I. Introduction

Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. Wavelets are the result of collective efforts that recognized common threads between ideas and concepts that had been independently developed and investigated by distinct research communities. They provide a unifying framework for decomposing images, volumes, and time series data into their elementary constituents across scale. Although a relatively recent construct, wavelets have become a tool of choice for engineers, physicists and mathematicians, leading to efficient solutions in time and space frequency analysis problems, as well as a multitude of other applications. One of the consequences is that wavelet methods of analysis and representation are presently having a significant impact on the science of signal/image processing. The application of wavelet theory concepts to the area of signal/image processing has made significant advances in the usage of these imaging modalities to different applications.

There are already historical anecdotes and folklore associated with them; an entertaining account of which can be found in the book of Barbara Burke Hubbard [1,4]. Readers who want to dive deeper into the subject have the daunting task of choosing among over 200 books written on wavelets.

This special issue is devoted to the recent developments in the applications of wavelet theory techniques to image processing. We received 18 papers, of which 8 were accepted for publication. The topics covered in this issue cover a wide range of research areas in the wavelets and their applications including image compression, Synthetic aperture radar Interferogram analysis, Bolt in Railway Maintenance, classification, content image retrieval, and authentication problem

II. Scanning through the issue

The first paper by G. A. Papakostas, D. A. Karras, B. G. Mertzios and Y. S. Boutalis introduces a new method for extracting feature sets with improved reconstruction and classification performance in computer vision applications. The main idea of this paper is to propose a procedure for obtaining surrogates of the compressed versions of very reliable feature sets without affecting significantly their reconstruction and recognition properties. The surrogate feature vector is of lower dimensionality and thus more appropriate for pattern recognition tasks. The proposed feature extraction method combines the advantages of the multiresolution analysis of the wavelet theory, with the high discriminative nature of Zernike moment sets. The resulted feature vector is used as a classification feature, in order to achieve high recognition rates in a typical pattern recognition system. The results of the experimental study support the validity and the strength of the proposed method.

The recently developed JPEG 2000 standard, which incorporates wavelet at the core of its compression technique, provides many excellent features compared to other presently available image compression standards. But in the case of mobile networks, decoding a large JPEG 2000 image at a time at the end port will result in bigger memory and circuit requirements and consequently higher price for the end port. Algorithms have been proposed in the past to divide an image to smaller units like tiles or streams in an intermediate gateway computer, and then send them sequentially to the end port. In this way the end port can do the decoding one unit at a time requiring less resource. But the image division process itself that runs in the gateway is calculation and memory intensive. So the need to process a large number of images in such a mobile network can lay a severe burden on the gateway. The paper by Sadeque Mohammad Hanif and Kôki Abe discuss two different approaches for reducing the resource requirements in dividing a 2D DWT image data into smaller tiles. An extensive evaluation of resource efficiency and derived image quality with the two approaches has been done in this paper.

Rail inspection is an area were methods of wavelet processing hold great promise. Rail inspection is a very important task in railway maintenance for traffic safety issues and in preventing dangerous situations. Monitoring railway infrastructure is an important aspect in which the periodical inspection of rail rolling plane is required. Up to the present days the inspection of the railroad is operated manually by trained personnel. A human operator walks along the rail track searching for rail anomalies. This monitoring way is not more acceptable for its slowness and subjectivity. The paper by P.L. Mazzeo, E. Stella, M. Nitti, A. Distante present a vision based technique to detect automatically the presence or absence of the fastening elements that fix the rail to the sleepers.The images are acquired by a digital line scan camera installed under a train. Subsequently these images are pre-processed by using wavelet transform with Haar and Daubechies approximation coefficients. The obtained coefficients are fed as input to two different neural networks: the first one identifies the bolts candidates and the second one validates the bolt recognition process. The final detecting system has been applied to a long sequence of real images showing a high reliability robustness and good performances

