Showing papers on "Multiresolution analysis published in 2004"

Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition

Abstract: Since Chavez proposed the highpass filtering procedure to fuse multispectral and panchromatic images, several fusion methods have been developed based on the same principle: to extract from the panchromatic image spatial detail information to later inject it into the multispectral one. In this paper, we present new fusion alternatives based on the same concept, using the multiresolution wavelet decomposition to execute the detail extraction phase and the intensity-hue-saturation (IHS) and principal component analysis (PCA) procedures to inject the spatial detail of the panchromatic image into the multispectral one. The multiresolution wavelet decomposition has been performed using both decimated and undecimated algorithms and the resulting merged images compared both spectral and spatially. These fusion methods, as well as standard IHS-, PCA-, and wavelet-based methods have been used to merge Systeme Pour l'Observation de la Terre (SPOT) 4 XI and SPOT 4 M images with a ratio 4:1. We have estimated the validity of each fusion method by analyzing, visually and quantitatively, the quality of the resulting fused images. The methodological approaches proposed in this paper result in merged images with improved quality with respect to those obtained by standard IHS, PCA, and standard wavelet-based fusion methods. For both proposed fusion methods, better results are obtained when an undecimated algorithm is used to perform the multiresolution wavelet decomposition.

Gradient-based multiresolution image fusion

Abstract: A novel approach to multiresolution signal-level image fusion is presented for accurately transferring visual information from any number of input image signals, into a single fused image without loss of information or the introduction of distortion. The proposed system uses a "fuse-then-decompose" technique realized through a novel, fusion/decomposition system architecture. In particular, information fusion is performed on a multiresolution gradient map representation domain of image signal information. At each resolution, input images are represented as gradient maps and combined to produce new, fused gradient maps. Fused gradient map signals are processed, using gradient filters derived from high-pass quadrature mirror filters to yield a fused multiresolution pyramid representation. The fused output image is obtained by applying, on the fused pyramid, a reconstruction process that is analogous to that of conventional discrete wavelet transform. This new gradient fusion significantly reduces the amount of distortion artefacts and the loss of contrast information usually observed in fused images obtained from conventional multiresolution fusion schemes. This is because fusion in the gradient map domain significantly improves the reliability of the feature selection and information fusion processes. Fusion performance is evaluated through informal visual inspection and subjective psychometric preference tests, as well as objective fusion performance measurements. Results clearly demonstrate the superiority of this new approach when compared to conventional fusion systems.

Wavelet-based neural network for power disturbance recognition and classification

Abstract: In this paper, a prototype wavelet-based neural-network classifier for recognizing power-quality disturbances is implemented and tested under various transient events. The discrete wavelet transform (DWT) technique is integrated with the probabilistic neural-network (PNN) model to construct the classifier. First, the multiresolution-analysis technique of DWT and the Parseval's theorem are employed to extract the energy distribution features of the distorted signal at different resolution levels. Then, the PNN classifies these extracted features to identify the disturbance type according to the transient duration and the energy features. Since the proposed methodology can reduce a great quantity of the distorted signal features without losing its original property, less memory space and computing time are required. Various transient events tested, such as momentary interruption, capacitor switching, voltage sag/swell, harmonic distortion, and flicker show that the classifier can detect and classify different power disturbance types efficiently.

Biometric verification using thermal images of palm-dorsa vein patterns

Abstract: A novel approach to personal verification using the thermal images of palm-dorsa vein patterns is presented in this paper. The characteristics of the proposed method are that no prior knowledge about the objects is necessary and the parameters can be set automatically. In our work, an infrared (IR) camera is adopted as the input device to capture the thermal images of the palm-dorsa. In the proposed approach, two of the finger webs are automatically selected as the datum points to define the region of interest (ROI) on the thermal images. Within each ROI, feature points of the vein patterns (FPVPs) are extracted by modifying the basic tool of watershed transformation based on the properties of thermal images. According to the heat conduction law (the Fourier law), multiple features can be extracted from each FPVP for verification. Multiresolution representations of images with FPVPs are obtained using multiple multiresolution filters (MRFs) that extract the dominant points by filtering miscellaneous features for each FPVP. A hierarchical integrating function is then applied to integrate multiple features and multiresolution representations. The former is integrated by an inter-to-intra personal variation ratio and the latter is integrated by a positive Boolean function. We also introduce a logical and reasonable method to select a trained threshold for verification. Experiments were conducted using the thermal images of palm-dorsas and the results are satisfactory with an acceptable accuracy rate (FRR:2.3% and FAR:2.3%). The experimental results demonstrate that our proposed approach is valid and effective for vein-pattern verification.

Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry

Abstract: We present an analysis of a spatial carrier-fringe pattern in three-dimensional (3-D) shape measurement by using the wavelet transform, a tool excelling for its multiresolution in the time- and space-frequency domains. To overcome the limitation of the Fourier transform, we introduce the Gabor wavelet to analyze the phase distributions of the spatial carrier-fringe pattern. The theory of wavelet transform profilometry, an accuracy check by means of a simulation, and an example of 3-D shape measurement are shown.

Transmission line distance protection based on wavelet transform

Abstract: Wavelet transform (WT) has the ability to decompose signals into different frequency bands using multiresolution analysis (MRA). It can be utilized in detecting faults and to estimate the phasors of the voltage and current signals, which are essential for transmission line distance protection. A digital distance-protection scheme for transmission lines based on analyzing the measured voltage and current signals at the relay location using WT with MRA is presented in this paper. The scheme has been tested by both computer simulation and experimentally. The tests presented include solid ground faults, phase faults, high impedance and nonlinear ground faults, and line charging.

Wavelet Packet-Autocorrelation Function Method for Traffic Flow Pattern Analysis

Abstract: Accurate, timely forecasting of traffic flow is of key importance in effective management of traffic congestion in intelligent transportation systems. A detailed understanding of properties of traffic flow is essential for building a reliable forecasting model. The discrete wavelet packet transform (DWPT) provides more coefficients than the conventional discrete wavelet transform (DWT), representing additional subtle details of a signal. In wavelet multiresolution analysis, an important decision is the selection of the decomposition level. This paper proposes a statistical autocorrelation function (ACF) for the selection of the decomposition level in wavelet multiresolution analysis of traffic flow time series. A hybrid wavelet packet-ACF method is proposed for analysis of traffic flow time series and determining its self-similar, singular, and fractal properties. A DWPT-based approach combined with a wavelet coefficients penalization scheme and soft thresholding is presented for denoising the traffic flow. The proposed methodology provides a powerful tool in removing the noise and identifying singularities in the traffic flow. The methods created in this work are of value in developing accurate traffic-forecasting models.

Multiresolution techniques for the detection of gravitational-wave bursts

Abstract: We present two search algorithms that implement logarithmic tiling of the time–frequency plane in order to efficiently detect astrophysically unmodelled bursts of gravitational radiation. The first is a straightforward application of the dyadic wavelet transform. The second is a modification of the windowed Fourier transform which tiles the time–frequency plane for a specific Q. In addition, we also demonstrate adaptive whitening by linear prediction, which greatly simplifies our statistical analysis. This is a methodology paper that aims to describe the techniques for identifying significant events as well as the necessary pre-processing that is required in order to improve their performance. For this reason we use simulated LIGO noise in order to illustrate the methods and to present their preliminary performance.

Pedestrian detection for driver assistance using multiresolution infrared vision

Abstract: This paper describes a system for pedestrian detection in infrared images, which has been implemented on an experimental vehicle equipped with an infrared camera. The proposed system has been tested in many situations and has proven to be efficient and with a very low false-positive rate. It is based on a multiresolution localization of warm symmetrical objects with specific size and aspect ratio; anyway, because road infrastructures and other road participants may also have such characteristics, a set of matched filters is included in order to reduce false detections. A final validation process, based on human shape's morphological characteristics, is used to build the list of pedestrian appearing in the scene. Neither temporal correlation nor motion cues are used in this first part of the project: the processing is based on the analysis of single frames only.

Multiscale likelihood analysis and complexity penalized estimation

Abstract: We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L 2 function, a given likelihood function has an alternative representation as a product of conditional densities reflecting information in both the data and the parameter vector localized in position and scale. The framework is developed as a set of sufficient conditions for the existence of such factorizations, formulated in analogy to those underlying a standard multiresolution analysis for wavelets, and hence can be viewed as a multiresolution analysis for likelihoods. We then consider the use of these factorizations in the task of nonparametric, complexity penalized likelihood estimation. We study the risk properties of certain thresholding and partitioning estimators, and demonstrate their adaptivity and near-optimality, in a minimax sense over a broad range of function spaces, based on squared Hellinger distance as a loss function. In particular, our results provide an illustration of how properties of classical wavelet-based estimators can be obtained in a single, unified framework that includes models for continuous, count and categorical data types.

