Compressão Seletiva de Imagens Coloridas com Detecção Automática de Regiões de Interesse

There has been an increasing tendency on the use of selective image compression, since several applications make use of digital images and the loss of information in certain regions is not allowed in some cases. However, there are applications in which these images are captured and stored automatically making it impossible to the user to select the regions of interest to be compressed in a lossless manner. A possible solution for this matter would be the automatic selection of these regions, a very difficult problem to solve in general cases. Nevertheless, it is possible to use intelligent techniques to detect these regions in specific cases. This work proposes a selective color image compression method in which regions of interest, previously chosen, are compressed in a lossless manner. This method uses the wavelet transform to decorrelate the pixels of the image, competitive neural network to make a vectorial quantization, mathematical morphology, and Huffman adaptive coding. There are two options for automatic detection in addition to the manual one: a method of texture segmentation, in which the highest frequency texture is selected to be the region of interest, and a new face detection method where the region of the face will be lossless compressed. The results show that both can be successfully used with the compression method, giving the map of the region of interest as an input

GPS Satellite Kinematic Relative Positioning: Analyzing and Improving the Functional Mathematical Model Using Wavelets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Determinacão do período orbital de sistemas binários clipsantes

In this work is presented a new method for the determination of the orbital period (Porb) of eclipsing binary systems based on the wavelet technique. This method is applied on 18 eclipsing binary systems detected by the CoRoT (Convection Rotation and planetary transits) satellite. The periods obtained by wavelet were compared with those obtained by the conventional methods: box Fitting (EEBLS) for detached and semi-detached eclipsing binaries; and polynomial methods (ANOVA) for contact binary systems. Comparing the phase diagrams obtained by the different techniques the wavelet method determine better Porb compared with EEBLS. In the case of contact binary systems the wavelet method shows most of the times better results than the ANOVA method but when the number of data per orbital cicle is small ANOVA gives more accurate results. Thus, the wavelet technique seems to be a great tool for the analysis of data with the quality and precision given by CoRoT and the incoming photometric missions.

Análise das curvas de luz do CoroT usando diferentes processos comparativos: estimando períodos de rotação estelar

One of the main goals of CoRoT Natal Team is the determination of rotation period for thousand of stars, a fundamental parameter for the study of stellar evolutionary histories. In order to estimate the rotation period of stars and to understand the associated uncertainties resulting, for example, from discontinuities in the curves and (or) low signal-to-noise ratio, we have compared three different methods for light curves treatment. These methods were applied to many light curves with different characteristics. First, a Visual Analysis was undertaken for each light curve, giving a general perspective on the different phenomena reflected in the curves. The results obtained by this method regarding the rotation period of the star, the presence of spots, or the star nature (binary system or other) were then compared with those obtained by two accurate methods: the CLEANest method, based on the DCDFT (Date Compensated Discrete Fourier Transform), and the Wavelet method, based on the Wavelet Transform. Our results show that all three methods have similar levels of accuracy and can complement each other. Nevertheless, the Wavelet method gives more information about the star, from the wavelet map, showing the variations of frequencies over time in the signal. Finally, we discuss the limitations of these methods, the efficiency to give us informations about the star and the development of tools to integrate different methods into a single analysis

Representações espectrais de sistemas complexos: aplicações à síntese de superfícies brownianas fracionárias anisotrópicas, filtragem de sinais e identificação de correlações

In this thesis, we study the application of spectral representations to the solution of problems in seismic exploration, the synthesis of fractal surfaces and the identification of correlations between one-dimensional signals. We apply a new approach, called Wavelet Coherency, to the study of stratigraphic correlation in well log signals, as an attempt to identify layers from the same geological formation, showing that the representation in wavelet space, with introduction of scale domain, can facilitate the process of comparing patterns in geophysical signals. We have introduced a new model for the generation of anisotropic fractional brownian surfaces based on curvelet transform, a new multiscale tool which can be seen as a generalization of the wavelet transform to include the direction component in multidimensional spaces. We have tested our model with a modified version of the Directional Average Method (DAM) to evaluate the anisotropy of fractional brownian surfaces. We also used the directional behavior of the curvelets to attack an important problem in seismic exploration: the atenuation of the ground roll, present in seismograms as a result of surface Rayleigh waves. The techniques employed are effective, leading to sparse representation of the signals, and, consequently, to good resolutions

Mathematical tests about the existence and applications of PPS-wavelets in function approximation problems

Neural networks and wavelet transform have been recently seen as attractive tools for developing eficient solutions for many real world problems in function approximation. Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. So, mathematical model is a very important tool to guarantee the development of the neural network area. In this article we will introduce one series of mathematical demonstrations that guarantee the wavelets properties for the PPS functions. As application, we will show the use of PPS-wavelets in pattern recognition problems of handwritten digit through function approximation techniques.

