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Digital Images

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Title: Digital Images


1
Digital Images
  • digitize photographs or individual frames of
    digitized video
  • Representation of Grayscale Images
  • pixels, brightness or intensity 8 bits 256
    different intensity levels
  • Bitmap arrangement of these pixel values in a
    contiguous region of memory
  • Framestore / frame buffer memory used to store
    bitmapped image data
  • Color Image
  • three values to represent each pixel

2
Parameters of Digital Images
  • image size
  • if an original picture resolution is 300 dpi
    (dots per inch), then number of pixels (samples)
    per inch required should be at least 300.
    Otherwise, the digital image will be distorted
  • pixel depth the number of bits used to represent
    each pixel
  • amount of data D xyb
  • 512 pixels by 512 lines with pixel depth 24 bits
    768KB

3
Image Compression
  • exploiting redundancies in images and human
    perception properties
  • neighboring samples on a scanning line are
    normally similar (spatial redundancy )
  • predictive coding techniques and other techniques
    such as transform coding
  • Human tolerate some information loss
  • achieve a high compression ratio perception
    sensitivities are different for different signal
    patterns

4
Spatial Subsampling
  • don't have to retain every original pixel to keep
    the contents of the image
  • Encoder one pixel every few pixels is selected
    and transmitted (or stored)
  • Decoder missing pixels are interpolated based on
    the received pixels (Alternatively, display the
    smaller spatially subsampled images)
  • If pixels are represented with luminance and
    chrominance components
  • chrominance subsampled at a higher ratio and
    quantized more coarsely

5
Predictive Coding
  • sample values of spatially neighboring picture
    elements are correlated
  • One-dimensional prediction algorithms use
    correlation of adjacent picture elements within
    the scan line
  • line-to-line and frame-to-frame correlation and
    are denoted as two-dimensional and
    three-dimensional prediction

6
Transform Coding
  • decorrelate the image pixels convert
    statistically dependent image elements into
    independent coefficients
  • concentrate the energy of an image onto only a
    few coefficients, so that the redundancy in the
    image can be removed
  • original image is usually divided into a number
    of rectangular blocks or subimages
  • apply unitary mathematical transform to each
    subimage
  • transforms the subimage from the spatial domain
    into a frequency domain
  • If the data in the spatial domain is highly
    correlated, the resulting data in the frequency
    domain will be in a suitable form for data
    reduction with techniques such as Huffman coding
    and run-length coding

7
Transform Coding (2/2)
  • takes advantage of the statistical dependencies
    of image elements for redundancy reduction
  • Karhunen-Loeve transform (KLT), the discrete
    cosine transform (DCT), the Walsh-Hadamard
    transform (WHT) and the discrete Fourier
    transform (DFT)
  • KLT is the most efficient , DCT is most widely
    used
  • practical transform coding system
  • select the transform type, block size
  • apply the selected transform
  • select and efficiently quantize those transformed
    coefficients to be retained for transmission or
    storage

8
Vector Quantization(1/2)
  • Shannon's rate-distortion theory better
    performance can always be achieved by coding
    vectors (a group of values) instead of scalars
    (individual values).
  • vector quantizer a mapping Q of K-dimensional
    Euclidean space RK into a finite subset Y of RK
  • Q RK?Y, Y (x'i i 1, 2, . . . . N), and x'i
    is the ith vector in Y.
  • Y (a VQ codebook or VQ table ) is the set of
    reproduction vectors
  • N is the number of vectors

9
Vector Quantization(2/2)
  • Encoder
  • each data vector x belonging to RK is matched or
    approximated with a codeword in the codebook
    address or index of that codeword is transmitted
  • decoder
  • index is mapped back to the codeword codeword
    is used to represent the original data vector
  • image block size is (n x n) pixels and each pixel
    is represented by m bits, theoretically, (2m)nxn
    types of blocks are possible
  • In practice, only a limited number of
    combinations that occur most often

10
Fractal Image Coding
  • A fractal
  • an image of a texture or shape expressed as one
    or more mathematical formulas
  • a geometric form whose irregular details recur at
    different scales and angles, which can be
    described by affine or fractal transformations
    (formulas)
  • Fractal Geometry IBM mathematician Benoit B.
    Mandelbrot, The Fractal Geometry of Nature, 1977
  • Fractals have historically been used to generate
    images
  • Fractal formulas can now be used to describe
    almost all real-world pictures
  • Fractal image compression is the inverse of
    fractal image generation
  • fractal image compression searches for sets of
    fractals in a digitized image that describe and
    represent the entire image
  • The codes are "rules" for reproducing the various
    sets of fractals that, in turn, regenerate the
    entire image
  • Lossy compression
  • Compression is slow, decompression is fast

