This code implements a wavelet transform-based image coder for grayscale images. The coder is not the most sophisticated--it's a simple transform coder--but each individual piece of the transform coder has been chosen for high performance. The coder is quite effective, despite its lack of more sophisticated features such as zerotrees. It yields performance comparable to Shapiro's EZW coder (J. M. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients", IEEE Trans. on Signal Processing, v. 41, no. 12, pp. 3445-3463, Dec. 1993). It is designed to be a foundation upon which more more sophisticated coders can be built--there's no need to reinvent the wheel if you're working on only one aspect of the coding process.
| Target ratio | Actual ratio | RMS error | PSNR (dB) | PSNR for EZW |
|---|---|---|---|---|
| 4:1 | 4.02:1 | 1.66 | 43.71 | |
| 8:1 | 8.00:1 | 2.73 | 39.42 | 39.55 |
| 16:1 | 16.01:1 | 3.96 | 36.18 | 36.28 |
| 32:1 | 32.01:1 | 5.60 | 33.17 | 33.17 |
| 64:1 | 64.08:1 | 7.86 | 30.22 | 30.23 |
| 128:1 | 129.26:1 | 10.48 | 27.72 | 27.54 |
(Numbers for more state of the art wavelet coders can be found here, courtesy of the Image Communications Lab at UCLA)
Source code: (Version 0.3, last modified 1/29/97): wavelet.0.3.tar.gz
Version 0.3 fixes a bug in the allocator so that actual rates are much closer to target rates. Also, it uses binary files for I/O which should fix some problems that people using Windows 95 were having. Coefficients default to floats rather than reals, which should save a lot of memory. Also a bug and a few memory leaks in the WaveletTransform constructors have been fixed. Some people have complained about my Makefile because it only works with gmake. If you write a better one, please send it to me! This package is also available via anonymous ftp from ftp.cs.dartmouth.edu in the directory /pub/gdavis.
NOTE: This is an alpha version of the code! It is documented, but not completely. Eventually I hope to add a tutorial to the distribution. There are one or two known (minor) bugs. Upgrades will be supplied on the web at irregular intervals. Caveat surfer.
Standard test images: A number of "standard" test images have been included in the source distribution. Note that several versions of these images exist. The included Lena image is from the RPI site, ftp://ipl.rpi.edu/pub/image/still/usc. The Barbara image comes from Alan Gersho's lab at U.C. Santa Barbara. The Goldhill image is from R. Joshi at Washington State U. These images can be found together at John Villasenor's Image Communications Lab site. Additional commonly used images can be obtained from the U. Waterloo BragZone). Note, however, that the versions of the Lena and Barbara images at the U. Waterloo site are not the same as the ones used in many of the papers cited here.
The code has been designed for experimentation. It's very modular and should allow for simple replacements of individual components. One can easily replace the quantizer, the entropy coder, and the wavelet filters.
If you do modify/upgrade/replace sections of this code, I would very much appreciate hearing about it. I hope to make this construction kit a collaborative effort with a whole range of modules supplied by different researchers. A wish list of future improvements is included at the end of this file. I will provide WWW links to any extensions people provide.
A transform coder consists of 3 basic steps.
The entropy coding, quantization routines, and bit allocation are very general-purpose. They will work with a whole variety of transforms, including DCT's, wavelet packets, local trig bases, etc. Moreover, they have been designed with the expectation that other features such as zerotrees or perceptual weighting will be added later. Implementing more sophisticated coders such as those described in Z. Xiong, K. Ramchandran and M. T. Orchard, ``Wavelet Packets Image Coding Using Space-frequency Quantization", Preprint, 1996 and Z. Xiong, K. Ramchandran and M. T. Orchard, "Space-frequency Quantization for Wavelet Image Coding", to appear in IEEE Trans. Image Processing, 1997 (see Z. Xiong's articles on line) should be relatively easy to do given this code. The current transform routine should be fairly straightforward to extend to perfom wavelet packet decompositions.
The wavelet transform implements symmetrized boundaries and works for images of (more or less) arbitrary sizes, as long as the aspect ratio is less than 2:1 (the aspect ratio limitation should be straightforward to eliminate, but I haven't gotten around to it). For the full details on how to perform such a transform, see Chris Brislawn, "Classification of nonexpansive symmetric extension transforms for multirate filter banks," Los Alamos Tech Report LA-UR-94-1747. Also the Los Alamos ftp site for some tutorial code.
The filters included with the wavelet transform include some of the best known for image coding. It includes the set from J. Villasenor, B. Belzer, J. Liao, "Wavelet Filter Evaluation for Image Compression," IEEE Transactions on Image Processing, Vol. 2, pp. 1053-1060, August 1995. There are a few extra filters from Brislawn's code, a few Daubechies filters, and a new (unpublished) 18/10 filter that Villasenor's group has found effective. I've also just added a 7/9 pair from J. E. Odegard and C. S. Burrus, "Smooth biorthogonal wavelets for applications in image compression," in Proceedings of DSP Workshop, Loen, Norway, September 1996. This pair yields superior results to the standard Antonini pair for EZW on Barbara.
Two sets of quantizers are included. The first set performs a uniform quantization and is fairly straightforward. The second is an embedded family of quantizers fully described in D. Taubman and A. Zakhor, "Multirate 3-D subband coding of video", IEEE Transactions on Image Processing, Vol 3, No. 5, Sept, 1994. The quantizers are equivalent to those used in J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Transactions on Signal Processing, Vol. 41, No. 12, pp. 3445-3462, Dec. 1993, but are coupled with a more effective entropy coding scheme.
Two sets of adaptive entropy coding schemes are also included. The first performs histogram adaptation with escape codes (see Text Compression, by Bell, Cleary and Witten). The escape codes keeps rare symbols from adding too much to the overall symbol cost during early stages of histogram adaptation. The second coder is an embedded coder designed for use with the embedded quantizer above (See Taubman and Zakhor for full details). It adapts very quickly and is very effective.
The arithmetic coder is based on an implementation of Alistair Moffat's linear time coding histogram (see Moffat's online papers) ). The implementation is courtesy of John Danskin, and the full distribution (most of which is included here) may be obtained here.
The bit allocation routines are based on integer programming algorithms described in Y. Shoham and A. Gersho, "Efficient bit allocation for an arbitrary set of quantizers," IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 36, No. 9, pp. 1445-1453, Sept 1988. They provide optimal or near-optimal allocations for the quantizers included here.
If you want your code added to the distribution, please make sure it's well documented and debugged! I can either include your code or add a link to it on this page.
Wed Jan 29 1997.