Comparative study between RBF and radial-PPS neural networks

The study of function approximation is motivated by the human limitation and inability to register and manipulate with exact precision the behavior variations of the physical nature of a phenomenon. These variations are referred to as signals or signal functions. Many real world problem can be formulated as function approximation problems and from the viewpoint of artificial neural networks these can be seen as the problem of searching for a mapping that establishes a relationship from an input space to an output space through a process of network learning. Several paradigms of artificial neural networks (ANN) exist. Here we will be investigated a comparative of the ANN study of RBF with radial Polynomial Power of Sigmoids (PPS) in function approximation problems. Radial PPS are functions generated by linear combination of powers of sigmoids functions. The main objective of this paper is to show the advantages of the use of the radial PPS functions in relationship traditional RBF, through adaptive training and ridge regression techniques.

Human face verification based on multidimensional Polynomial Powers of Sigmoid (PPS)

In this paper, we described how a multidimensional wavelet neural networks based on Polynomial Powers of Sigmoid (PPS) can be constructed, trained and applied in image processing tasks. In this sense, a novel and uniform framework for face verification is presented. The framework is based on a family of PPS wavelets,generated from linear combination of the sigmoid functions, and can be considered appearance based in that features are extracted from the face image. The feature vectors are then subjected to subspace projection of PPS-wavelet. The design of PPS-wavelet neural networks is also discussed, which is seldom reported in the literature. The Stirling Universitys face database were used to generate the results. Our method has achieved 92 % of correct detection and 5 % of false detection rate on the database.

A fully adaptive multiresolution scheme for shock computations

The scheme is based on Ami Harten's ideas (Harten, 1994), the main tools coming from wavelet theory, in the framework of multiresolution analysis for cell averages. But instead of evolving cell averages on the finest uniform level, we propose to evolve just the cell averages on the grid determined by the significant wavelet coefficients. Typically, there are few cells in each time step, big cells on smooth regions, and smaller ones close to irregularities of the solution. For the numerical flux, we use a simple uniform central finite difference scheme, adapted to the size of each cell. If any of the required neighboring cell averages is not present, it is interpolated from coarser scales. But we switch to ENO scheme in the finest part of the grids. To show the feasibility and efficiency of the method, it is applied to a system arising in polymer-flooding of an oil reservoir. In terms of CPU time and memory requirements, it outperforms Harten's multiresolution algorithm.The proposed method applies to systems of conservation laws in 1Dpartial derivative(t)u(x, t) + partial derivative(x)f(u(x, t)) = 0, u(x, t) is an element of R-m. (1)In the spirit of finite volume methods, we shall consider the explicit schemeupsilon(mu)(n+1) = upsilon(mu)(n) - Deltat/hmu ((f) over bar (mu) - (f) over bar (mu)-) = [Dupsilon(n)](mu), (2)where mu is a point of an irregular grid Gamma, mu(-) is the left neighbor of A in Gamma, upsilon(mu)(n) approximate to 1/mu-mu(-) integral(mu-)(mu) u(x, t(n))dx are approximated cell averages of the solution, (f) over bar (mu) = (f) over bar (mu)(upsilon(n)) are the numerical fluxes, and D is the numerical evolution operator of the scheme.According to the definition of (f) over bar (mu), several schemes of this type have been proposed and successfully applied (LeVeque, 1990). Godunov, Lax-Wendroff, and ENO are some of the popular names. Godunov scheme resolves well the shocks, but accuracy (of first order) is poor in smooth regions. Lax-Wendroff is of second order, but produces dangerous oscillations close to shocks. ENO schemes are good alternatives, with high order and without serious oscillations. But the price is high computational cost.Ami Harten proposed in (Harten, 1994) a simple strategy to save expensive ENO flux calculations. The basic tools come from multiresolution analysis for cell averages on uniform grids, and the principle is that wavelet coefficients can be used for the characterization of local smoothness.. Typically, only few wavelet coefficients are significant. At the finest level, they indicate discontinuity points, where ENO numerical fluxes are computed exactly. Elsewhere, cheaper fluxes can be safely used, or just interpolated from coarser scales. Different applications of this principle have been explored by several authors, see for example (G-Muller and Muller, 1998).Our scheme also uses Ami Harten's ideas. But instead of evolving the cell averages on the finest uniform level, we propose to evolve the cell averages on sparse grids associated with the significant wavelet coefficients. This means that the total number of cells is small, with big cells in smooth regions and smaller ones close to irregularities. This task requires improved new tools, which are described next.

