Showing papers on "Multiresolution analysis published in 2002"

Multiresolution gray-scale and rotation invariant texture classification with local binary patterns

Abstract: Presents a theoretically very simple, yet efficient, multiresolution approach to gray-scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions. The method is based on recognizing that certain local binary patterns, termed "uniform," are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature. We derive a generalized gray-scale and rotation invariant operator presentation that allows for detecting the "uniform" patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis. The proposed approach is very robust in terms of gray-scale variations since the operator is, by definition, invariant against any monotonic transformation of the gray scale. Another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table. Experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns.

Context-driven fusion of high spatial and spectral resolution images based on oversampled multiresolution analysis

Abstract: This paper compares two general and formal solutions to the problem of fusion of multispectral images with high-resolution panchromatic observations. The former exploits the undecimated discrete wavelet transform, which is an octave bandpass representation achieved from a conventional discrete wavelet transform by omitting all decimators and upsampling the wavelet filter bank. The latter relies on the generalized Laplacian pyramid, which is another oversampled structure obtained by recursively subtracting from an image an expanded decimated lowpass version. Both the methods selectively perform spatial-frequencies spectrum substitution from an image to another. In both schemes, context dependency is exploited by thresholding the local correlation coefficient between the images to be merged, to avoid injection of spatial details that are not likely to occur in the target image. Unlike other multiscale fusion schemes, both the present decompositions are not critically subsampled, thus avoiding possible impairments in the fused images, due to missing cancellation of aliasing terms. Results are presented and discussed on SPOT data.

Multiresolution Markov models for signal and image processing

Abstract: Reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts-in particular, making ties to topics such as wavelets and multigrid methods. A third goal is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for self-similar and 1/f processes. We also illustrate how these methods have been used in practice.

Directional multiresolution image representations

Abstract: Efficient representation of visual information lies at the foundation of many image processing tasks, including compression, filtering, and feature extraction. Efficiency of a representation refers to the ability to capture significant information of an object of interest in a small description. For practical applications, this representation has to be realized by structured transforms and fast algorithms. Recently, it has become evident that commonly used separable transforms (such as wavelets) are not necessarily best suited for images. Thus, there is a strong motivation to search for more powerful schemes that can capture the intrinsic geometrical structure of pictorial information. This thesis focuses on the development of new "true" two-dimensional representations for images. The emphasis is on the discrete framework that can lead to algorithmic implementations. The first method constructs multiresolution, local and directional image expansions by using non-separable filter banks. This discrete transform is developed in connection with the continuous-space curvelet construction in harmonic analysis. As a result, the proposed transform provides an efficient representation for two-dimensional piecewise smooth signals that resemble images. The link between the developed filter banks and the continuous-space constructions is set up in a newly defined directional multiresolution analysis. The second method constructs a new family of block directional and orthonormal transforms based on the ridgelet idea, and thus offers an efficient representation for images that are smooth away from straight edges. Finally, directional multiresolution image representations are employed together with statistical modeling, leading to powerful texture models and successful image retrieval systems.

A First Course in Wavelets with Fourier Analysis

Abstract: 0. Inner Product Spaces. 1. Fourier Series. 2. The Fourier Transform. 3. Discrete Fourier Analysis. 4. Wavelet Analysis. 5. Multiresolution Analysis. 6. The Daubechies Wavelets. 7. Other Wavelet Topics. Appendix A. Technical Matters. Appendix B. Matlab Routines. Bibliography.

Wavelet Algorithms for High-Resolution Image Reconstruction

Abstract: High-resolution image reconstruction refers to the reconstruction of high-resolution images from multiple low-resolution, shifted, degraded samples of a true image. In this paper, we analyze this problem from the wavelet point of view. By expressing the true image as a function in ${\cal L}({\Bbb R}^2)$, we derive iterative algorithms which recover the function completely in the ${\cal L}$ sense from the given low-resolution functions. These algorithms decompose the function obtained from the previous iteration into different frequency components in the wavelet transform domain and add them into the new iterate to improve the approximation. We apply wavelet (packet) thresholding methods to denoise the function obtained in the previous step before adding it into the new iterate. Our numerical results show that the reconstructed images from our wavelet algorithms are better than that from the Tikhonov least-squares approach. Extension to super-resolution image reconstruction, where some of the low-resolution images are missing, is also considered.