11
Fractal Coding
12
Wavelet Compression Practical Coding Systems
  • Wavelet Compression basic principle similar to
    that of DCT-based compression to transform
    signals from the time domain into a new domain
  • Practical Coding Systems
  • (a) Spatial and temporal subsampling
  • (b) DPCM based on motion estimation and
    compensation
  • (c) Two-dimensional DCT
  • (d) Huffman coding
  • (e) Run-length coding

13
JPEG - Still Image Compression Standard
  • Joint Photographic Experts Group
  • continuous-tone (multilevel) still images
  • grayscale and color
  • handle full-motion video the application is
    called motion JPEG or MJPEG
  • four modes of operation
  • Lossy sequential DCT-based encoding
  • Expanded lossy DCT-based encoding
  • Lossless encoding
  • Hierarchical encoding

14
4 modes
  • Lossy sequential DCT-based encoding
  • each image component is encoded
  • in a single left-to-right, top-to-bottom scan
  • called baseline mode
  • Expanded lossy DCT-based encoding
  • progressive coding, in which the image is encoded
    in multiple scans to produce a quick, rough
    decoded image when the transmission bandwidth is
    low.
  • Lossless encoding exact reproduction
  • Hierarchical encoding encoded in multiple
    resolutions

15
Baseline mode (1/4)
  • source image data
  • normally transformed into luminance component Y
    and two chrominance components U and V
  • U and V are normally spatially-sampled in both
    the horizontal and vertical direction by a factor
    of 2
  • take advantage of the lower sensitivity of human
    perception to the chrominance signals
  • original sample values are in the range 0,
    2b-1, assuming b bits are used for each sample
  • values are shifted into the range -2b-1,
    2b-1-1, centering on zero
  • to allow a low-precision calculation in the DCT
  • For baseline, 8 bits are used for each sample
  • the original value range of 0, 255 is shifted
    to -128, 127.

16
Baseline mode (2/4)
  • Then, each component is divided into blocks of 8
    x 8 pixels
  • A two-dimensional forward DCT (FDCT) is applied
    to each block of data.
  • Result an array of 64 coefficients with energy
    concentrated in the first few coefficients
  • quantized these coefficients, using quantization
    values specified in the quantization tables
  • the quantization values can be adjusted to trade
    between compression ratio and compressed image
    quality
  • Quantization is carried out by dividing the DCT
    coefficients by the corresponding specified
    quantization value

17
Baseline mode (3/4)
  • The quantized coefficients are zigzag scanned to
    obtain a one-dimensional sequence of data for
    Huffman coding
  • The first coefficient is called the DC
    coefficient, which represents the average
    intensity of the block
  • The rest of the coefficients (1 to 63) are called
    AC coefficients
  • zigzag scanning is to order the coefficients in
    increasing order of spectral frequencies
  • the coefficients of high frequencies are mostly
    zero, the zigzag scanning will result in mostly
    zeros at the end of the scan
  • leading to higher Huffman and run-length coding
    efficiency.

18
Baseline mode (4/4)
  • The DC coefficient is DPCM coded relative to the
    DC coefficient of the previous block.
  • AC coefficients are run-length coded.
  • DPCM-coded DC coefficients and run-length-coded
    AC coefficients are then Huffman coded.
  • The output of the entropy coder is the compressed
    image data.

19
Sequential DCT-based encoding
20
JBIG
  • an ISO standard (Joint Bi-level Image experts
    Group)
  • The intent of JBIG is to replace the current,
    less effective group 3 and group 4 fax algorithms
  • a lossless compression algorithm for binary (one
    bit/ pixel) images.
  • JBIG compression
  • based on a combination of predictive and
    arithmetic coding
  • used on grayscale or even color images for
    lossless compression
  • simply applying the algorithm 1 bit plane at a
    time

21
Arithmetic Coding (I)
  • Probability
  • , A, B, E, G, I 0.1
  • L 0.2
  • S, T 0.1
  • Range
  • 0.0, 0.1), A0.1, 0.2), , I0.5,
    0.6)
  • L0.6, 0.8), S0.8, 0.9), T0.9, 1.0)
  • Coding BILL GATES

