Quaternionic Wavelet Transform (QWT) already exist but it dealt with greyscale images. In this paper we propose a quaternionic wavelet transform aimed to colour image processing. To encode colour information in our new transformation, a pixel in the spatial domain is represented by a quaternion as described by Sangwine. First, we propose to use the discrete quaternionic Fourier transform to study the spectral information of the colour image. It is well known that the frequency space of a real signal is a complex hermitian signal, we then studied the digital spectral domain of the quaternionic Fourier transform in order to analyze symmetry properties. This study gives us one characterization of the colour Fourier domain. Second we use the quaternion formalism to define a wavelet transform for colour images. We propose to generalize the filter bank construction to quaternionic formalism. Especially, we describe conditions on quaternionic filters to obtain a perfect reconstruction. We build a first colour quaternionic filter bank: the colour Shannon Wavelet. This family of functions are based on a windowing process in the quaternionic Fourier space.

Lighting uniformity is always an issue in visual inspection of industrial parts. While the human visual system is quite able to cope with this kind of problem, artificial vision systems are subject to false and no detection rate increase when the lighting conditions are not well mastered. If many authors have proposed various methods to unbiase image, most of the time they are designed in an "ad hoc" way and they are very dependent on the experimental conditions. It can be shown that a large class of the inhomogeneities in images due to lighting conditions can be reasonably modelled by a polynomial dependency of the luminance. The wavelet analysis theory proposes a lot of bases with various number of vanishing moments. By keeping only some wavelet coeffcients it is possible to reconstruct an unbiased signal in which the interesting features, characterized by there resolution pertinence range, are cleaned from the polynomial variations supposed to be due to inhomogeneous lighting conditions. In this paper, after a brief presentation of a realistic lighting model, we show that the luminance image can be approximated by a polynomial function. Then we propose a method, based on a partial reconstruction after multiresolution analysis, allowing to remove approximately the polynomial component of the signal. Two variants are also proposed to improve the performance by either detecting more precisely the polynomial component, either limiting the error occurring when neglecting the approximation signal in the reconstruction process. A simulation in 1D and 2D illustrates these propositions. Some results obtained on examples of real artificial vision inspection problems are finally given.

The aim of industrial process control is to convert measurements, taken while the process is evolving, into parameters which can be used to control the process. To be of practical use this must all be computationally efficient allowing real-time feedback. Electrical tomography measurements have the potential to provide useful data without intruding into the industrial process, but produce highly correlated and noisy data, and hence need sensitive analysis. The commonly used approaches, based on regularized image reconstruction are slow, and still require image post-processing to extract control parameters. An alternative approach is to directly work with the measurement data. We demonstrate an approach using wavelets to relate such electrical measurements to the state of flow within a pipe, and hence classify the state of the flow to one of a number of regimes. Wavelets are an ideal tool for our purpose since their multi-scale nature enables the efficient description of both transient and long-term signals. The resulting wavelet models can be used to classify flow into one of a set of regimes, either for later study of the flow profile or for monitoring of an ongoing process. We illustrate our methods by application to simulated data sets.

Nowadays, a large variety of emerging applications (clickable, video, interactive high definition television, intelligent interfaces) do not only process the multimedia content (audio, video, 3D,...) but some additional data directly connected to it, as well. This enrichment information is usuall transmitted and stored as an additional independent stream (metadata). Such an approach can be restrictive sometimes, mainly for the networks/application with strict bandwidth and/or protocol constraints. An alternative solution is advanced and discussed in this paper. The principle consists in transmitting the metadata via in-band channels obtained by means of data hiding (watermarking) techniques. The challenge is to design data hiding techniques reaching the trade off among transparency (the enrichment process should not alter the perceptual quality of the host media), robustness (possibility to recover the metadata at the end user even when the high distortions occur through the channel) and data payload (the amount of metadata which can be inserted). The paper investigates the feasibility of such techniques by evaluating the maximal data payload (the watermarking capacity) under given robustness and transparency constraints. The results are compared to the resources needed by some existing enrichment applications. The experiments are carried out in collaboration with the French mobile service operator SFR (Vodafone Group) and consider video sequences watermarked in the DWT domain.