A family of wavelet-based stereo image coders

Abstract: We propose novel algorithms for stereoscopic image coding based on the hierarchical decomposition of stereo information. The proposed schemes, based on the wavelet transform and zerotree quantization, are endowed with excellent progressive transmission capability and retain the option for perfect reconstruction of the original image pair. Experimental evaluation shows that the resulting methods produce superior results when compared with other algorithms for stereo image coding. This is achieved without introducing blocking artifacts and with the valuable additional convenience of the production of embedded bitstreams.

Wavelets, fractals, and radial basis functions

Abstract: Wavelets and radial basis functions (RBFs) lead to two distinct ways of representing signals in terms of shifted basis functions RBFs, unlike wavelets, are nonlocal and do not involve any scaling, which makes them applicable to nonuniform grids Despite these fundamental differences, we show that the two types of representation are closely linked together through fractals First, we identify and characterize the whole class of self-similar radial basis functions that can be localized to yield conventional multiresolution wavelet bases Conversely, we prove that for any compactly supported scaling function /spl phi/(x), there exists a one-sided central basis function /spl rho//sub +/(x) that spans the same multiresolution subspaces The central property is that the multiresolution bases are generated by simple translation of /spl rho//sub +/ without any dilation We also present an explicit time-domain representation of a scaling function as a sum of harmonic splines The leading term in the decomposition corresponds to the fractional splines: a recent, continuous-order generalization of the polynomial splines

Adaptive image denoising using scale and space consistency

Abstract: This paper proposes a new method for image denoising with edge preservation, based on image multiresolution decomposition by a redundant wavelet transform. In our approach, edges are implicitly located and preserved in the wavelet domain, whilst image noise is filtered out. At each resolution level, the image edges are estimated by gradient magnitudes (obtained from the wavelet coefficients), which are modeled probabilistically, and a shrinkage function is assembled based on the model obtained. Joint use of space and scale consistency is applied for better preservation of edges. The shrinkage functions are combined to preserve edges that appear simultaneously at several resolutions, and geometric constraints are applied to preserve edges that are not isolated. The proposed technique produces a filtered version of the original image, where homogeneous regions appear separated by well-defined edges. Possible applications include image presegmentation, and image denoising.

Building nonredundant adaptive wavelets by update lifting

Abstract: textAdaptive wavelet decompositions appear useful in various applications in image and video processing, such as image analysis, compression, feature extraction, denoising and deconvolution, or optic flow estimation. For such tasks it may be important that the multiresolution representations take into account the characteristics of the underlying signal and do leave intact important signal characteristics such as sharp transitions, edges, singularities or other regions of interest. In this paper, we propose a technique for building adaptive wavelets by means of an extension of the lifting scheme. The classical lifting scheme provides a simple yet flexible method for building new, possibly nonlinear, wavelets from existing ones. It comprises a given wavelet transform, followed by a prediction and an update step. The update step in such a scheme computes a modification of the approximation signal, using information in the detail band. It is obvious that such an operation can be inverted, and therefore the perfect reconstruction property is guaranteed. In this paper we propose a lifting scheme including an adaptive update lifting and a fixed prediction lifting step. The adaptivity consists hereof that the system can choose between two different update filters, and that this choice is triggered by the local gradient of the original signal. If the gradient is large (in some seminorm sense) it chooses one filter, if it is small the other. In this paper we derive necessary and sufficient conditions for the invertibility of such an adaptive system for various scenarios.

Adaptive wavelet graph model for Bayesian tomographic reconstruction

Abstract: We introduce an adaptive wavelet graph image model applicable to Bayesian tomographic reconstruction and other problems with nonlocal observations. The proposed model captures coarse-to-fine scale dependencies in the wavelet tree by modeling the conditional distribution of wavelet coefficients given overlapping windows of scaling coefficients containing coarse scale information. This results in a graph dependency structure which is more general than a quadtree, enabling the model to produce smooth estimates even for simple wavelet bases such as the Haar basis. The inter-scale dependencies of the wavelet graph model are specified using a spatially nonhomogeneous Gaussian distribution with parameters at each scale and location. The parameters of this distribution are selected adaptively using nonlinear classification of coarse scale data. The nonlinear adaptation mechanism is based on a set of training images. In conjunction with the wavelet graph model, we present a computationally efficient multiresolution image reconstruction algorithm. This algorithm is based on iterative Bayesian space domain optimization using scale recursive updates of the wavelet graph prior model. In contrast to performing the optimization over the wavelet coefficients, the space domain formulation facilitates enforcement of pixel positivity constraints. Results indicate that the proposed framework can improve reconstruction quality over fixed resolution Bayesian methods.