Although interferometric synthetic aperture radar applications are well established, the improvement of the interferometry technique and the quality of its products are desirable to further enhance its capabilities. Since the late 80s, many applications of radar interferometry have been developed, including the observation of ground motion over agricultural areas, creating high-accuracy digital terrain models, and deformation monitoring of the earth’s crust with millimeter accuracy at very dense spatial sampling. In addition, interferometric synthetic aperture radar has proven to be a viable method for measuring surface deformation associated with subsidence due to underground mining activities. The paper by A. K. Helmy, H.M. Onsi , H. El-Deib, M.G. Darwish deals with the interferometric synthetic aperture radar deformation problem. They use dual tree complex wavelet transform for interferogram filtering. The main concern of the this paper is to lower the residues count mean while preserving the location and jump height of the lines of phase discontinuity. The results are compared to both of Daubechies’ real orthogonal max flat filter, and pivot median filter.

Wavelet networks (WNs) were introduced by Zhang and Benveniste in 1992 as a combination of artificial neural networks and wavelet decomposition. Since then, however, WNs have received only little attention. We believe, that the potential of WNs is generally underestimated. WNs have the advantage, that the wavelet coefficients are directly related to the image information through the wavelet transform. In addition, the parameters of the wavelets in the WNs are subject to optimization, which results in a direct relation between the represented function and the optimized wavelets, lead to a considerable data reduction (thus making subsequent algorithms much more efficient) as well as in wavelets that can be used as an optimized filter bank. The paper by O. Jemai, C. Ben Amar deals with the compression problem in the wavelet networks framework.

Two other areas where wavelets have achieved great success is content-based image retrieval and recoverable image content authentication. The paper by Ibrahim El-Henawy, Mohamed Eisa, A. E. Elalfi , Hans Burkhardt deal with the problem of content based image retrieval in the wavelet framework. It presents an image retrieval method based on nonlinear monomial kernel function and Gabor filters. Colour features are found by calculating the 3D colour histogram after applying the monomial kernel function on the image. Texture features are found by calculating the mean and standard deviation of the Gabor filtered image. Experimental results are shown and discussed. The paper by Yuan-Liang Tang and Chih-Jung Hung deal with the recoverable image content authentication problem. The algorithm starts with dividing the image into blocks, followed by computation of their intensity means. By carefully establishing the relations among image blocks, this method is able to identify malicious changes made on the image, while very insensitive to common image processing. In addition, the introduced system is able to recover the tampered blocks using different recovery strategies according to the characteristics of the image blocks. The experimental results clearly demonstrate that the proposed algorithm is very effective both for tamper proofing and image recovery applications.

The paper by M. Leo, T. D’Orazio, P. Spagnolo, and A. Distante deals with ball detection in Soccer Images. It is one of the applications of the most general problem of object recognition, where the approach mainly used is based on classifying the pattern images after a suitable pre-processing. The paper compared two different pre-processing techniques: the initial vectorial representation of the image has been projected both on the Haar basis and on the basis extracted from the Independent Component Analysis (ICA). The coefficients of the new representation in the ICA and Wavelet subspaces are supplied as input to a neural classifier. ICA and Wavelet representations have been chosen since they are well suited to increase the inter class differences and decrease the intra class ones. The experimental results on real soccer images show that the classification performances applying the ICA and Wavelet pre-processing techniques are quite the same and that combining ICA and Wavelet the percentage of pattern recognition can be further increased.

Acknowledgments.

The board editors would like to take this opportunity to thank all those authors who submitted papers, and all of the reviewers who took such care in reviewing these papers. As editors, we hope that the papers in this issue will stimulate further progress in this direction. We believe that the best is yet to come.

1. B. Burke Hubbard, The world according to wavelets. Wellesley, MA: A K Peters, 1998.
2. L. Debnath, Wavelet Transform and Their Applications, Springer-Verlag, Hardcover, Published November 2000.

III. BibTex of Contents (Table of Contents)