Robust fault diagnosis in power distribution systems based on fuzzy ARTMAP neural network-aided evidence theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Processamento e interpretação de dados 2D e 3D de GPR :aplicações no imageamento de feições kársticas e estruturas de dissolução no campo de petróleo de Fazenda Belém-CE

In Fazenda Belém oil field (Potiguar Basin, Ceará State, Brazil) occur frequently sinkholes and sudden terrain collapses associated to an unconsolidated sedimentary cap covering the Jandaíra karst. This research was carried out in order to understand the mechanisms of generation of these collapses. The main tool used was Ground Penetrating Radar (GPR). This work is developed twofold: one aspect concerns methodology improvements in GPR data processing whilst another aspect concerns the geological study of the Jandaíra karst. This second aspect was strongly supported both by the analysis of outcropping karst structures (in another regions of Potiguar Basin) and by the interpretation of radargrams from the subsurface karst in Fazenda Belém. It was designed and tested an adequate flux to process GPR data which was adapted from an usual flux to process seismic data. The changes were introduced to take into account important differences between GPR and Reflection Seismic methods, in particular: poor coupling between source and ground, mixed phase of the wavelet, low signal-to-noise ratio, monochannel acquisition, and high influence of wave propagation effects, notably dispersion. High frequency components of the GPR pulse suffer more pronounced effects of attenuation than low frequency components resulting in resolution losses in radargrams. In Fazenda Belém, there is a stronger need of an suitable flux to process GPR data because both the presence of a very high level of aerial events and the complexity of the imaged subsurface karst structures. The key point of the processing flux was an improvement in the correction of the attenuation effects on the GPR pulse based on their influence on the amplitude and phase spectra of GPR signals. In low and moderate losses dielectric media the propagated signal suffers significant changes only in its amplitude spectrum; that is, the phase spectrum of the propagated signal remains practically unaltered for the usual travel time ranges. Based on this fact, it is shown using real data that the judicious application of the well known tools of time gain and spectral balancing can efficiently correct the attenuation effects. The proposed approach can be applied in heterogeneous media and it does not require the precise knowledge of the attenuation parameters of the media. As an additional benefit, the judicious application of spectral balancing promotes a partial deconvolution of the data without changing its phase. In other words, the spectral balancing acts in a similar way to a zero phase deconvolution. In GPR data the resolution increase obtained with spectral balancing is greater than those obtained with spike and predictive deconvolutions. The evolution of the Jandaíra karst in Potiguar Basin is associated to at least three events of subaerial exposition of the carbonatic plataform during the Turonian, Santonian, and Campanian. In Fazenda Belém region, during the mid Miocene, the Jandaíra karst was covered by continental siliciclastic sediments. These sediments partially filled the void space associated to the dissolution structures and fractures. Therefore, the development of the karst in this region was attenuated in comparison to other places in Potiguar Basin where this karst is exposed. In Fazenda Belém, the generation of sinkholes and terrain collapses are controlled mainly by: (i) the presence of an unconsolidated sedimentary cap which is thick enough to cover completely the karst but with sediment volume lower than the available space associated to the dissolution structures in the karst; (ii) the existence of important structural of SW-NE and NW-SE alignments which promote a localized increase in the hydraulic connectivity allowing the channeling of underground water, thus facilitating the carbonatic dissolution; and (iii) the existence of a hydraulic barrier to the groundwater flow, associated to the Açu-4 Unity. The terrain collapse mechanisms in Fazenda Belém occur according to the following temporal evolution. The meteoric water infiltrates through the unconsolidated sedimentary cap and promotes its remobilization to the void space associated with the dissolution structures in Jandaíra Formation. This remobilization is initiated at the base of the sedimentary cap where the flow increases its abrasion due to a change from laminar to turbulent flow regime when the underground water flow reaches the open karst structures. The remobilized sediments progressively fill from bottom to top the void karst space. So, the void space is continuously migrated upwards ultimately reaching the surface and causing the sudden observed terrain collapses. This phenomenon is particularly active during the raining season, when the water table that normally is located in the karst may be temporarily located in the unconsolidated sedimentary cap

