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.
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
green cones blue cones red cones Color: Response Patterns 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 23=8 • Additive color relations: red+green+blue=white
A Psycho-Physical Encoding RGB 101 100 110 010 011 001 101 110 000 111 Wavelength
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
1 1 1 1 1 1 1 White 111 110 101 Med Gray 100 0 0 0 0 0 0 0 011 010 Black 001 000 Quantization • Evenly divide signal levels • Assign a unique binary number to each recognized level • Match signal with recognized levels and round any intermediate signal level to the nearest recognized level • 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, 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
