Spatial modeling techniques for mapping and characterization of acid sulfate soils

Acid sulfate (a.s.) soils constitute a major environmental issue. Severe ecological damage results from the considerable amounts of acidity and metals leached by these soils in the recipient watercourses. As even small hot spots may affect large areas of coastal waters, mapping represents a fundamental step in the management and mitigation of a.s. soil environmental risks (i.e. to target strategic areas). Traditional mapping in the field is time-consuming and therefore expensive. Additional more cost-effective techniques have, thus, to be developed in order to narrow down and define in detail the areas of interest. The primary aim of this thesis was to assess different spatial modeling techniques for a.s. soil mapping, and the characterization of soil properties relevant for a.s. soil environmental risk management, using all available data: soil and water samples, as well as datalayers (e.g. geological and geophysical). Different spatial modeling techniques were applied at catchment or regional scale. Two artificial neural networks were assessed on the Sirppujoki River catchment (c. 440 km2) located in southwestern Finland, while fuzzy logic was assessed on several areas along the Finnish coast. Quaternary geology, aerogeophysics and slope data (derived from a digital elevation model) were utilized as evidential datalayers. The methods also required the use of point datasets (i.e. soil profiles corresponding to known a.s. or non-a.s. soil occurrences) for training and/or validation within the modeling processes. Applying these methods, various maps were generated: probability maps for a.s. soil occurrence, as well as predictive maps for different soil properties (sulfur content, organic matter content and critical sulfide depth). The two assessed artificial neural networks (ANNs) demonstrated good classification abilities for a.s. soil probability mapping at catchment scale. Slightly better results were achieved using a Radial Basis Function (RBF) -based ANN than a Radial Basis Functional Link Net (RBFLN) method, narrowing down more accurately the most probable areas for a.s. soil occurrence and defining more properly the least probable areas. The RBF-based ANN also demonstrated promising results for the characterization of different soil properties in the most probable a.s. soil areas at catchment scale. Since a.s. soil areas constitute highly productive lands for agricultural purpose, the combination of a probability map with more specific soil property predictive maps offers a valuable toolset to more precisely target strategic areas for subsequent environmental risk management. Notably, the use of laser scanning (i.e. Light Detection And Ranging, LiDAR) data enabled a more precise definition of a.s. soil probability areas, as well as the soil property modeling classes for sulfur content and the critical sulfide depth. Given suitable training/validation points, ANNs can be trained to yield a more precise modeling of the occurrence of a.s. soils and their properties. By contrast, fuzzy logic represents a simple, fast and objective alternative to carry out preliminary surveys, at catchment or regional scale, in areas offering a limited amount of data. This method enables delimiting and prioritizing the most probable areas for a.s soil occurrence, which can be particularly useful in the field. Being easily transferable from area to area, fuzzy logic modeling can be carried out at regional scale. Mapping at this scale would be extremely time-consuming through manual assessment. The use of spatial modeling techniques enables the creation of valid and comparable maps, which represents an important development within the a.s. soil mapping process. The a.s. soil mapping was also assessed using water chemistry data for 24 different catchments along the Finnish coast (in all, covering c. 21,300 km2) which were mapped with different methods (i.e. conventional mapping, fuzzy logic and an artificial neural network). Two a.s. soil related indicators measured in the river water (sulfate content and sulfate/chloride ratio) were compared to the extent of the most probable areas for a.s. soils in the surveyed catchments. High sulfate contents and sulfate/chloride ratios measured in most of the rivers demonstrated the presence of a.s. soils in the corresponding catchments. The calculated extent of the most probable a.s. soil areas is supported by independent data on water chemistry, suggesting that the a.s. soil probability maps created with different methods are reliable and comparable.

Spectral Retinal Images Reconstruction

While red-green-blue (RGB) image of retina has quite limited information, retinal multispectral images provide both spatial and spectral information which could enhance the capability of exploring the eye-related problems in their early stages. In this thesis, two learning-based algorithms for reconstructing of spectral retinal images from the RGB images are developed by a two-step manner. First, related previous techniques are reviewed and studied. Then, the most suitable methods are enhanced and combined to have new algorithms for the reconstruction of spectral retinal images. The proposed approaches are based on radial basis function network to learn a mapping from tristimulus colour space to multi-spectral space. The resemblance level of reproduced spectral images and original images is estimated using spectral distance metrics spectral angle mapper, spectral correlation mapper, and spectral information divergence, which show a promising result from the suggested algorithms.

