common image compression formats
DESCRIPTION
Overview of JPEG, JPEG2000, EZW, and S+P SPIHTTRANSCRIPT
Overview of Common Image Compression Formats
Clyde A. Lettsome, PhD, P.E.
Georgia Institute of Technology Center for Signal and Image Processing
Outline
Introduction Block Transform Method Subband Transform Method Performance References
Introduction
Georgia Institute of Technology Center for Signal and Image Processing
Figure 2.1 Basic Compression Encoder Decoder Block Diagram.
Block Transform Method
Pack high energy data at the beginning
Baseline JPEG Algorithm– Joint Photographic Experts Group or JPEG – Discrete Cosine Transform (DCT) – Based on DCT II
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Block Transform Method
– JPEG Transform and Quantization Procedure
1. Divide image into 8x8 blocks
2. Apply the cosine transform
3. Round to the nearest integer
4. Maintain the dominant coefficients, a quantization weighting matrix Q[k1,k2]. smaller coefficients are placeded in the upper left corner while larger coefficients are placed in the lower right corner.
5. Coefficients are then rounded to the nearest integers
6. Unwrapping the remaining non-zero coefficients as shown in the next figure
7. DC components of each block is then extracted and encoded using the first order backward difference
8. AC non-zero components of each block are then collected and encoded using runlength coding. The general idea behind runlength coding is to encode repetitive sequences of values using a symbol
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Block Transform Method
Georgia Institute of Technology Center for Signal and Image Processing
Block Transform Method
JPEG Entropy Coder Huffman coding is performed by:
1. Ordering the symbols in descending order
2. Merging the symbols with the lowest probabilities and reordering the resulting symbols in decreasing order of probability to form a tree
3. With the tree from step 2 in place, bit values (ones or zeros) are assigned to each branch of the tree starting from the right side and progressing to the left.
Georgia Institute of Technology Center for Signal and Image Processing
Subband Transform Method
Georgia Institute of Technology Center for Signal and Image Processing
Figure 2.2 Two-band analysis-synthesis filter bank
X=½X(-z) [H0(-z)G0(z) + H1(-z)G1(z)] + ½X(z) [H0(z)G0(z) + H1(z)G1(z)],
[H0(-z)G0(z) + H1(-z)G1(z)]
[H0(z)G0(z) + H1(z)G1(z)].
Subband Transform Method
Important Developments in subband coding– subband transform is based on multi-rate
equation first mentioned by Schafer and Rabiner to improve coding efficiency
– Perfect reconstruction (PR) which was first introduced by Croiser, Estaban and Galand when they introduced Quadrature Mirror Filters (QMF)
– Exact reconstruction (ER) discovered by Smith and Barnwell and verified by Mintzer.
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Subband Transform Method
EZW– Developed by JM Shapiro in 1993
Georgia Institute of Technology Center for Signal and Image Processing
Figure 2.3 Octave-band decomposition
Subband Transform Method
The quantization coding technique for the EZW is based on three principals (8).1. partial ordering of the wavelet transformed
elements based on magnitude, with the order of transmission based on subset partitioning algorithm,
2. ordering the bit transmission of refined bits,
3. exploitation of the coefficient similarities across different levels of decomposition
Georgia Institute of Technology Center for Signal and Image Processing
Subband Transform Method
The SPIHT Method– Developed by Said Pearlman– Transform based on EZW with additional
discoveries symmetric extension developed by Smith and Eddins Daubechies 9/7 filters Haar filters Filter switching independent threshold is set for each subband thresholds in the highpass subbands are much more
restrictive than they are in the lowpass subbands
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Subband Transform Method
SPIHT’s Entropy CoderArithmetic coder - tends to perform better than
the Huffman coder in terms of reaching entropy1. The approach is based on a partitioning rule that
maps the input dynamically to a sub-interval of the line segment by sub-dividing the unit interval successively.
2. With each input symbol, the sub-interval is computed by finding the low end-point, the high-endpoint, and then the range.
3. sub-intervals are then mapped to binary codewords before being transmitted
Georgia Institute of Technology Center for Signal and Image Processing
Subband Transform Method
JPEG2000– Similar to SPIHT– Constructed by the Joint Photographic Experts
Group1. images are first tiled
2. dc level shifted by subtracting the same quantity 2P-1, from the coefficient
3. JPEG group added the LeGall 5/3 biorthogonal CQF filters
Entropy coder– the arithmetic coder is the coder of choice
Georgia Institute of Technology Center for Signal and Image Processing
Subband Transform Method
Georgia Institute of Technology Center for Signal and Image Processing
Figure 2.6 Transform block diagram in the JPEG2000 compression coder.
Performance
Georgia Institute of Technology Center for Signal and Image Processing
References
AFD10, Pavement Management Systems. "Delivery of Pavement Distress Data from Automated Systems." Transportation Research Board, 2007.
2. Huffman, D. A. A Method for the Construction of Minimum-Redundancy Codes. Proceedings of the IRE 'Vol.' 40, No. 9 1952, pp. 1098-101.
3. Jones, C. An Efficient Coding System for Long Source Sequences. Information Theory, IEEE Transactions on 'Vol.' 27, No. 3 1981, pp. 280-91.
4. Pennebaker, William B., and Joan L. Mitchell. Jpeg Still Image Data Compression Standard. New York: Van Nostrad Reinhold, 1993.
5. Woods, J., and S. O'Neil. Subband Coding of Images. Acoustics, Speech and Signal Processing, IEEE Transactions on 'Vol.' 34, No. 5 1986, pp. 1278-88.
6. Schafer, R. W., and L. R. Rabiner. A Digital Signal Processing Approach to Interpolation. Proceedings of the IEEE 'Vol.' 61, No. 6 1973, pp. 692-702.
7. Smith, M., and T. Barnwell. A Procedure for Designing Exact Reconstruction Filter Banks for Tree-Structured Subband Coders. Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '84., 1984.
8. Shapiro, J. M. Embedded Image Coding Using Zerotrees of Wavelet Coefficients. Signal Processing, IEEE Transactions on 'Vol.' 41, No. 12 1993, pp. 3445-62.
9. Said, A., and W. A. Pearlman. A New, Fast, and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees. Circuits and Systems for Video Technology, IEEE Transactions on 'Vol.' 6, No. 3 1996, pp. 243-50.
10. Smith, M. J. T., and S. L. Eddins. Analysis/Synthesis Techniques for Subband Image Coding. Acoustics, Speech and Signal Processing, IEEE Transactions on 'Vol.' 38, No. 8 1990, pp. 1446-56.
11. Daubechies, Ingrid. Orthonormal Bases of Compactly Supported Wavelets Ii: Variations on a Theme. SIAM J. Math. Anal. 'Vol.' 24, No. 2 1993, pp. 499-519.
12. Skodras, A., C. Christopoulos, and T. Ebrahimi. The Jpeg 2000 Still Image Compression Standard. Signal Processing Magazine, IEEE 'Vol.' 18, No. 5 2001, pp. 36-58.
13. Kaul, V., J. Tsai, and R. Mersereau. A Quantitative Performance Evaluation of Pavement Distress Segmentation Methods. ASCE Journal of Transportation Engineering (submitted) 2008.
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