digital representations digital video special effects fall 2006
TRANSCRIPT
Digital Representations
Digital Video Special Effects
Fall 2006
Analog-to-Digital (A-D) Conversion
Sampling Quantization Coding
Sampling -- Analog to Discrete
Analog signal to discrete-time signal x(t) --> x[n]
Sampling procedure
f(t) is the sampling function
Simple sampling x[n] = x(t=n), i.e., f(t)=(t)
dtnTtftxnTx )()(][
Reconstruction: Discrete to Analog
Can we reconstruct analog signal from its discrete time samples? x[n] --> x(t) ? Generally not.
Nyquist (Shannon) sampling theorem for bandlimited signals If the simple sampling rate is at least twice bandwidth of th
e analog signal, the analog signal can be perfectly reconstructed:
)(sinc)()( T nTtnTxtxn
Quantization -- Digitization
Discrete-time signal digital signal Quantization error Quantization level
How many bits to represent one sample? Trade-off between error and bit rate (communication band
width)
Nonlinear quantization Pre-compression and de-compression ( law and A law)
Vector quantization
Raw Data Rate
Sampling frequency= f (Hz) Each sample represented by R bits Raw data rate (bit rate):
T = f x R (bits per second, or bps)
Digital Audio Signals
Frequency band of sound: human hearing frequency range: 20Hz-20 KHz.
Sampling rate > 40 KHz (Actual sampling rate of CD-Audio = 44.1 KHz)
Bit rate for CD quality audio signal (44.1 KHz, Quantization:16 bits, 2 channels):T = 44100 x 16 x 2 (bits per second, or bps)
CD quality stereo sound 10.6 MB / min
Examples Sampling Rate
(KHz) Quantization level (bits)
Bit Rate (Kbps)
Telephone 8 8 64
AM Radio 16 16 256
FM Radio 22.05 16 352.8
CD Stereo 44.1 16 1411.2
DAT 48 16 1536
DVD (Stereo)
192 24 9216
Speech Signals Properties
Human ear: most sensitive to 600Hz-6000Hz Quasi-stationary for around 30 ms Characteristic maxima -- formants
Speech analysis and synthesis Speech components, e.g., vowels and consonants
MIDI
A protocol that enables computer, synthesizers, keyboards, and other musical device to communicate with each other.
Bit rate: 31.25Kbps A MIDI file stores the messages regarding sp
ecific musical actions. Commands, instead of actual waveforms, are
saved. One minute of MIDI: 4KB storage.
Digital Image Representation Picture elements (pixels)
Sampling, quantization Higher dimensional image -- voxels Bi-level images (black/0 or white/1) Grayscale images
1 byte/pixel: 256 gray levels
Color images True color: RGB 24bits/pixel
Image size, e.g. VGA 640x480 Grayscale image: 307,200 bytes True color image: 921,600 bytes
Graphics Format
Graphics primitives and attributes 2-D objects: lines, rectangles, circles, ellipses, tex
t strings, etc. Attributes: line style, line width, color, etc.
High-level representation: structured, object-based
Low-level representation: bitmap
Computer Graphics Computer animation Computer Generated Images (CGI) Photo-realistic rendering
Video Signal Requirements
Aspect ratio: TV 4/3; HDTV16/9 Luminance and chrominance Continuity of motion > 15 frames/s
TV 30 or 25 frames/s, movie 24 frames/s Flicker. Marginal at least 50 refresh cycles/s
Movie: 2x24=48 TV: Half picture by line-interleaving
Scanning rate: at lease 25Hz, finish one frame in 1/25s
Color Representation in Video RGB, normalized R=G=B=1 -- white color YUV signal
Y=0.30R+0.59G+0.11B (Luminance) U=(B-Y) x 0.493, V=(R-Y) x 0.877 (Chrominance channels) Example: PAL, CD-I and DVI (Digital Video Interactive) video.
YIQ signal Y=0.30R+0.59G+0.11B (Luminance) I=0.60R-0.28G-0.32B, Q=0.21R-0.52G+0.31B Example: NTSC
Avoid cross talk between luminance and colors: S-Video video signals separate the luminance and chrominance information into two separate analog signals.
Subsampling in Video
Different spatial sampling rates for different chrominance channels
Human beings are more sensitive to luminance (using more samples) while less sensitive to colors (using less samples).
Different resolution for different components Y:C1:C2 -- 4:2:2
Subsampling and upsampling techniques
Computer Video Format
CGA (Color Graphics Adapter): 4 colors, 320x200x2bits = 16,000 bytes
EGA: 640x350x4bits = 112,000 bytes VGA: 640x480x8bits = 307,000 bytes SVGA: 800x600 pixels XGA: 1024x768 pixels SXGA: 1280x1024 pixels
Video Quality VCR Quality -- SIF (MPEG1)
NTSC: 240x352; PAL: 288x352 per frame Videoconferencing quality
CIF (Common Interchange Format) -- H.261 288x352, subsampling 4:1:1(halving both direction) Q: what is the raw bit rate of CIF video (30frames/s)?
QCIF (Quarter CIF) 144x176, subsampling 4:1:1(halving both direction) Q: what is the raw bit rate of QCIF video (30frames/s)
Super-CIF: 576x704, subsampling 4:1:1(halving both direction)
The Need for Compression
Take, for example, a video signal with resolution 320x240 and 256 (8 bits) colors,30 frames per second
Raw bit rate = 320x240x8x30 = 18,432,000 bits = 2,304,000 bytes = 2.3 MB
A 90 minute movie would take 2.3x60x90 MB = 12.44 GB
Without compression, data storage and transmission would pose serious problems!
Data Compression
Data compression requires the identification and extraction of source redundancy.
In other words, data compression seeks to reduce the number of bits used to store or transmit information.
Lossless Compression
Lossless compression can recover the exact original data after compression.
It is used mainly for compressing database records, spreadsheets or word processing files, where exact replication of the original is essential.
Examples: Run Length Encoding (RLE), Lempel Ziv Welch (LZW), Huffman Coding.
Lossy Compression
Result in a certain loss of accuracy in exchange for a substantial increase in compression.
More effective when used to compress images and voice where losses outside visual or aural perception can be tolerated.
Most lossy compression techniques can be adjusted to different quality levels.
Example: DCT(JPEG), MPEG
Compression Ratio
Compression ratio
original data size ------------------------- : 1compressed data size