Large amplitude motions in the S1 state of formic acid /

A detailed theoretical investigation of the large amplitude motions in the S, excited electronic state of formic acid (HCOOH) was done. This study focussed on the the S, «- So electronic band system of formic acid (HCOOH). The torsion and wagging large amplitude motions of the S, were considered in detail. The potential surfaces were simulated using RHF/UHF ab-initio calculations for the two electronic states. The energy levels were evaluated by the variational method using free rotor basis functions for the torsional coordinates and harmonic oscillator basis functions for the wagging coordinates. The simulated spectrum was compared to the slit-jet-cooled fluorescence excitation spectrum allowing for the assignment of several vibronic bands. A rotational analysis of certain bands predicted that the individual bands are a mixture of rotational a, b and c-type components.The electronically allowed transition results in the c-type or Franck-Condon band and the electronically forbidden, but vibronically allowed transition creates the a/b-type or Herzberg-Teller components. The inversion splitting between these two band types differs for each band. The analysis was able to predict the ratio of the a, b and c-type components of each band.

Modes de représentation pour l'éclairage en synthèse d'images

Réalisé en cotutelle avec l'Université Bordeaux 1 (France)

Non-negative matrix decomposition approaches to frequency domain analysis of music audio signals

On étudie l’application des algorithmes de décomposition matricielles tel que la Factorisation Matricielle Non-négative (FMN), aux représentations fréquentielles de signaux audio musicaux. Ces algorithmes, dirigés par une fonction d’erreur de reconstruction, apprennent un ensemble de fonctions de base et un ensemble de coef- ficients correspondants qui approximent le signal d’entrée. On compare l’utilisation de trois fonctions d’erreur de reconstruction quand la FMN est appliquée à des gammes monophoniques et harmonisées: moindre carré, divergence Kullback-Leibler, et une mesure de divergence dépendente de la phase, introduite récemment. Des nouvelles méthodes pour interpréter les décompositions résultantes sont présentées et sont comparées aux méthodes utilisées précédemment qui nécessitent des connaissances du domaine acoustique. Finalement, on analyse la capacité de généralisation des fonctions de bases apprises par rapport à trois paramètres musicaux: l’amplitude, la durée et le type d’instrument. Pour ce faire, on introduit deux algorithmes d’étiquetage des fonctions de bases qui performent mieux que l’approche précédente dans la majorité de nos tests, la tâche d’instrument avec audio monophonique étant la seule exception importante.

Les algorithmes de haute résolution en tomographie d'émission par positrons : développement et accélération sur les cartes graphiques

La tomographie d’émission par positrons (TEP) est une modalité d’imagerie moléculaire utilisant des radiotraceurs marqués par des isotopes émetteurs de positrons permettant de quantifier et de sonder des processus biologiques et physiologiques. Cette modalité est surtout utilisée actuellement en oncologie, mais elle est aussi utilisée de plus en plus en cardiologie, en neurologie et en pharmacologie. En fait, c’est une modalité qui est intrinsèquement capable d’offrir avec une meilleure sensibilité des informations fonctionnelles sur le métabolisme cellulaire. Les limites de cette modalité sont surtout la faible résolution spatiale et le manque d’exactitude de la quantification. Par ailleurs, afin de dépasser ces limites qui constituent un obstacle pour élargir le champ des applications cliniques de la TEP, les nouveaux systèmes d’acquisition sont équipés d’un grand nombre de petits détecteurs ayant des meilleures performances de détection. La reconstruction de l’image se fait en utilisant les algorithmes stochastiques itératifs mieux adaptés aux acquisitions à faibles statistiques. De ce fait, le temps de reconstruction est devenu trop long pour une utilisation en milieu clinique. Ainsi, pour réduire ce temps, on les données d’acquisition sont compressées et des versions accélérées d’algorithmes stochastiques itératifs qui sont généralement moins exactes sont utilisées. Les performances améliorées par l’augmentation de nombre des détecteurs sont donc limitées par les contraintes de temps de calcul. Afin de sortir de cette boucle et permettre l’utilisation des algorithmes de reconstruction robustes, de nombreux travaux ont été effectués pour accélérer ces algorithmes sur les dispositifs GPU (Graphics Processing Units) de calcul haute performance. Dans ce travail, nous avons rejoint cet effort de la communauté scientifique pour développer et introduire en clinique l’utilisation des algorithmes de reconstruction puissants qui améliorent la résolution spatiale et l’exactitude de la quantification en TEP. Nous avons d’abord travaillé sur le développement des stratégies pour accélérer sur les dispositifs GPU la reconstruction des images TEP à partir des données d’acquisition en mode liste. En fait, le mode liste offre de nombreux avantages par rapport à la reconstruction à partir des sinogrammes, entre autres : il permet d’implanter facilement et avec précision la correction du mouvement et le temps de vol (TOF : Time-Of Flight) pour améliorer l’exactitude de la quantification. Il permet aussi d’utiliser les fonctions de bases spatio-temporelles pour effectuer la reconstruction 4D afin d’estimer les paramètres cinétiques des métabolismes avec exactitude. Cependant, d’une part, l’utilisation de ce mode est très limitée en clinique, et d’autre part, il est surtout utilisé pour estimer la valeur normalisée de captation SUV qui est une grandeur semi-quantitative limitant le caractère fonctionnel de la TEP. Nos contributions sont les suivantes : - Le développement d’une nouvelle stratégie visant à accélérer sur les dispositifs GPU l’algorithme 3D LM-OSEM (List Mode Ordered-Subset Expectation-Maximization), y compris le calcul de la matrice de sensibilité intégrant les facteurs d’atténuation du patient et les coefficients de normalisation des détecteurs. Le temps de calcul obtenu est non seulement compatible avec une utilisation clinique des algorithmes 3D LM-OSEM, mais il permet également d’envisager des reconstructions rapides pour les applications TEP avancées telles que les études dynamiques en temps réel et des reconstructions d’images paramétriques à partir des données d’acquisitions directement. - Le développement et l’implantation sur GPU de l’approche Multigrilles/Multitrames pour accélérer l’algorithme LMEM (List-Mode Expectation-Maximization). L’objectif est de développer une nouvelle stratégie pour accélérer l’algorithme de référence LMEM qui est un algorithme convergent et puissant, mais qui a l’inconvénient de converger très lentement. Les résultats obtenus permettent d’entrevoir des reconstructions en temps quasi-réel que ce soit pour les examens utilisant un grand nombre de données d’acquisition aussi bien que pour les acquisitions dynamiques synchronisées. Par ailleurs, en clinique, la quantification est souvent faite à partir de données d’acquisition en sinogrammes généralement compressés. Mais des travaux antérieurs ont montré que cette approche pour accélérer la reconstruction diminue l’exactitude de la quantification et dégrade la résolution spatiale. Pour cette raison, nous avons parallélisé et implémenté sur GPU l’algorithme AW-LOR-OSEM (Attenuation-Weighted Line-of-Response-OSEM) ; une version de l’algorithme 3D OSEM qui effectue la reconstruction à partir de sinogrammes sans compression de données en intégrant les corrections de l’atténuation et de la normalisation dans les matrices de sensibilité. Nous avons comparé deux approches d’implantation : dans la première, la matrice système (MS) est calculée en temps réel au cours de la reconstruction, tandis que la seconde implantation utilise une MS pré- calculée avec une meilleure exactitude. Les résultats montrent que la première implantation offre une efficacité de calcul environ deux fois meilleure que celle obtenue dans la deuxième implantation. Les temps de reconstruction rapportés sont compatibles avec une utilisation clinique de ces deux stratégies.

