visual scene?

Answer 58

cannot detect high SFs, less ability to detect fine detail in the visual scene

Question 59

You can work out what a child SEES at different ages, but how would you generate an image that represents what an infant sees? (2)

Answer 59

1. Need to determine the infant’s CSF for different sinewaves 2. Break down the image for sinewave components (fourier transform)

Question 60

How would you test the CSF of a goldfish?

Answer 60

= use with food as an alternative form of preferential looking, ie. preferential feeding

Question 61

Campbell & Robson = What part of the CSF tells you about a person’s spatial acuity threshold? / the upper frequency cutoff?

Answer 61

the bottom right part of the CSF with the highest contrast with the highest spatial frequencies

Question 62

Imagine a vision test where all the letters are the same size but they slowly decrease in contrast, what is this measuring?

Answer 62

contrast sensitivity / acuity, size is kept constant

Question 63

Imagine a vision test where all the letters are the same contrast but they slowly decrease in size, what is this measuring?

Answer 63

spatial acuity, not contrast acuity

Question 64

What is the difference between 20/20 and 20/60 vision?

Answer 64

20/20 vision = both you and average person can resolve it at 6m 20/60 vision = you can resolve something at 20ft (6m) while the average person can resolve it at 60ft (18m)

Question 65

What is the upper frequency cutoff / maximum spatial frequency for humans, cats and eagles? Why do eagles have very high SFs?

Answer 65

1. Humans = 30cpd 2. Cats = 20cpd 3. Eagles = 140cpd The high spatial frequency content of the eagle is more beneficial to detecting prey from high heights above ground, so evolved to resolve very high spatial frequencies at a distance

Question 66

Consider a cat and a human viewing the Norwegian-blue parrot. Why do the differences in the CSF of the cats and humans make sense given the differences in our behaviours?

Answer 66

1. The Cat has higher sensitivity to low CFs, so the cat might be better at detecting the actual presence of the bird (outline, shape) compared to a human. 2. The human might be better at detecting finer details of the bird,, eg. the feather structure, lines of the head. 3. The cat will be better at detecting the bird in especially in subthreshold/low light conditions, since a cat is more of a predator to birds than humans, so the presence of the bird is more important than the fine detail of the bird

Question 67

What 3 things do you need to predict the visibility of a stimulus?

Answer 67

1. Object’s Fourier (SF) spectrum 2. The observer’s CSF (contrast sensitivity function) 3. Then perceived image is given by = Stimulus Fourier spectrum * CSF

Question 68

What does our high sensitivity to SFs imply from an evolutionary basis?

Answer 68

Humans high sensitivity to SFs means we have cells tuned to very small receptive fields (might have evolved from what environments we have evolved in, eg. fine motor activity or living in forests with a lot of visual detail)