IMAGES

FINAL REPORT
DCT Transform
Haar Wavelet Transform
quantization methods
results
conclusions

REFERENCES/LINKS

DISCRETE COSINE TRANSFORM

Out of the image compression techniques available, transform coding is the preferred method.   Since energy distribution varies with each image, compression in the spatial domain is not an easy task. Images do however tend to compact their energy in the frequency domain making compression in the frequency domain much more effective.  Transform coding is simply the compression of the images in the frequency domain.   Transform coefficients are used to maximize compression.  For lossless compression, the coefficients must not allow for the loss of any information.

The Discrete Cosine Transform (DCT) is an example of transform coding.  The current JPEG standard uses the DCT as its basis.  The DC relocates the highest energies to the upper left corner of the image.   The lesser energy or information is relocated into other areas.

The DCT is fast.  It can be quickly calculated and is best for images with smooth edges like photos with human subjects.   The DCT coefficients are all real numbers unlike the Fourier Transform.  The Inverse Discrete Cosine Transform (IDCT) can be used to retrieve the image from its transform representation. 

DCT:

IDCT:

HISTORY OF JPEG

The DCT is the transform used in JPEG compression.   "Joint Photographic Experts Group" is the original name of the committee that created the JPEG format. The standard was a joint effort by three of the world's largest standards organizations: The International Organization for Standardization (ISO), the International Telegraph and Telephone Consultative Committee (CCITT), and the International Electrotechnical Commission (IEC). The JPEG project began back in 1982.   The goal was to create a data compression standard that would display an image within one second down a 64 Kbits/sec ISDN line.   Eventually, the format would be able to send loss-less images.  The standard was intended for natural, real world scenes. It was designed to compress natural pictures that are smooth and curved and have no jagged edges.

The project began under ISO as Working Group 8 but later merged with CCITT. The Joint Photographic Experts Group, actually a subcommittee of ISO, was then formed in 1986 in order to avoid competing standards among the three standards organizations.  After testing of numerous schemes, the Adaptive Discrete Cosine Transform (DCT) was chosen to be the core of the JPEG format.  Three years later, the merged ISO/IEC committee gave their approval to make the JPEG the standard.  It was drafted as the ISO Committee Draft 10918 or Digital Compression and Coding of Continuous-Tone Still Images. It was officially standardized as the International Standard ISO 10918-1.

JPEG has been in existence for nearly a decade.  Revisions updating JPEG to make use of  our current text-based technologies are in progress. This project has been in progress since August 1998. The project team isdeveloping a JPEG format that provides more compression options and better images which take up the same amount of space. It is said that the core of
JPEG 2000 is Wavelet technology. The release date has been set for January
2000, but implementation will probably take some time.

   

Contact the authors:
nofences@rice.edu
heidit@caam.rice.edu
hard@rice.edu
bwang@rice.edu