Multilevel Analysis of Trunk Surface Measurements for Noninvasive Assessment of Scoliosis Deformities.

Study Design. Reliability study. Objectives. To assess between-acquisition reliability of new multilevel trunk cross sections measurements, in order to define what is a real change when comparing 2 trunk surface acquisitions of a same patient, before and after surgery or throughout the clinical monitoring. Summary of Background Data. Several cross-sectional surface measurements have been proposed in the literature for noninvasive assessment of trunk deformity in patients with adolescent idiopathic scoliosis (AIS). However, only the maximum values along the trunk are evaluated and used for monitoring progression and assessing treatment outcome. Methods. Back surface rotation (BSR), trunk rotation (TR), and coronal and sagittal trunk deviation are computed on 300 cross sections of the trunk. Each set of 300 measures is represented as a single functional data, using a set of basis functions. To evaluate between-acquisition variability at all trunk levels, a test-retest reliability study is conducted on 35 patients with AIS. A functional correlation analysis is also carried out to evaluate any redundancy between the measurements. Results. Each set of 300 measures was successfully described using only 10 basis functions. The test-retest reliability of the functional measurements is good to very good all over the trunk, except above the shoulders level. The typical errors of measurement are between 1.20° and 2.2° for the rotational measures and between 2 and 6 mm for deviation measures. There is a very strong correlation between BSR and TR all over the trunk, a moderate correlation between coronal trunk deviation and both BSR and TR, and no correlation between sagittal trunk deviation and any other measurement. Conclusion. This novel representation of trunk surface measurements allows for a global assessment of trunk surface deformity. Multilevel trunk measurements provide a broader perspective of the trunk deformity and allow a reliable multilevel monitoring during clinical follow-up of patients with AIS and a reliable assessment of the esthetic outcome after surgery.