Wavelet transforms for vector fields using omnidirectionally balanced multiwavelets

Abstract: Vector wavelet transforms for vector-valued fields can be implemented directly from multiwavelets; however, existing multiwavelets offer surprisingly poor performance for transforms in vector-valued signal-processing applications. In this paper, the reason for this performance failure is identified, and a remedy is proposed. A multiwavelet design criterion known as omnidirectional balancing is introduced to extend to vector transforms the balancing philosophy previously proposed for multiwavelet-based scalar-signal expansion. It is shown that the straightforward implementation of a vector wavelet transform, namely, the application of a scalar transform to each vector component independently, is a special case of an omnidirectionally balanced vector wavelet transform in which filter-coefficient matrices are constrained to be diagonal. Additionally, a family of symmetric-antisymmetric multiwavelets is designed according to the omnidirectional-balancing criterion. In empirical results for a vector-field compression system, it is observed that the performance of vector wavelet transforms derived from these omnidirectionally-balanced symmetric-antisymmetric multiwavelets is far superior to that of transforms implemented via other multiwavelets and can exceed that of diagonal transforms derived from popular scalar wavelets.

A multiresolution approach for texture synthesis using the circular harmonic functions

Abstract: In this paper, an unsupervised model-based texture reproduction technique is described. In accordance with the Julesz's (1962) conjecture, the statistical properties of the prototype up to the second order are copied in order to generate a synthetic texture perceptually indistinguishable from the given sample. However, this task is accomplished using a hybrid approach which operates partially in the spatial domain and partially in a multiresolution domain. The latter employed is the circular harmonic function (CHF) domain since it has been proven to be well suited for mimicking the behavior of the human visual system (HVS). This approach allows, for a wide range of textures typologies, obtaining synthetic textures that better match the prototype with respect to the ones obtained using techniques based on the Julesz's conjecture operating only in the spatial domain, and to dramatically reduce the computational complexity of similar methods operating only in the multiresolution domain.

Wavelet transform analysis of heart rate variability during myocardial ischaemia.

Abstract: Analysis of heart rate variability (HRV) is a valuable, non-invasive method for quantifying autonomic cardiac control in humans. Frequency-domain analysis of HRV involving myocardial ischaemic episodes should take into account its non-stationary behaviour. The wavelet transform is an alternative tool for the analysis of non-stationary signals. Fourteen patients have been analysed, ranging from 40 to 64 years old and selected from the European Electrocardiographic ST-T Database (ESDB). These records contain 33 ST episodes, according to the notation of the ESDB, with durations of between 40s and 12min. A method for analysing HRV signals using the wavelet transform was applied to obtain a time-scale representation for very low-frequency (VLF), low-frequency (LF) and high-frequency (HF) bands using the orthogonal multiresolution pyramidal algorithm. The design and implementation using fast algorithms included a specially adapted decomposition quadrature mirror filter bank for the frequency bands of interest. Comparing a normality zone against the ischaemic episode in the same record, increases in LF (0.0112±0.0101 against 0.0175±0.0208s2Hz−1; p<0.1) and HF (0.0011±0.0008 against 0.0017±0.0020s2Hz−1; p<0.05) were obtained. The possibility of using these indexes to develop an ischaemic-episode classifier was also tested. Results suggest that wavelet analysis provides useful information for the assessment of dynamic changes and patterns of HRV during myocardial ischaemia.

Multiresolution reconstruction in fan-beam tomography

Abstract: In this paper, a new multiresolution reconstruction approach for fan-beam tomography is established. The theoretical development assumes radial wavelets. An approximate reconstruction formula based on a near-radial quincunx multiresolution scheme is proposed. This multiresolution algorithm allows to compute both the quincunx approximation and detail coefficients of an image from its fan-beam projections. Simulations on mathematical phantoms show that wavelet decomposition is acceptable for small beam angles but deteriorates at high angles. The main applications of the method are denoising and wavelet-based image analysis.

Wavelet based palm print recognition

Abstract: Palm print is a new biometric method to recognize a person. Features in a palm print include principal lines, wrinkles and ridges, etc. The fact that the principal lines, wrinkles and ridges have different resolutions motivates us to analyze the palm print using a multiresolution analysis method. A novel palm print feature, named wavelet energy features (WEF), is defined employing wavelet which is a powerful tool of multiresolution analysis. In this paper. WEF can reflect the wavelet energy distribution of the principal lines, wrinkles and ridges in several directions at different wavelet decomposition levels (scales), so its ability to discriminate palms is very strong. To compute with ease is another virtue of WEF. The very high recognition rates obtained in experiments shows the effectiveness of the proposed method.