22
Arithmetic Coding (I)
  • initial low0.0, high 1.0
  • B - 0.2, 0.3), low 0.2, high 0.3
  • I -0.5, 0.6), low 0.25, high 0.26
  • (0.3-0.2) 0.5 0.05 (0.3-0.2)0.6 0.06
  • L -0.6, 0.8), low 0.256 , high 0.258
  • (0.26-0.25)0.6 .006, (.26-.25).8.008
  • L -0.6, 0.8), low 0.2572 , high 0.2576
  • .002.6 .0012, .002.8.0016

23
Arithmetic Coding (II)
  • -0.0, 0.1), low 0.25720 , high 0.25724
  • .00040.0 0, .00040.1.00004
  • G .257216, .257220
  • A .2572164, .2572168
  • T .25721676, .2572168
  • E .257216772, .257216776
  • S .2572167752, .2572167756

24
Decode msg .2572167752
  • reverse operation
  • within 0.2, 0.3) B - 0.2, 0.3)
  • B, (msg-0.2)/(0.3-0.2) .572167752 (msg)
  • I -0.5, 0.6), (msg-0.5)/(0.6-0.5).72167752
  • L-0.6, 0.8), (.72167752-.6)/(.8-.6).6083876
  • 0.8
  • S-0.8,0.9), (0.8-0.8)/(0.9-0.8) 0
  • END
  • chose a binary close to low

25
JPEG-2000 (1/2)
  • provide a lower bit-rate mode of operation than
    the existing JPEG and JBIG standards
  • replace and provide better rate distortion and
    subjective image quality
  • handle images larger than 64K x 64K pixels
    without having to use tiling
  • use a single decompression algorithm for all
    images to avoid the problems of mode
    incompatibility (sometimes encountered with
    existing standards)
  • designed with transmission in noisy environments
    in mind
  • also efficient to compress computer-generated
    images
  • handle the mix of bilevel and continuous tone
    images required for interchanging and/or storing
    compound documents as part of document imaging
    systems
  • in both lossless and lossy formats

26
JPEG-2000 (2/2)
  • allow progressive transmission of images
  • allow images to be reconstructed with increasing
    pixel accuracy and spatial resolution.
  • transmittable in real-time over low bandwidth
    channels to devices with limited memory space
    (e.g., a printer buffer).
  • allow specific areas of an image to be compressed
    with less distortion than others
  • provide
  • facilities for content-based description of the
    images
  • mechanisms for watermarking, labeling, stamping,
    and encrypting images.
  • still images are compatible with MPEG-4 moving
    images
  • Using Wavelet compression

27
Digital Video Representation (1/3)
  • A digital video sequence consists of a number of
    frames or images that have to be played out at a
    fixed rate.
  • The frame rate of a motion video is determined by
    three major factors.
  • high enough to deliver motion smoothly.
  • most motion can be delivered smoothly frame rate
    25 frames per second
  • the higher the frame rate, the higher the
    transmit bandwidth
  • high frame rate, more images (frames) must be
    transmitted in the same amount of time, so higher
    bandwidth is required.
  • So bandwidth at least 25 frames per second to
    deliver most scenes smoothly

28
Digital Video Representation (2/3)
  • 3. when the phosphors in the display devices are
    hit by an electron beam, they emit light for a
    short time, typically for a few milliseconds.
  • phosphors do not emit more light unless they are
    hit again by the electron beam.
  • the image on the display disappears if it is not
    redisplayed (refreshed) after this short period.
  • If the refresh interval is too large, the display
    has an annoying flickering appearance
  • refreshed at least 50 times per second to prevent
    flicker - bandwidth!!
  • Use interlace techniquethe same amount of
    bandwidth is used but flicker is avoided to a
    large extent
  • more than one vertical scan is used to reproduce
    a complete frame.
  • Each vertical scan is called a field.
  • Broadcast television uses a 21 interlace - 2
    vertical scan (fields) for a complete frame.
  • one vertical scan (called the odd field) displays
    all the odd lines of a frame,
  • a second vertical scan (called the even field)
    displays the even lines.

29
D.V. Representation (3/3)
  • 25 frames per second, the field rate is 50
    fields per second
  • 25 frames (50 fields) per second rate is used in
    television systems (PAL) in European countries
  • China, and Australia. The 30 frames (60 fields)
    per second rate is used in the television systems
    (NTSC) of North America and Japan
  • field numbers 50 and 60 were chosen to match the
    frequencies of electricity power distribution
    networks
  • two major characteristics of video
  • a time dimension
  • a huge amount of data to represent
  • a 10-minute video sequence with image size 512
    pixels by 512 lines, pixel depth of 24 bits/pixel
    and frame rate 30 frames/s 600305125123
    13.8 GB storage
  • So, video compression is essential.