The transmission of images over heterogeneous networks to a large variety of terminals induces the need for efficient scalable image coding, and adapted error control mechanisms to protect the compressed bit stream against degradations caused by packet losses. In this context, we propose an optimal joint source channel coding (JSCC) approach combined with unequal error protection (UEP) of the transmitted data packets enabling an error-resilient transmission of embedded wavelet-based coded images over binary erasure channels. We theoretically show that the average expected rate-distortion function of the separately encoded subbands is convex with monotonically decreasing slopes and prove that a similar conclusion with bounds on the allowable code rates can be drawn when transmitting an increasing number of fixed-length packets. Based on these proofs we conclude that the developed JSCC-allocation process can rely on a Lagrangian-multiplier method. In order to reduce the computational complexity of the allocation mechanism, we propose a novel Viterbi-based search-algorithm, which determines for every subband the near-optimum number of packets and their corresponding code-rates. We show that our proposed solution results in significant complexity reductions while providing very near-to-optimal performance. The experimental results show that when the channel estimation matches the real channel that the use of UEP can deliver significantly better results than the use of EEP.

The heterogeneous nature of modern communications stems from the need of transmitting digital information through various types of mediums to a large variety of end-user terminals. In this context, simultaneously providing a scalable source representation and resilience against transmission errors is of primary importance. MESHGRID, which is part of the MPEG-4 AFX standard, is a scalable 3D object representation method especially designed to address the heterogeneous nature of networks and clients in modern communication systems. A MESHGRID object comprises one or several surface layers attached to and located within a volumetric reference-grid. In this paper we focus on the errorresilience aspects of MESHGRID and propose a novel approach for scalable error-resilient coding of MESHGRID's reference-grid. An unequal error protection approach is followed, to acquaint for the different error-sensitivity levels characterizing the various resolution and quality layers produced by the reference-grid coder. The code rates to be employed for each layer are determined by solving a joint source and channel coding problem. The L-infinite distortion metric is employed instead of the classical L-2 norm, typically used in case of images and video. In this context, a novel fast algorithm for solving the optimization problem is proposed. The proposed approach allows for real-time implementations. The experimental results demonstrate the benefits brought by error resilient coding of the reference grid. We conclude that the proposed approach offers resilience against transmission errors while preserving all the scalability features and animation capabilities that characterize MESHGRID.

Focusing on the transmission of JPEG2000 images, the purpose of the present paper is to study the impact of the distortion model on a UEP algorithm and address the specific issues of having a potentially sub-optimal source model based on a training image set. We demonstrate that a source independent model has no visible impact on the performance for various JPEG2000 transmission scenarios, while enabling a low-complexity practical implementation of the optimization algorithm.

Signals and images in industrial applications are often subject to strong disturbances and thus require robust methods for their analysis. Since these data are often non-stationary, time-scale or time-frequency tools have demonstrated effectiveness in their handling. More specifically, wavelet transforms and other filter bank generalizations are particularly suitable, due to their discrete implementation. We have recently investigated a specific family of filter banks, the M-band dual-tree wavelet, which provides state of the art performance for image restoration. It generalizes an Hilbert pair based decomposition structure, first proposed by N. Kingsbury and further investigated by I. Selesnick. In this work, we apply this frame decomposition to the analysis of two examples of signals and images in an industrial context: detection of structures and noises in geophysical images and the comparison of direct and indirect measurements resulting from engine combustion.

Manufacturing processes are generally monitored by observing uniformly sampled process signals collected from application specific sensors. Effective process monitoring and control requires identification of different types of variations, including recurring patterns, in process variables. From the process control view point, any repeating patterns in the process measurements will warrant an investigation into potentially assignable causes. In order to devise an effective process control scheme, a novel method for identifying the repeated occurrence of patterns in process measurements is described in this paper. First the sampled process signal is decomposed into signals of different resolution using a wavelet transform. Next, a frequency index is assigned to every sampling point of the process signal at every resolution level to improve the pattern recognition. Recurring patterns are first detected at different resolutions and are then integrated to arrive at the final results. The experimental results show that the method used in this work accurately detects a broader family of recurring patterns even in the presence of noise.

