Role of Sinusoids in Spatial Vision Flashcards
Describe Fourier Analysis?
Any periodic pattern can be expressed as a sum of trigonometric functions
Any 2D images, no matter how complex, can be created from or decomposed into set of sinusoidal patterns
Have to find right combo of sinewave parameters e.g. spatial freq, contrast, intation or phase of each sinusoidal component and add them together to construct image want to create.
Adding sinewave gratings –> Fourier synthesis
Once synthesise, or any image, reverse process is also possible. Can decompose the patterns into the sinewave grating components
What is Fourier Analysis of Images?
- In theory, any image can be decomposed into group of basic sinewave components using Fourier analysis
- e.g. digital image composed of 502 x 357 pixels –> Fourier analysis will find ~50,000 sinewave gratings, each of which have just the right parameters to add up to the image
Describe Luminance Changes Across Space?
- Objects are distinguishable from each other & from surroundings by variations in light and colour that they reflect
- Spatial Filtering w/ Fourier Analysis can extract more detailed spatial info by analysing how luminance changes across space in an image
Describe Low Pass Filtering?
-Filters out higher freq. info & passes only lower freq. info
-Filtered image is quite blurry & lost all fine details & only shows overall structure of a scene where luminance changes slowly & smoothly
Describe Low Pass Filtering?
-Filters out higher freq. info & passes only lower freq. info
-Filtered image is quite blurry & lost all fine details & only shows overall structure of a scene where luminance changes slowly & smoothly
Describe Band Pass Filtering?
- Only middle spatial freq. can pass
- Low spatial freq. & high spatial freq. info are filtered out
- Resulting image still blurry but there is the overall shape & dot pattern of object looks slightly clearer & can now start to be distinguished from background
Describe High Pass Filtering?
- Only contains high spatial freq. info & filters out all low spatial freq.
- Can see sharp conotour & boundares of objects & patterns but no info about slow fluctuation in overall luminance is lost
Describe the testing of an optical system with sinewave?
- Any image-forming optical system including human eye create less than perfect images
- In general, optical systems transfer light pattern in object
- Some info of image is lost & typically the lost info is contrast
- Testing quality of optical system e.g. lens of camera:
o 1st need to choose set of test sine-wave gratings of 100% contrast w/ various spatial frequencies
o Then pass them through optical system one by one & observe image formed by system & when look at image after optical system then will see that resulting image is still same sinusoidal pattern/ same spatial frequency orientation & phase but w/ slightly less contrast
Amount of loss in contrast ↑ as spatial frequency ↑ - General rule: any optical device actually lose contrast info & amount of contrast loss from this transfer through optical system can be quantified as a modulation transfer function
Describe Modulation (Contrast) Transfer?
- Modulation is same as contrast here – denotes fact that contrast is result of amplitude modulation of sinewave grating
- Test objects start at 100% contrast but when transferred through any optical system then there is a loss in contrast higher freq, more contrast is loss
Describe Modulation Transfer Function (MTF)?
- Relative loss of contrast in image compared to object
- Ratio of image contrast to original object contrast
- MT is plotted against spatial frequency (cycles per visual degree angle)
- If ideal optical system, there will be no loss in the modulation transfer -> perfect optical system will transfer all info from original image or object when it is going through the system
- In an actual optical system, the modulation transfer function is followed where the lowest freq info is preserved well but ratio is going down as spatial freq. of object increases
Describe Modulation Transfer Function of eye?
- Human visual system has similar opticsa
- When image goes through eye, resulting image shows a similar pattern except it has lower contrast especially at higher spatial frequencies
o So much contrast is lost at highest spatial frequencies that stripes are no longer visible just plain grey - MTF of eye characterises optical performance of eye
- MTF at lowest spatial freq is essentially 100% but drops off as spatial freq ↑ quite quickly & drops to zero at ~70 cycles per degree
o Spatial freq where MTF drops to zero – where it cuts x-axis is known as cutoff spatial frequency
o Optical performance is worse for myopes & so image will look blurry especially at higher spatial frequencies compared to emmetropes
o Not much loss in low spatial frequencies but myopes lose lot more in higher spatial frequencies - Cutoff spatial frequency for myopes is ~30 cycles per degree – almost half of emmetropes cutoff spatial frequency typical effect of refractive errors & they tend to reduce MTF of eye at high spatial frequencies only
- Optical scatters e.g. in cataract tend to reduced MTF at both high & low spatial frequencies
Describe testing performance of visual system?
- Human visual system is not just about the optical system
- Can think of retinal image as end product of eye’s optical system but MTF of eye only characterises front-end of our visual system
- To arrive final perception of object, retinal image should be transformed into electrical signals that are further processed by brain
- Having good vision requires both good optics as well as healthy neural processing
- When test vision, really testing whole visual system – human contrast sensitivity
Describe Contrast Sensitivity Function (CSF)?
- Characteristic function relating contrast sensitivity (CS) across range of spatial freqs (SF)
- Measure of overall performance of entire visual system, how its sensitivity to contrast changes w/ different spatial scale
- Can think of CSF as MTF of entire visual system
- Way to evaluate performance of entire visual system (=optics + neural processing)
- Like MTF, sinewave gratings are used to measure CSF
- CS is computed by measuring contrast threshold for a given SF & taking the reciprocal of the threshold Unlike measuring MT where 100% contrast of sinewave gratings are used, contrast of sinewave gratings will change to measure contrast thresholds for each spatial freq tested
- According to Fourier’s theorem/transformation, any spatially varying signal or image in luminance can be represented as a linear combo of sinewaves
- If know how system responds to range of luminance changes in sinewave gratings, can also predict system’s performance to any image
o Visual system’s CS – measured in relative difference in luminance can be tested w/ sinusoidal gratings across range of spatial freqs representing detail of image
