Experiments and Results

This section will describe three pieces of code, along with their results, that we have implemented in order to experiment with wavelet-based texture retrieval. The third application is, more precisely, derived from the problem of texture characterization and similarity since it will tackle the challenging issues of texture synthesis and compression:

• In a first attempt to perform fast texture retrieval, we have implemented a simple method based on the mean and standard deviation of wavelet coefficients. As already exposed, the idea is to consider the first raw moment and the square root of the second raw moment of responses to filter banks as meaningful in term of textures specificities. Euclidean distance between these two quantities at different scales and for each subband can then be taken as a good estimate of texture similarity.
• The second algorithm follows the approach proposed by [1] and relies on generalized Gaussian density model. The main point, in that case, is that the distribution of wavelet coefficients at each scale and each subband is well fitted by a GGD. Computation of the Kullback-Leibler distance(KLD) between the parameters $(\alpha, \beta)$ of each GGD has been proved to provide a better similarity estimate. We will give results verifying this statement.
• Finally, we decided to further investigate the ability of GGDs to model wavelet coefficients and to use this property to achieve good compression rate on texture images. The idea will be to code almost a whole subband by only two floating point numbers $(\alpha, \beta)$.

We have tested our algorithms on textures extracted from the MIT Vision Texture (VisTex) database available at http://vismod.www.media.mit.edu. It contains 512x512 color images from natural scenes. We have written a small csh script that takes a bunch of these original images, convert them into gray-scale data and build a text file indicating the number of images in the database and their names. However, as opposed to Do and Vetterli in [1], we keep images at their original size. This reduces redundancy in the database and will further stress the algorithm.
We have also experimented with transformation of the gray levels dynamics. In order to reduce the bias of the retrieval process, we have normalized textures images to zero mean and unit variance. This will be shown later to produce better results. We have to notice here that it is pretty easy to reach high retrieval rates if the database is chosen in a proper way. We have included different types of images in our database ranging from metal to mountains. This will also naturally emphasize the limits of the algorithm.