Digitization Informatics INFO I101 January 26, 2004 John 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.

Raster Image Digitizaztion Grid –Resolution Quantization –Bit-depth –Color cf. Vector Graphics

1280  960 Great Sand Dunes, Colorado (IRS satellite image;

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 cones green 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, Blue 2 3 =8 Additive color relations: red+green+blue=white

A Psycho-Physical Encoding Wavelength  110 RGB

More Colors Recognize more levels in each channel –2 bits per channel: 2 6 = 64 colors –4 bits per channel: 2 12 = 4096 colors –8 bits per channel: 2 24 = 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

Quantization Black White Med Gray 1.Evenly divide signal levels 2.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 numbers

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, , ,... –positive, negative, rational, real, imaginary... We’ll stick to whole numbers for now

Binary counting Start with zero: 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

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