Digitization

Informatics INFO I101January 26, 2004John C.Paolillo

Mars “Anomalies”

• Are the photos from various Mars missions faked?

• Do the existing photos show evidence of civilized life?

• Do the photos show evidence of martians?

Etc.

http://rush.digitalchainsaw.com/marspath.html

Raster Image Digitizaztion

• Grid– Resolution

• Quantization– Bit-depth– Color

cf. Vector Graphics

1280 960

Great Sand Dunes, Colorado (IRS satellite image; www.spaceimaging.com)

640 480

320 240

160 120

80 60

256 Grays

16 Grays

4 Grays

Black and White

Digital Artifacts

• Pixelation (“jaggies”)– From discretization of the analog signal

• shape• color/gray level

• Resolution mismatches– cause geometric distortions as error accumulates

• Fix: digital interpolation – dithering– anti-aliasing (especially with fonts)

Color

Color Perception

3 Electron guns, aimed at 3 different colors of phosphor dots — analog signals

3 types of retinal sensor cells, sensitive to 3 different bands of light

Color: Response Patterns

red conesgreen cones blue cones

Wavelength

The Eight-Color World

• Eight colors: black, yellow, magenta, red, cyan, green, blue, white

• Three color tubes on a TV monitor: Red, Green, Blue23=8

• Additive color relations: red+green+blue=white

A Psycho-Physical Encoding

Wavelength

RGB

101 100 110 010 011 001 101

000 111

More Colors

• Recognize more levels in each channel– 2 bits per channel: 26 = 64 colors– 4 bits per channel: 212 = 4096 colors– 8 bits per channel: 224 = 16,777,216 colors

• Except for 3-bit and 24 bit colors, most standard colors are not in multiples of 3 bits– 8 bits (256 colors)– 16 bits (32,768 colors)(8 bits is a convenient storage unit)

The Color Table

• A table of some convenient number of values– 4, 16, 256, etc.

• Each location in the table is mapped to some higher resolution color value (24 bit)– Some locations may be unused (mapped to black)

• A monitor typically uses only one color table at a time

Signal Levels

• Intensity is analog• Levels are digital

How do we convert analog intensity to digital levels?

• Quantization: convert analog signals to digital numbers

Quantization1

0

1

0

1

0

1

0

1

0

1

0

1

0Black

White

Med Gray

1. Evenly divide signal levels2. Assign a unique binary

number to each recognized level

3. Match signal with recognized levels and round any intermediate signal level to the nearest recognized level

4. Report the signal as a list of binary numbers000

111

100

011

010

001

110

101

Counting in Binary

• Two values: 0, 1• Each digit is a power of 2

– 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...– Fractions: 0.5, 0.25, 0.125, 0.0625, 0.03125, ...– positive, negative, rational, real, imaginary...We’ll stick to whole numbers for now

Binary counting• Start with zero: 00000• Add 1: 00001• Adding 1 more carries: 00010• Add 1: 00011• Adding 1 more carries 2x: 00100• Add 1: 00101 Etc. OR:• Divide the full range into 2 halves, 0 (low) and 1• Divide each range again for each next bit• Stop with the last bit

End