Robust speech features based on wavelet transform with application to speaker identification

Abstract: An effective and robust speech feature extraction method is presented. Based on the time-frequency multiresolution property of the wavelet transform, the input speech signal is decomposed into various frequency channels. For capturing the characteristics of an individual speaker, the linear predictive cepstral coefficients of the approximation channel and entropy value of the detail channel for each decomposition process are calculated. In addition, an adaptive thresholding technique for each lower resolution is also applied to remove the influence of noise interference. Experimental results show that using this mechanism not only effectively reduces the influence of noise interference but also improves the recognition performance. Finally, the proposed method is evaluated on the MAT telephone speech database for text-independent speaker identification using the group vector quantisation identifier. Some popular existing methods are also evaluated for comparison, and the results show that the proposed feature extraction algorithm is more effective and robust than the other existing methods. In addition, the performance of the proposed method is very satisfactory even in a low SNR environment corrupted by Gaussian white noise.

Multispectral image sharpening using a shift-invariant wavelet transform and adaptive processing of multiresolution edges

Abstract: Enhanced false color images from mid-IR, near-IR (NIR), and visible bands of the Landsat thematic mapper (TM) are commonly used for visually interpreting land cover type. Described here is a technique for sharpening or fusion of NIR with higher resolution panchromatic (Pan) that uses a shift-invariant implementation of the discrete wavelet transform (SIDWT) and a reported pixel-based selection rule to combine transform coefficients. There can be contrast reversals (e.g., at soil-vegetation boundaries between NIR and visible band images) and consequently degraded sharpening and edge artifacts. To improve performance for these conditions, I used a local area-based correlation technique originally reported for comparing image-pyramid-derived edges for the adaptive processing of wavelet-derived edge data. Also, using the redundant data of the SIDWT improves edge data generation. There is additional improvement because sharpened subband imagery is used with the edge-correlation process. A reported technique for sharpening three-band spectral imagery used forward and inverse intensity, hue, and saturation transforms and wavelet-based sharpening of intensity. This technique had limitations with opposite contrast data, and in this study sharpening was applied to single-band multispectral-Pan image pairs. Sharpening used simulated 30-m NIR imagery produced by degrading the spatial resolution of a higher resolution reference. Performance, evaluated by comparison between sharpened and reference image, was improved when sharpened subband data were used with the edge correlation.

Wavelet analysis of matrix–valued time–series

Abstract: The construction of matrixvalued filters for multiresolution analysis of matrixvalued timeseries is studied. Several different designs are explicitly derived corresponding to perfect reconstruction...

Multiresolution-based segmentation of calcifications for the early detection of breast cancer

Abstract: Clusters of microcalcifications in a mammogram may be an early indication of breast cancer. Unfortunately, due to size, shape and limited contrast from surrounding normal tissue, microcalcifications can occasionally be hard to detect in computer-aided detection (CAD) systems. These CAD systems can also be slow compared to a radiologist's performance when reviewing film-screen mammography. The research described here investigates a rapid, multiresolution-based approach combined with wavelet analysis to provide an accurate segmentation of potential calcifications. An initial multiresolution approach to fuzzy c-means (FCM) segmentation is employed to rapidly distinguish medically significant tissues. Tissue areas chosen for high-resolution analysis are broken into multiple windows. Within each window, wavelet analysis is used to generate a contrast image, and a local FCM segmentation generates an estimate of local intensity. A simple two-rule fuzzy system then combines intensity and contrast information to derive fuzzy memberships of pixels in the high-contrast, bright pixel class. A double threshold is finally applied to this fuzzy membership to detect and segment calcifications. This sequence of steps is shown to approach detection rates of conventional classifier designs and may therefore be useful as a pre-processing module for these systems to improve speed. Results are reported for 25 images obtained from the Digital Database for Screening Mammography (DDSM).

Spherical harmonic analysis and synthesis for global multiresolution applications

Abstract: On the Earth and in its neighborhood, spherical harmonic analysis and synthesis are standard mathematical procedures for scalar, vector and tensor fields. However, with the advent of multiresolution applications, additional considerations about convolution filtering with decimation and dilation are required. As global applications often imply discrete observations on regular grids, computational challenges arise and conflicting claims about spherical harmonic transforms have recently appeared in the literature. Following an overview of general multiresolution analysis and synthesis, spherical harmonic transforms are discussed for discrete global computations. For the necessary multi-rate filtering operations, spherical convolutions along with decimations and dilations are discussed, with practical examples of applications. Concluding remarks are then included for general applications, with some discussion of the computational complexity involved and the ongoing investigations in research centers.

