The Wavelet Digest Homepage
Return to the homepage
Search the complete Wavelet Digest database
Help about the Wavelet Digest mailing list
About the Wavelet Digest
The Digest The Community
 Latest Issue  Back Issues  Events  Gallery
The Wavelet Digest
   -> Volume 7, Issue 6

Software: Applet demonstrates the wavelet transform of an image
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
Lode Nachtergaele (

PostPosted: Tue Jun 30, 1998 2:54 pm    
Subject: Software: Applet demonstrates the wavelet transform of an image
Reply with quote

#12 Software: Applet demonstrates the wavelet transform of an image

Dear wavelet researcher,

on the web page
an applet is provided that demonstrates a wavelet transform in action
on an image.

The applet implements a forward and backward wavelet transform defined
in the MPEG4 standard Version 1 (ISO/IEC JTC/SC29/WG11 N1902,
Fribourg, Oct. 1997, Paragraph 10 Annex A Coding transforms).

The wavelet transform is implemented by means of the lifting scheme
(See papers of Wim Sweldens [DS96] for an explanation about this
scheme.) The implemented synthesis filters corresponds to a Cohen -
Daubechies - Feauveau biorthogonal 3/9 taps filter with the following
coefficients :

Lowpass = {32,64,32}*2^(-13/2)
Highpass = {3,6,-16,-38,90,-38,-16,6,3}*2^(-13/2)

There are 2 vanishing moments in the primal wavelet and 4 in the dual
wavelet [UW97]. The primal wavelet with 2 vanishing moments is :
t_1(z) = -1/2 * z^-1 - 1/2
The dual wavelet with 4 vanishing moments is :
s_1(z) = -3/64 * z^-1 - 19/64 + 19/64 * z - 3/64 * z^2

Remark that the denominators are powers of two. This is of interest when
considering implementation efficiency.

The JAVA implementation uses integers and hence is lossless. This
means that the two pictures on the left are exactly the same when the
applet is finished! Moreover, unlike in many other implementations,
the image width and height must not be a power of two.

This applet concentrates on the wavelet transform. No compression is
being done.



[DS96] I. Daubechies, W. Sweldens, "Factoring Wavelet Transform into
Lifting Steps," AT&T internal report BL0112170-960927-20TM, September
1996. Online at
[UW97] Geert Uytterhoeven, Filip Van Wulpen, Maarten Jansen, Dirk Roose
and Adhemar Bultheel, "WAILI: Wavelets with Integer Lifting", Report
TW262, July 1997. Online at

Lode Nachtergaele
Kapeldreef 75 Phone: +32 (0)16 28.15.12 Fax: +32 (0)16 28.15.15
B-3001 Leuven Belgium
All times are GMT + 1 Hour
Page 1 of 1

Jump to: 

disclaimer -
Powered by phpBB

This page was created in 0.026787 seconds : 18 queries executed : GZIP compression disabled