Localização de faltas em linhas de transmissão usando morfologia matemática

This work an algorithm for fault location is proposed. It contains the following functions: fault detection, fault classification and fault location. Mathematical Morphology is used to process currents obtained in the monitored terminals. Unlike Fourier and Wavelet transforms that are usually applied to fault location, the Mathematical Morphology is a non-linear operation that uses only basic operation (sum, subtraction, maximum and minimum). Thus, Mathematical Morphology is computationally very efficient. For detection and classification functions, the Morphological Wavelet was used. On fault location module the Multiresolution Morphological Gradient was used to detect the traveling waves and their polarities. Hence, recorded the arrival in the two first traveling waves incident at the measured terminal and knowing the velocity of propagation, pinpoint the fault location can be estimated. The algorithm was applied in a 440 kV power transmission system, simulated on ATP. Several fault conditions where studied and the following parameters were evaluated: fault location, fault type, fault resistance, fault inception angle, noise level and sampling rate. The results show that the application of Mathematical Morphology in faults location is very promising

Estudo de Fractalidade e Evolução Dinâmica de Sistemas Complexos

In this work, the study of some complex systems is done with use of two distinct procedures. In the first part, we have studied the usage of Wavelet transform on analysis and characterization of (multi)fractal time series. We have test the reliability of Wavelet Transform Modulus Maxima method (WTMM) in respect to the multifractal formalism, trough the calculation of the singularity spectrum of time series whose fractality is well known a priori. Next, we have use the Wavelet Transform Modulus Maxima method to study the fractality of lungs crackles sounds, a biological time series. Since the crackles sounds are due to the opening of a pulmonary airway bronchi, bronchioles and alveoli which was initially closed, we can get information on the phenomenon of the airway opening cascade of the whole lung. Once this phenomenon is associated with the pulmonar tree architecture, which displays fractal geometry, the analysis and fractal characterization of this noise may provide us with important parameters for comparison between healthy lungs and those affected by disorders that affect the geometry of the tree lung, such as the obstructive and parenchymal degenerative diseases, which occurs, for example, in pulmonary emphysema. In the second part, we study a site percolation model for square lattices, where the percolating cluster grows governed by a control rule, corresponding to a method of automatic search. In this model of percolation, which have characteristics of self-organized criticality, the method does not use the automated search on Leaths algorithm. It uses the following control rule: pt+1 = pt + k(Rc − Rt), where p is the probability of percolation, k is a kinetic parameter where 0 < k < 1 and R is the fraction of percolating finite square lattices with side L, LxL. This rule provides a time series corresponding to the dynamical evolution of the system, in particular the likelihood of percolation p. We proceed an analysis of scaling of the signal obtained in this way. The model used here enables the study of the automatic search method used for site percolation in square lattices, evaluating the dynamics of their parameters when the system goes to the critical point. It shows that the scaling of , the time elapsed until the system reaches the critical point, and tcor, the time required for the system loses its correlations, are both inversely proportional to k, the kinetic parameter of the control rule. We verify yet that the system has two different time scales after: one in which the system shows noise of type 1 f , indicating to be strongly correlated. Another in which it shows white noise, indicating that the correlation is lost. For large intervals of time the dynamics of the system shows ergodicity

Application of wavelets to the evaluation of phantom images for mammography quality control

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Decomposition and Noise Removal Method Combining Diffusion Equation and Wave Atoms for Textured Images

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)