Wavelet-based fingerprint image retrieval

This paper presents a novel approach for personal identification based on a wavelet-based fingerprint retrieval system which encompasses three image retrieval tasks, namely, feature extraction, similarity measurement, and feature indexing.     

Wavelet-based filters for accurate computation of derivatives

Let be a smooth function whose derivative of a given order must be computed. The signal is affected by two kinds of perturbation. The perturbation caused by the presence of the machine epsilon of the computer may be considered to be an extremely high-frequency noise of very small amplitude. The way to minimize its effect consists of choosing an appropriate value for the step size of the difference quotient.

The second perturbation, caused by the presence of noise, requires first the signal to be treated in some way. It is the purpose of this work to construct a wavelet-based band-pass filter that deals with the two cited perturbations simultaneously. In effect our wavelet acts like a ``smoothed difference quotient" whose stepsize is of the same order as that of the usual difference quotient. Moreover the wavelet effectively removes the noise and computes the derivative with an accuracy equal to the one obtained by the corresponding difference quotient in the absence of noise.

     

A review of Bandlet methods for geometrical image representation

This article reviews bandlet approaches to geometric image representations. Orthogonal bandlets using an adaptive segmentation and a local geometric flow well suited to capture the anisotropic regularity of edge structures. They are constructed with a “bandletization” which is a local orthogonal transformation applied to wavelet coefficients. The approximation in these bandlet bases exhibits an asymptotically optimal decay for images that are regular outside a set of regular edges. These bandlets can be used to perform image compression and noise removal. More flexible orthogonal bandlets with less vanishing moments are constructed with orthogonal grouplets that group wavelet coefficients alon a multiscale association field. Applying a translation invariant grouplet transform over a translation invariant wavelet frame leads to state of the art results for image denoising and super-resolution.     

Sparse directional image representations using the discrete shearlet transform

In spite of their remarkable success in signal processing applications, it is now widely acknowledged that traditional wavelets are not very effective in dealing multidimensional signals containing distributed discontinuities such as edges. To overcome this limitation, one has to use basis elements with much higher directional sensitivity and of various shapes, to be able to capture the intrinsic geometrical features of multidimensional phenomena. This paper introduces a new discrete multiscale directional representation called the discrete shearlet transform. This approach, which is based on the shearlet transform, combines the power of multiscale methods with a unique ability to capture the geometry of multidimensional data and is optimally efficient in representing images containing edges. We describe two different methods of implementing the shearlet transform. The numerical experiments presented in this paper demonstrate that the discrete shearlet transform is very competitive in denoising applications both in terms of performance and computational efficiency.     

Wavelet-based limiting performance analysis of mechanical systems subject to transient disturbances

Wavelets are used as the basis functions for control forces in the limiting performance analysis of a mechanical system subject to transient loading. The limiting performance problem, an open-loop control problem, can then be treated as a mathematical programming problem. A numerical example is presented to illustrate the effectiveness of using wavelets. Conventional approximate representations of the control function are interpreted in terms of the scaling function and multiresolution.     

Wavelet-based two-level methods for image restoration

Wavelet-based multilevel approach is a promising method for image restoration problems. In this paper, a method for image restoration based on combining the symmlets family with two-level technique is proposed. A key feature is that the symmlets have many flexible attributes that lead to better stability and less artifacts. Computational experiments show that symmlets-based two-level method yields smaller relative errors and more stable results.     

Fuzziness index driven fuzzy relaxation algorithm and applications to image processing

An improved fuzzy relaxation algorithm for image contrast enhancement is introduced, the relationship between the convergence regions and the parameters in the transformations defined by the algorithm is shown, which is essential to the successful application of this algorithm. Furthermore, in order to measure the quality of an enhanced image, an index of fuzziness is used in this paper to evaluate the performance of the fuzzy relaxation scheme. This extended index of fuzziness is used as a criterion for automatically stopping the fuzzy relaxation process. The analytical result is tested by experiments of image contrast enhancement.     

Adaptive order polynomial algorithm in a multiwavelet representation scheme

We have developed a new strategy to reduce the storage requirements of a multivariate function in a multiwavelet framework. We propose that alongside the commonly used adaptivity in the grid refinement one can also vary the order of the representation k as a function of the scale n. In particular the order is decreased with increasing refinement scale. The consequences of this choice, in particular with respect to the nesting of scaling spaces, are discussed and the error of the approximation introduced is analyzed. The application of this method to some examples of mono- and multivariate functions shows that our algorithm is able to yield a storage reduction up to almost 60%. In general, values between 30 and 40% can be expected for multivariate functions. Monovariate functions are less affected but are also much less critical in view of the so called “curse of dimensionality”.     

Multiple-cue saliency measurement and optimized image composition for image retargeting

We present a novel image retargeting approach for high-definition displaying based on multiple-cue salient region extraction and optimized image composition, which allows resizing an image into user-specified aspect ratios while preserving prominent visual salient image information. Firstly, we sum up six properties for measuring the salient objects and apply them to region extraction. Then, according to our optimized rules of image composition, we evaluate the aesthetic scores with different extracted sub-images. Finally, we sort out the target image with the highest aesthetic score and retarget it to fit the final scale of displaying. The experimental results show the performance and effectiveness of our approach.     