Active infrared thermography is a non-destructive testing (NDT) technique used for non-contact inspection of components and materials by temporal mapping of thermal patterns by means of infrared imaging. Through the application of a short heat pulse, thermal waves of various amplitudes and frequencies are launched into the specimen allowing a signal analysis based on amplitude and phase information (pulsed phase thermography PPT). The wavelet transform (with complex wavelets) can be used with PPT data in a similar way as the classical Fourier transform however with the advantage of preserving time information of the signal which can then be correlated to defect depth, and in this way allowing a quantitative evaluation. In this paper we review the methodology of PPT and the associated signal analysis (Fourier analysis, wavelet analysis) to obtain quantitative defect depth information. We compare and discuss the results of thermal FEM simulations with experimental data and show the advantages of wavelet based signal analysis for defect depth measurements and material characterization.

We used a method designed to fuse imagery from different sensor types. The method uses different forward transforms of input images and a common transform to reconstruct the final result. When measuring the average relative entropy of the fused results, we found that our method gave generally better results when compared to a more conventional approach. We found that reconstruction filters with a small number of zeros seemed to give the best performance.

Both reduction of the bone mass and a degradation of the microarchitecture of the bone tissue are indicators of the osteoporosis disease. This is why radiographies of the calcaneus are very often used in order to analyze and describe both the texture and the structure of the bone. Therefore, a great effort is devoted to texture analysis by sophisticated image processing tools. In this paper, we propose a method for extracting information from a multiresolution representation of the radiological images that facilitates the graphic detection of the osteoporosis. The main contribution of this work relies on the statistical processing of the wavelet-based extracted features that are employed to graphically discriminate between stwo kinds of Osteoporotic Patients (OP1: vertebral fracture, OP2: other fractures) and Control Patients (CP). Graphical discrimination is obtained by an estimation of patients classes' densities by a multivariate kernel density estimation method, the axes result from a linear discriminant analysis between OP1/CP and OP2/CP. Classification and statistical tests carried out on a set of radiographies with their own ground truth validate the ability of discrimination of the proposed features extracted from M-band wavelet transform

We compared performance between the wavelet multiscale edge detection and the scale-space edge detection methods for lithography metrology. First, in order to determine a suitable wavelet, we evaluated the edge detection performance of the wavelet multiscale edge detection method with various types of wavelet families where a modeled SE signal of photoresist with shot noise was used. From the measurement results of average line widths and line edge roughnesses (LERs), the first-order derivative Gaussian wavelet was determined to be the suitable one for the measurement from SE signals of photoresist. Next, the performances were compared. As to the LER measurement, the difference between the two methods was little. However, for average line widths, the wavelet multiscale edge detection method had better performance than the scale-space edge detection method when SNR was lower than 5. Lastly, we applied the two methods to a noisy SEM image of photoresist. The wavelet multiscale edge detection method gave almost the same line width roughness as that of the scale-space edge detection method, though the former took a longer processing time. By setting the wavelet scale space properly, the processing time can be reduced.

This paper presents a decision support system for power load forecast and the learning of influence patterns of the socio-economic and climatic factors on the power consumption based on mathematical and computational intelligenge methods, with the purpose of defining the future power consumption of a given region, as well as to provide a mean for the analysis of correlations between the power consumption and these factors. Here we use a linear modelo of regression for the forecasting, also presenting a comparative analysis with neural networks, to prove its efectiveness; and also Bayesian networks for the learning of causal relationships from the data.

We reduced noise in images using a higher-order, correlation-based method. In this approach, wavelet coefficients were classified as either mostly noise or mostly signal based on third-order statistics. Because the higher than second-order moments of the Gaussian probability function are zero, the third-order correlation coefficient may not have a statistical contribution from Gaussian noise. Using a detection algorithm derived from third-order statistics, we determined if a wavelet coefficient was noisy by looking at its third-order correlation coefficient. Using imagery of space shuttle tiles, our results showed that the minimum mean-squared error obtained using third-order statistics was often less than that using second-order statistics.

Video sequences are often distorted by noise and are usually found in interlaced format throughout the TV video chain. Joint noise reduction and deinterlacing of such image sequences in interlaced format is a challenging task, required by various applications such as video surveillance or video quality improvement for TFT TV-sets, projectors, plasma panels and LCD screens which display video in progressive format. In this paper, we propose a novel, wavelet-domain joint deinterlacer and denoiser. We apply the wavelet decomposition to each field of the interlaced sequence and perform spatio-temporal interpolation and denoising in the wavelet domain in a motion-compensated manner. Hence, the processed wavelet bands are not only denoised but also have twice as more horizontal lines. We split these full resolution processed bands into odd and even lines, on which we separately perform two inverse wavelet transforms. Each of these inverse transforms uses the same filter bank that is the dual of the decomposition filter bank. As a final step the odd and even lines being the outputs of the two inverse wavelet transforms are merged in order to produce the denoised sequence in progressive format. The results of the proposed algorithm show good performance of the proposed joint deinterlacing and denoising scheme, for various noise levels tested. Specifically, the noise is efficiently removed and the spatio-temporal interpolation is performed in a superior manner without introducing significant visible artifacts.

