Transform Methods and Image Compression

An introduction to JPEG and wavelet transform techniques using Octave and Matlab.
Conclusion

The discussion of JPEG and wavelets has centered on gray-scale images. Color images may assign a red, green and blue triple (rgb) to each pixel, although other choices are possible. Color specified in terms of brightness, hue and saturation, known as luminance-chrominance representations, may be desirable from a compression viewpoint, since the human visual system is more sensitive to errors in the luminance component than in chrominance (see Resources 7). Given a color representation, JPEG and wavelet schemes can be applied to each of the three planes.

This article was adapted from a recent book (see Resources 3). More information, such as details of the smoothing procedure, along with the scripts and complete documentation may be obtained from our web site (see Resources 4).

Information on Matlab (for GNU/Linux and other platforms) is available through http://www.mathworks.com/. Octave is developed by John W. Eaton with contributions from many folks, and is distributed under the GNU General Public License. Complete sources and ready-to-run executables for several platforms are available via anonymous ftp from ftp.che.wisc.edu in the /octave directory. An introduction to Octave appeared in a previous Linux Journal article (see Resources 6) and on-line information can be found via http://www.che.wisc.edu/octave/.

Resources

Greg A. Harris joined the faculty at Auburn University after completing a degree in mathematics at the University of Nebraska-Lincoln. Along with Darrel Hankerson and Peter D. Johnson, Jr., he is the author of Introduction to Information Theory and Data Compression, CRC Press, 1997. The photograph was taken in Zion National Park during winter 1997.

Darrel Hankerson joined the faculty at Auburn University after completing a degree in mathematics at the University of Utah. Along with Greg A. Harris and Peter D. Johnson, Jr., he is the author of Introduction to Information Theory and Data Compression, CRC Press, 1997.

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