A Nash-game approach to joint image restoration and segmentation

We propose a game-theoretic approach to simultaneously restore and segment noisy images. We define two players: one is restoration, with the image intensity as strategy, and the other is segmentation with contours as strategy. Cost functions are the classical relevant ones for restoration and segmentation, respectively. The two players play a static game with complete information, and we consider as solution to the game the so-called Nash equilibrium. For the computation of this equilibrium we present an iterative method with relaxation. The results of numerical experiments performed on some real images show the relevance and efficiency of the proposed algorithm.     

Wavelet-based cepstrum calculation

In this paper we present a new wavelet-based algorithm for low-cost computation of the cepstrum. It can be used for real time precise pitch determination in automatic speech and speaker recognition systems. Many wavelet families are examined to determine the one that works best. The results confirm the efficacy and accuracy of the proposed technique for pitch extraction.     

Stochasticity in the image greenhouse model

The potential impacts of climate change are a major issue in the Greenhouse debate. Various models and particularly IMAGE (Integrated Model to Assess the Greenhouse Effect), are being used by the IPCC to investigate climate change. The IMAGE model has been reduced to a system of differential equations and incorporates various initial conditions and model parameters. These initial conditions and parameter values are not known precisely and are subject to variability of various forms. This paper briefly describes the mathematical form of IMAGE and then investigates the stochastic properties of the model. Particular attention is paid to the propagation and amplification of assumed distributions for the initial conditions and certain key physical parameters. The IMAGE model appears to be quite robust with respect to these stochastic characteristics.     

New advances in digital image processing

Enhancement of noisy image data is a very challenging issue in many research and application areas. In the last few years, non-linear filters, feature extraction, high dynamic range imaging methods based on soft computing models have been shown to be very effective in removing noise without destroying the useful information contained in the image data. In this paper new image processing techniques are introduced in the above mentioned fields, thus contributing to the variety of advantageous possibilities to be applied. The main intentions of the presented algorithms are (1) to improve the quality of the image from the point of view of the aim of the processing, (2) to support the performance, and parallel with it (3) to decrease the complexity of further processing using the results of the image processing phase.     

A novel variational model for image segmentation

In this paper, we propose a new variational model for image segmentation. Our model is inspired by the complex Ginzburg-Landau model and the semi-norm defined by us. This new model can detect both the convex and concave parts of images. Moreover, it can also detect non-closed edges as well as quadruple junctions. Compared with other methods, the initialization is completely automatic and the segmented images obtained by using our new model could keep fine structures and edges of the original images very effectively. Finally, numerical results show the effectiveness of our model.     

Wavelet-based dynamic time warping

Dynamic Time Warping (DTW), a pattern matching technique traditionally used for restricted vocabulary speech recognition, is based on a temporal alignment of the input signal with the template models. The principal drawback of DTW is its high computational cost as the lengths of the signals increase. This paper shows extended results over our previously published conference paper, which introduces an optimized version of the DTW that is based on the Discrete Wavelet Transform (DWT).     

A new wavelet multigrid method

The standard multigrid procedure performs poorly or may break down when used to solve certain problems, such as elliptic problems with discontinuous or highly oscillatory coefficients. The method discussed in this paper solves this problem by using a wavelet transform and Schur complements to obtain the necessary coarse grid, interpolation, and restriction operators. A factorized sparse approximate inverse is used to improve the efficiency of the resulting method. Numerical examples are presented to demonstrate the versatility of the method.     

Inverse diagnostic problems associated with image processing

Translated from Chislennye Metody Resheniya Obratnykh Zadach Matematicheskoi Fiziki, pp. 9–20.     

An optimal control problem in image processing

As a starting point, we present a control problem in mammographic image processing which leads to non-standard penalty terms and involves a degenerate parabolic PDE which has to be controlled in the coefficients. We then discuss the classical conditional gradient method from constrained optimization and propose a generalization for non-convex functionals which covers the conditional gradient method as well as the recently proposed iterative shrinkage method of Daubechies, Defrise and De Mol for the solution of linear inverse problems with sparsity promoting penalty terms. We prove that this new algorithm converges. This also gives a deeper understanding of the iterative shrinkage method. Further, we show an application to the above-mentioned control problem in image processing. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

小波分析与模糊系统分析的联系

讨论小波基函数与模糊集隶属函数之间的联系 ,证明模糊系统研究与应用中的隶属函数都可以由称之为简单小波的母函数表出 ,反之每一简单小波也可以由某一隶属函数表出 ,从而验证简单小波类与某一隶属函数类的一一对应关系。该结果进一步揭示模糊推理和模糊控制的实质 ,为在模糊系统辨识、模糊控制和模糊数据分析等诸多领域充分利用近代小波分析的成果提供新思路