30
Video Compression
  • by reducing redundancies and exploiting human
    perception properties
  • it also has spatial redundancies
  • neighboring images in a video sequence are
    normally similar. (called temporal redundancy)
  • removed by applying predictive coding between
    images
  • reduce temporal redundanciesMotion Estimation
    and Compensation
  • each picture is divided into fixed-size blocks.
  • A closest match for each blockis found in the
    previous picture

31
Motion Estimation and Compensation
  • The position displacement between these two
    blocks is called the motion vector
  • A difference block is obtained by calculating
    pixel-by-pixel differences
  • The motion vector and pixel difference block are
    then encoded and transmitted

32
MPEG (1/2)
  • MPEG was established in 1988 in the framework of
    the Joint ISO/IEC Technical Committee (JTC 1) on
    Information Technology.
  • develop standards for coded representation of
    moving pictures, associated audio, and their
    combination when used for storage and retrieval
    on digital storage media (DSM).
  • The DSM concept includes conventional storage
    devices, such as CD-ROMs, tape drives, Winchester
    disks, writable optical drives, as well as
    telecommunication channels such as ISDNs and
    local area networks (LANs).
  • MPEG-4 work item was proposed in May 1991 and
    approved in July 1993

33
MPEG (2/2)
  • The group had three original work items
    nicknamed MPEG-1, MPEG-2, and MPEG-3
  • coding of moving pictures and associated audio up
    to 1.5, 10, and 40 Mbps.
  • MPEG-1 VHS-quality video (360 x 280 pixels at 30
    pictures per second) at the bit rate around 1.5
    Mbps. The rate of 1.5 Mbits was chosen because
    the throughput of CD-ROM drives at that time was
    about that rate.
  • MPEG-2 was to code CCIR 601 digital-television-qua
    lity video (720 x 480 pixels at 30 frames per
    second) at a bit rate between 2 to 10 Mbps.
  • MPEG-3 was to code HDTV-quality video at a bit
    rate around 40 Mbps. Later on, it was realized
    that functionality supported by the MPEG-2
    requirements covers MPEG-3 requirements, thus the
    MPEG-3 work item was dropped in July 1992.

34
MPEG Parts
  • three main parts
  • MPEG-Videocompression of video signals
  • MPEG-Audioconcerned with the compression of a
    digital audio signal
  • MPEG-Systems deals with the issue of
    synchronization and multiplexing of multiple
    compressed audio and video bitstreams
  • a fourth part called Conformance
  • specifies the procedures for determining the
    characteristics of coded bitstreams and for
    testing compliance with the requirements stated
    in Systems, Video, and Audio.
  • only specify the syntax of coded bitstreams
  • so that decoders conforming to these standards
    can decode the bitstream.
  • The standards do not specify how to generate the
    bitstream.
  • This allows innovation in designing and
    implementing encoders

35
Standards for Composite Multimedia Documents
  • SGML (Standard Generalized Markup Language)
  • std. syntax for defining Document Type
    Definitions of classes of structured info.
  • HTML is a class of DTD of SGML
  • Open Document Arch. logical layout components
    of documents, interchange format
  • Acrobat Portable Document Format
  • Hypermedia/Time-Based Structuring Language
    (HyTime) represent hypermedia doc. using SGML
    interrelation of doc. components according to any
    quantifiable dimension
  • MHEG OO model for MM interchange

36
Major Characteristics and Requirements of
Multimedia Data and Applications
  • Storage and Bandwidth Requirements
  • Semantic Structure of Multimedia Information
  • Delay and Delay Jitter Requirements
  • Temporal and Spatial Relationships among Related
    Media
  • Subjectiveness and Fuzziness of the Meaning of
    Multimedia Data

37
Major Characteristics and Requirements (2/3)
  • Storage and Bandwidth Requirements
  • Measure
  • storage bytes, MB
  • bandwidth bps, Mbps
  • images (storage) XYdepth (B, MB)
  • audio,video (bandwidth) bps, Mbsp
  • audio sampling rate bits/sample
  • video frame-unit
  • Semantic Structure of Multimedia Information
  • no obvious structure (vs. alphanumeric)
  • features or contents have to be extracted from
    raw MM data

38
Major Characteristics and Requirements (3/3)
  • Delay and Delay Jitter Requirements
  • time-dependent continuous media
  • MIRSs are interactive (delay, response time)
  • Temporal and Spatial Relationships among Related
    Media
  • retrieval transmission of media be coordinated
    w.r.t. temporal relationship
  • synchronization
  • 1)mechanisms/tools for users to specify
  • 2)to guarantee overcome indeterministic nature
    of comm.
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