In this paper, we perform a statistical analysis of curvelet coefficients, making a distinction between two classes of coefficients: those representing useful image content and those dominated by noise. By investigating the marginal statistics, we develop a mixture prior for curvelet coefficients. Through analysis of the joint intra-band statistics, we find that white Gaussian noise is transformed by the curvelet transform into noise that is correlated in one direction and decorrelated in the perpendicular direction. This enables us to develop an appropriate local spatial activity indicator for curvelets. Finally, based on our findings, we develop a novel denoising method, inspired by a recent wavelet domain method ProbShrink. For textured images, the new method outperforms its wavelet-based counterpart and existing curvelet-based methods. For piecewise smooth images, performances are similar as existing methods.

When characterizing textures in the scope of recognition or segmentation, one can choose from a great number of existing features. Among them, features based on the wavelet decomposition provide good results and are already used in many applications. One key point for the success of these methods is the choice of the signature used to describe the sub-bands. The energy signature is the most popular, but others exist, with better efficiency. In this paper, we review some of them and bring improvements in their computation. We also show that combining spatial and statistical signatures increase their performance in texture classification problematics.

Visual browsing is an important way of searching for images in large databases. In image retrieval, a lot of problems have to be solved to get a good system: dimensionality curse, users' search context, size of the database, visual features. In this article, a method trying to attenuate these problems is proposed. Each features vector is organized into four signature vectors used in the classification process while building a fuzzy search tree that is proposed to users for visual browsing. Our system gives good results in terms of speed and accuracy by solving several problems of classical image retrieval methods.

Audio watermarking aims at ensuring the property rights for digital audio (music, speech). In this respest, some extra information, referred to as mark or watermark, is embedded into original (unmarked) clip. By detecting this information, the true owner should be identified and the copy maker should be tracked down. This paper starts by identifying the audio peculiarities under the watermarking framework. Then, the first method hybridising spread spectrum and side information principles for audio watermarking is advanced. This method meets the nowadays challenging reqirements of transparency, robustness, and data payload. The experiments were performed in collaboration with the French SFR (Vodafone Group) mobile service provider.

Texture analysis represents one of the main areas in image processing and computer vision. The current article describes how complex networks have been used in order to represent and characterized textures. More specifically, networks are derived from the texture images by expressing pixels as network nodes and similarities between pixels as network edges. Then, measurements such as the node degree, strengths and clustering coefficient are used in order to quantify properties of the connectivity and topology of the analyzed networks. Because such properties are directly related to the structure of the respective texture images, they can be used as features for characterizing and classifying textures. The latter possibility is illustrated with respect to images of textures, DNA chaos game, and faces. The possibility of using the network representations as a subsidy for DNA characterization is also discussed in this work.

One of the main factors for the success of the knowledge discovery process is related to the comprehensibility of the patterns discovered by the data mining techniques used. Among the many data mining techniques found in the literature, we can point the Bayesian networks as one of most prominent when considering the easiness of knowledge interpretation achieved in a domain with uncertainty. However, the static Bayesian networks present two basic disadvantages: the incapacity to correlate the variables, considering its behavior throughout the time; and the difficulty of establishing the optimum combination of states for the variables, which would generate and/or achieve a given requirement. This paper presents an extension for the improvement of Bayesian networks, treating the mentioned problems by incorporating a temporal model, using Markov chains, and for intermediary of the combination of genetic algorithms with the networks obtained from the data.

New image data mining mechanisms that enable content-based retrieval of images of interest from a large collection of satellite data of the Earth's aurorae are described. The mechanisms enable mining for wide aurorae, aurorae with large ovals, standard aurorae, and theta aurorae. Shape characteristics of these classes of aurorae are exploited by the mining mechanisms. Experimental results that benchmark the accuracy of the mechanisms are also presented.