Aditi Majumder, CS 112 Slide 1

CS 112 – Display Considerations

Aditi Majumder, CS 112 Slide 2

Display

Image generationGenerate digital imagesShould take care to have non-aliased images

Image ReconstructionGenerate a continuous image on the display

Aditi Majumder, CS 112 Slide 3

Image Reconstruction

Each pixel is not a point but an areaHow is that area lighted?

2D 1D

Ideal CaseIn practice

Spot WidthWider spots Narrower spots

Aditi Majumder, CS 112 Slide 4

Sampling

f s 2

-f s 2

f s 2 f s 3 f s - f s

f s 2 f s 3 f s - f s

Convolution

Aditi Majumder, CS 112 Slide 5

Reconstruction

f s 2

-f s 2

f s 2 f s 3 f s - f s

f s 2

-f s 2

Multiplication

Aditi Majumder, CS 112 Slide 6

Reconstruction (Wider Kernel)

f s 2

-f s 2

f s 2 f s 3 f s - f s

f s 2

-f s 2

PIXELIZATION: Lower frequency aliased as high frequency

Aditi Majumder, CS 112 Slide 7

Reconstruction (Narrower Kernel)

f s 2

-f s 2

f s 2 f s 3 f s - f s

f s 2

-f s 2

BLURRING: Removal of high frequencies

Aditi Majumder, CS 112 Slide 8

Aliasing artifacts (Right Width)

Aditi Majumder, CS 112 Slide 9

Wider Spots (Lost high frequencies)

Aditi Majumder, CS 112 Slide 10

Narrow Width (Jaggies, insufficient sampling)

Aditi Majumder, CS 112 Slide 11

Quantization

Digitization of colorGray scale – infinite grays between 0 and 1

8 bit representation – 256 levelsA range of grays represented by a single value

Any value is assigned to one of k valuesChoose number of levels and range of each level

Aditi Majumder, CS 112 Slide 12

Quantization Error

g

Q(g)

Quantization Error

Uniform Quantization

Maximum Error = ½ Step Size

Step Size

Aditi Majumder, CS 112 Slide 13

Human Perception

Use properties of human perceptionResponse CompressionResponse Expansion

Aditi Majumder, CS 112 Slide 14

Steven’s Power Law

P = KS n

P = PerceptionS = Stimulus

Strength

n>1.0 (Expansion)

n<1.0 (Compression)

Aditi Majumder, CS 112 Slide 15

Steven’s Power Law

P = KS n

P = PerceptionS = Stimulus

Strength

n>1.0 (Expansion)

n<1.0 (Compression)

Aditi Majumder, CS 112 Slide 16

Gamma Function

Inverse of human response curve for faithful representation of intensitiesCalled the gamma function

O = Iγ

Gamma Correction

Human Response

Display Gamma

Input Intensity

Out

put I

nten

sity

Aditi Majumder, CS 112 Slide 17

Capture devices (Camera)

Usually have the inverse gammeSimilar to human eye

So that images look good on displayCurrent cameras give you RAW images which are linear

Aditi Majumder, CS 112 Slide 18

Non-Uniform Quantization

Note how quantization changesNon-uniform step sizeMaximum Error

½ of maximum step size

# of levels is the color resolution

# of bits

Display Gamma

Input Intensity

Out

put I

nten

sity

Aditi Majumder, CS 112 Slide 19

Color Resolution

Analog Image 4 Steps 8 Steps 16 Steps

32 Steps64 Steps

Quantization Artifacts

Aditi Majumder, CS 112 Slide 20

Dithering

What if the color resolution is low?Newsprint – Bi-level, only black and white

Can we expand the # of colors?Spatial integration of eye

Trading off spatial resolution for intensity resolution

Aditi Majumder, CS 112 Slide 21

Dithering

Represented by a dither matrixnxn pixels, bi-level intensity, can produce n2+1 intensitiesIf more than two levels – k levels

n2. (k-1) +1Used for increasing the color resolution

0 2

1 3

Aditi Majumder, CS 112 Slide 22

Dithering

If more than two levels – k levelsn2. (k-1) +1For k = 4 (0,1,2,3) and n=2

Aditi Majumder, CS 112 Slide 23

Examples

Loss of tone and details(Intensity and Spatial Resolution)