A Multiresolution Approach to Regularization of Singular Operators and Fast Summation

Abstract: Singular and hypersingular operators are ubiquitous in problems of physics, and their use requires a careful numerical interpretation. Although analytical methods for their regularization have long been known, the classical approach does not provide numerical procedures for constructing or applying the regularized operator. We present a multiresolution definition of regularization for integral operators with convolutional kernels which are homogeneous or associated homogeneous functions. We show that our procedure yields the same operator as the classical definition. Moreover, due to the constructive nature of our definition, we provide concise numerical procedures for the construction and application of singular and hypersingular operators. As an application, we present an algorithm for fast computation of discrete sums and briefly discuss several other examples.

Multiresolution analysis for efficient, high precision all-electron density-functional calculations

Abstract: Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying techniques, we demonstrate that multiresolution analysis of all-electron calculations within density-functional theory can be carried out to a high precision with a computational effort comparable to that of the corresponding plane-wave pseudopotential calculation, which neither captures the full core physics nor is systematically improvable. With this approach, we present calculations of paramagnetic core-level shifts where local-density-functional theory is the sole uncontrolled approximation.

Hiding a logo watermark into the multiwavelet domain using neural networks

Abstract: This paper proposes a novel watermarking scheme for an image, in which a logo watermark is embedded into the multiwavelet domain of the image using neural networks. The multiwavelet domain provides us with a multiresolution representation of the image like the scalar wavelet case. However, there are four subblocks in the coarsest level of the multiwavelet domain, where there is only one in that of the scalar wavelet domain, and also there is a great similarity among these subblocks. According to these characteristics of the multiwavelet domain, we embed a bit of the watermark by adjusting the polarity between the coefficient in one subblock and the mean value of the corresponding coefficients in other three subblocks. Furthermore, we use a back-propagation neural network (BPN) to learn the characteristics of relationship between the watermark and the watermarked image. Due to the learning and adaptive capabilities of the BPN, the false recovery of the watermark can be greatly reduced by the trained BPN. Experimental results show that the proposed method has good imperceptibility and high robustness to common image processing operators.

Real-time reconstruction of wavelet encoded meshes for view-dependent transmission and visualization

Abstract: Wavelet methods for geometry encoding is a recently emerged superset of multiresolution analysis which has proven to be very efficient in term of compression and adaptive transmission of 3D content. The decorrelating power and space/scale localization of wavelets enable efficient compression of arbitrary meshes as well as progressive and local reconstruction. Recent techniques based on zerotree compression have shown to be among the best lossy mesh compression methods, while remaining compatible with selective transmission of geometric data at various level of detail. While some progressive reconstruction schemes have been proposed in the past, we show in this paper that this representation, recently proposed in the MPEG4 standard, can be efficiently used to perform real-time, view-dependent reconstruction of large meshes. The proposed system combines algorithms for local updates, cache management and server/client dialog. The local details management is an improvement of progressive reconstructions built on top of hierarchical structures. It enables fast, homogeneous accommodation and suppression of wavelet coefficients at any level of subdivision, with time complexity independent of the size of the reconstructed mesh. The cache structure wisely exploits the hierarchical character of the received data, in order to avoid redundant information transmission. The whole system enables the client to have total control on the quality of navigation according to its storage and processing capabilities, whatever the size of the mesh.

A new complex-directional wavelet transform and its application to image denoising

Abstract: This paper describes a new complex-directional expansive perfect reconstruction two-dimensional wavelet transform. Each complex wavelet is oriented along one of six possible directions, and the magnitude of each complex wavelet has a smooth bell-shape. The transform is based both on the complex dual-tree wavelet transform introduced by Kingsbury (see Phil. Trans. Royal Society London, A, September 1999 and Applied and Computational Harmonic Analysis, vol.10, no.3, p.234-53, 2001) and on the double-density DWT. It is designed so as to possess simultaneously the properties of the complex dual-tree DWT and the double-density DWT. The paper also describes a simple subband-dependent data-driven denoising algorithm for use with this transform. An example is shown to illustrate the performance of the denoising algorithm and the transform.