Wavelet-based multiresolution analysis of irregular surface meshes

Abstract: We extend Lounsbery's multiresolution analysis wavelet-based theory for triangular 3D meshes, which can only be applied to regularly subdivided meshes and thus involves a remeshing of the existing 3D data. Based on a new irregular subdivision scheme, the proposed algorithm can be applied directly to irregular meshes, which can be very interesting when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. This is very convenient in CAD (computer-assisted design), when the mesh has attributes such as texture and color information, or when the 3D mesh is used for simulations, and where a different connectivity could lead to simulation errors. The algorithm faces an inverse problem for which a solution is proposed. For each level of resolution, the simplification is processed in order to keep the mesh as regular as possible. In addition, a geometric criterion is used to keep the geometry of the approximations as close as possible to the original mesh. Several examples on various reference meshes are shown to prove the efficiency of our proposal.

Principal‐component analysis of multiscale data for process monitoring and fault diagnosis

Abstract: An approach is presented to multivariate statistical process control (MSPC) for process monitoring and fault diagnosis based on principal-component analysis (PCA) models of multiscale data. Process measurements, representing the cumulative effects of many underlying process phenomena, are decomposed by applying multiresolution analysis (MRA) by wavelet transformations. The decomposed process measurements are rearranged according to their scales, and PCA is applied to these multiscale data to capture process variable correlations occurring at different scales. Choosing an orthonormal mother wavelet allows each principal component to be a function of the process variables at only one scale level. The proposed method is discussed in the context of other multiscale approaches, and illustrated in detail using simulated data from a continuous stirred tank reactor (CSTR) system. A major contribution of the paper is to extend fault isolation methods based on contribution plots to multiscale approaches. In particular, once a fault is detected, the contributions of the variations at each scale to the fault are computed. These scale contributions can be very helpful in isolating faults that occur mainly at a single scale. For those scales having large contributions to the fault, one can further compute the variable contributions to those scales, thereby making fault diagnosis much easier. A comparison study is done through Monte Carlo simulation. The proposed method can enhance fault detection and isolation (FDI) performance when the frequency content of a fault effect is confined to a narrow-frequency band. However, when the fault frequency content is not localized, the multiscale approaches perform very comparably to the standard single-scale approaches, and offer no real advantage. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2891–2903, 2004

Multiscale approximation with hierarchical radial basis functions networks

Abstract: An approximating neural model, called hierarchical radial basis function (HRBF) network, is presented here. This is a self-organizing (by growing) multiscale version of a radial basis function (RBF) network. It is constituted of hierarchical layers, each containing a Gaussian grid at a decreasing scale. The grids are not completely filled, but units are inserted only where the local error is over threshold. This guarantees a uniform residual error and the allocation of more units with smaller scales where the data contain higher frequencies. Only local operations, which do not require any iteration on the data, are required; this allows to construct the network in quasi-real time. Through harmonic analysis, it is demonstrated that, although a HRBF cannot be reduced to a traditional wavelet-based multiresolution analysis (MRA), it does employ Riesz bases and enjoys asymptotic approximation properties for a very large class of functions. HRBF networks have been extensively applied to the reconstruction of three-dimensional (3-13) models from noisy range data. The results illustrate their power in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by MRA.

Normal Multiresolution Approximation of Curves

Abstract: A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction. In this paper we study properties such as regularity, convergence, and stability of a normal multiresolution analysis. In particular, we show that these properties critically depend on the underlying subdivision scheme and that, in general, the convergence of normal multiresolution approximations equals the convergence of the underlying subdivision scheme.

Analysis on multiresolution mosaic images

Abstract: Image mosaicing is the act of combining two or more images and is used in many applications in computer vision, image processing, and computer graphics. It aims to combine images such that no obstructive boundaries exist around overlapped regions and to create a mosaic image that exhibits as little distortion as possible from the original images. In the proposed technique, the to-be-combined images are first projected into wavelet subspaces. The images projected into the same wavelet space are then blended. Our blending function is derived from an energy minimization model which balances the smoothness around the overlapped region and the fidelity of the blended image to the original images. Experiment results and subjective comparison with other methods are given.

Multiresolution segmentation of natural images: from linear to nonlinear scale-space representations

Abstract: In this paper, we introduce a framework that merges classical ideas borrowed from scale-space and multiresolution segmentation with nonlinear partial differential equations. A nonlinear scale-space stack is constructed by means of an appropriate diffusion equation. This stack is analyzed and a tree of coherent segments is constructed based on relationships between different scale layers. Pruning this tree proves to be a very efficient tool for unsupervised segmentation of different classes of images (e.g., natural, medical, etc.). This technique is light on the computational point of view and can be extended to nonscalar data in a straightforward manner.

