Modeling of wavelet coefficient statistics using copulas (with application to image retrieval)

• GNU Scientific Library (GSL, version 1.14 and higher), download from http://www.gnu.org/software/gsl/
• Eigen3, download from http://eigen.tuxfamily.org

Lets assume that you installed GSL under '/Software/gsl', the Eigen include files are located at '/usr/include/eigen3' and you checked out the code at '/tmp/coptex'.

Note: The model estimation part of the code is written in MATLAB, the similarity measurement part is in C/C++ (under the directory 'sm').

Unfortunately, the code is not CMake'ified yet, so you have to change the 'Makefile'. You should only need to modify the line

COPT = -g -O3 -Wall -fomit-frame-pointer -ffast-math -msse3 -mfpmath=sse -I. -I/Users/rkwitt/Software/gsl/include -L/Users/rkwitt/Software/gsl/lib -I/opt/local/include/eigen3

by changing the elements

-I/Users/rkwitt/Software/gsl/include
-I/Software/gsl/include
-I/opt/local/include/eigen3

to

-I/Software/gsl/include
-L/Software/gsl/lib
-I/usr/include/eigen3

Then run 'make'.

To test the code, start MATLAB, and 'cd' into the base directory of coptex, i.e.,

cd '/tmp/coptex'

Next, edit the 'example.m' file and change

basedir = '/Users/rkwitt/Remote/coptex-read-only';
dumpdir = '/tmp/x';

to

basedir = '/tmp/coptex';
dumpdir = '/tmp/testdata';

where '/tmp/testdata' will be created when running

example

This will run a DT-CWT (Dual-Tree Complex Wavelet Transform) decomposition (using Nick Kingsbury's MATLAB code) on all test images and model the wavelet coefficient distributions on the third decomposition level by a Gaussian copula with Weibull margins. All estimated parameters will be stored under '/tmp/testdata' and a file list will be created that holds the basenames of all estimated models.

Finally, you can compute a similarity matrix for all testimages, using the estimated models, by running the 'copll' binary, i.e.,

cd /tmp/testdata
/tmp/coptex/sm/copll -B /tmp/testdata -D 18 -N 256 -l /tmp/testdata/filelist.txt -d /tmp/D.bin

'-D 18' means that we have 18 subbands on one level of a DT-CWT and '-N 256' says that there are 256 coefficients (16x16) on that level. For further details, see

/tmp/coptex/sm/copll --help

Please cite

@article{Kwitt11e,
  author = {R. Kwitt and P. Meerwald and A. Uhl},
  title = {Efficient Texture Image Retrieval Using Copulas in a Bayesian Framework},
  journal = {IEEE Transactions on Image Processing},
  year = {2011},
  volume = {20},
  number = {7},
  pages = {2063-2077}
}

if you use this code for your research.