Prediction of the Dst index using multiresolution wavelet models

Abstract: [1] A new identification approach is introduced for predicting the Dst index using multiresolution B-spline wavelet models based on an observational data set consisting of VBs, the solar wind parameter, as the input and the Dst index as the output. The relationship between the input VBs and output Dst is initially described using a B-spline wavelet model. This model is then simplified using an orthogonal least squares and error reduction ratio (OLS-ERR) algorithm by selecting the significant model terms to produce a parsimonious wavelet model. Forecasts of the Dst index are then computed based on this model.

Effect of time-dependent basis functions and their superposition error on atom-centered density matrix propagation (ADMP): connections to wavelet theory of multiresolution analysis.

Abstract: We present a rigorous analysis of the primitive Gaussian basis sets used in the electronic structure theory. This leads to fundamental connections between Gaussian basis functions and the wavelet theory of multiresolution analysis. We also obtain a general description of basis set superposition error which holds for all localized, orthogonal or nonorthogonal, basis functions. The standard counterpoise correction of quantum chemistry is seen to arise as a special case of this treatment. Computational study of the weakly bound water dimer illustrates that basis set superposition error is much less for basis functions beyond the 6-31+G(*) level of Gaussians when structure, energetics, frequencies, and radial distribution functions are to be calculated. This result will be invaluable in the use of atom-centered Gaussian functions for ab initio molecular dynamics studies using Born-Oppenheimer and atom-centered density matrix propagation.

An introduction to wavelet analysis with applications to vegetation time series

Abstract: Wavelets are relatively new mathematical tools that have proven to be quite useful for analyzing time series and spatial data. We provide a basic introduction to wavelet analysis which concentrates on their interpretation in the context of analyzing time series. We illustrate the use of wavelet analysis on time series related to vegetation coverage in the Arctic region.

Multiresolution moment filters: theory and applications

Abstract: We introduce local weighted geometric moments that are computed from an image within a sliding window at multiple scales. When the window function satisfies a two-scale relation, we prove that lower order moments can be computed efficiently at dyadic scales by using a multiresolution wavelet-like algorithm. We show that B-splines are well-suited window functions because, in addition to being refinable, they are positive, symmetric, separable, and very nearly isotropic (Gaussian shape). We present three applications of these multiscale local moments. The first is a feature-extraction method for detecting and characterizing elongated structures in images. The second is a noise-reduction method which can be viewed as a multiscale extension of Savitzky-Golay filtering. The third is a multiscale optical-flow algorithm that uses a local affine model for the motion field, extending the Lucas-Kanade optical-flow method. The results obtained in all cases are promising.

A wavelet-based approach to detecting liveness in fingerprint scanners

Abstract: In this work, a method to provide fingerprint vitality authentication, in order to improve vulnerability of fingerprint identification systems to spoofing is introduced. The method aims at detecting 'liveness' in fingerprint scanners by using the physiological phenomenon of perspiration. A wavelet based approach is used which concentrates on the changing coefficients using the zoom-in property of the wavelets. Multiresolution analysis and wavelet packet analysis are used to extract information from low frequency and high frequency content of the images respectively. Daubechies wavelet is designed and implemented to perform the wavelet analysis. A threshold is applied to the first difference of the information in all the sub-bands. The energy content of the changing coefficients is used as a quantified measure to perform the desired classification, as they reflect a perspiration pattern. A data set of approximately 30 live, 30 spoof, and 14 cadaver fingerprint images was divided with first half as a training data while the other half as the testing data. The proposed algorithm was applied to the training data set and was able to completely classify 'live' fingers from 'not live' fingers, thus providing a method for enhanced security and improved spoof protection.

Multiresolution modeling and estimation of multisensor data

Abstract: This paper presents a multiresolution multisensor data fusion scheme for dynamic systems to be observed by several sensors of different resolutions. A state projection equation is introduced to associate the states of a system at each resolution with others. This projection equation together with the state transition equation and the measurement equations at each of the resolutions construct a continuous-time model of the system. The model meets the requirements of Kalman filtering. In discrete time, the state transition is described at the finest resolution and the sampling frequencies of sensors decrease successively by a factor of two in resolution. We can build a discrete model of the system by using a linear projection operator to approximate the state space projection. This discrete model satisfies the requirements of discrete Kalman filtering, which actually offers an optimal estimation algorithm of the system. In time-invariant case, the stability of the Kalman filter is analyzed and a sufficient condition for the filtering stability is given. A Markov-process-based example is given to illustrate and evaluate the proposed scheme of multiresolution modeling and estimation with multiple sensors.

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 terms of compression and adaptive transmission of three-dimensional (3-D) 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 levels 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.