Face Recognition using Probabilistic Neural Networks

In this paper we address the problem of face detection and recognition of grey scale frontal view images. We propose a face recognition system based on probabilistic neural networks (PNN) architecture. The system is implemented using voronoi/ delaunay tessellations and template matching. Images are segmented successfully into homogeneous regions by virtue of voronoi diagram properties. Face verification is achieved using matching scores computed by correlating edge gradients of reference images. The advantage of classification using PNN models is its short training time. The correlation based template matching guarantees good classification results

Face Recognition using Probabilistic Neural Networks

n this paper we address the problem of face detection and recognition of grey scale frontal view images. We propose a face recognition system based on probabilistic neural networks (PNN) architecture. The system is implemented using voronoi/ delaunay tessellations and template matching. Images are segmented successfully into homogeneous regions by virtue of voronoi diagram properties. Face verification is achieved using matching scores computed by correlating edge gradients of reference images. The advantage of classification using PNN models is its short training time. The correlation based template matching guarantees good classification results.

A System for Offline Recognition of Handwritten Characters in Malayalam Script

In this paper, we propose a handwritten character recognition system for Malayalam language. The feature extraction phase consists of gradient and curvature calculation and dimensionality reduction using Principal Component Analysis. Directional information from the arc tangent of gradient is used as gradient feature. Strength of gradient in curvature direction is used as the curvature feature. The proposed system uses a combination of gradient and curvature feature in reduced dimension as the feature vector. For classification, discriminative power of Support Vector Machine (SVM) is evaluated. The results reveal that SVM with Radial Basis Function (RBF) kernel yield the best performance with 96.28% and 97.96% of accuracy in two different datasets. This is the highest accuracy ever reported on these datasets

Image Denoising Using Sure-Based Adaptive Thresholding In Directionlet Domain

The standard separable two dimensional wavelet transform has achieved a great success in image denoising applications due to its sparse representation of images. However it fails to capture efficiently the anisotropic geometric structures like edges and contours in images as they intersect too many wavelet basis functions and lead to a non-sparse representation. In this paper a novel de-noising scheme based on multi directional and anisotropic wavelet transform called directionlet is presented. The image denoising in wavelet domain has been extended to the directionlet domain to make the image features to concentrate on fewer coefficients so that more effective thresholding is possible. The image is first segmented and the dominant direction of each segment is identified to make a directional map. Then according to the directional map, the directionlet transform is taken along the dominant direction of the selected segment. The decomposed images with directional energy are used for scale dependent subband adaptive optimal threshold computation based on SURE risk. This threshold is then applied to the sub-bands except the LLL subband. The threshold corrected sub-bands with the unprocessed first sub-band (LLL) are given as input to the inverse directionlet algorithm for getting the de-noised image. Experimental results show that the proposed method outperforms the standard wavelet-based denoising methods in terms of numeric and visual quality

Quasi-Interpolation von Funktionen und Anwendungen auf Potentialprobleme

Ausgangspunkt der Dissertation ist ein von V. Maz'ya entwickeltes Verfahren, eine gegebene Funktion f : Rn ! R durch eine Linearkombination fh radialer glatter exponentiell fallender Basisfunktionen zu approximieren, die im Gegensatz zu den Splines lediglich eine näherungsweise Zerlegung der Eins bilden und somit ein für h ! 0 nicht konvergentes Verfahren definieren. Dieses Verfahren wurde unter dem Namen Approximate Approximations bekannt. Es zeigt sich jedoch, dass diese fehlende Konvergenz für die Praxis nicht relevant ist, da der Fehler zwischen f und der Approximation fh über gewisse Parameter unterhalb der Maschinengenauigkeit heutiger Rechner eingestellt werden kann. Darüber hinaus besitzt das Verfahren große Vorteile bei der numerischen Lösung von Cauchy-Problemen der Form Lu = f mit einem geeigneten linearen partiellen Differentialoperator L im Rn. Approximiert man die rechte Seite f durch fh, so lassen sich in vielen Fällen explizite Formeln für die entsprechenden approximativen Volumenpotentiale uh angeben, die nur noch eine eindimensionale Integration (z.B. die Errorfunktion) enthalten. Zur numerischen Lösung von Randwertproblemen ist das von Maz'ya entwickelte Verfahren bisher noch nicht genutzt worden, mit Ausnahme heuristischer bzw. experimenteller Betrachtungen zur sogenannten Randpunktmethode. Hier setzt die Dissertation ein. Auf der Grundlage radialer Basisfunktionen wird ein neues Approximationsverfahren entwickelt, welches die Vorzüge der von Maz'ya für Cauchy-Probleme entwickelten Methode auf die numerische Lösung von Randwertproblemen überträgt. Dabei werden stellvertretend das innere Dirichlet-Problem für die Laplace-Gleichung und für die Stokes-Gleichungen im R2 behandelt, wobei für jeden der einzelnen Approximationsschritte Konvergenzuntersuchungen durchgeführt und Fehlerabschätzungen angegeben werden.

Approximate Approximations and a Boundary Point Method for the Linearized Stokes System

The method of approximate approximations, introduced by Maz'ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Stokes problem in the whole space and for the Stokes boundary value problem in a bounded convex domain G subset R^2, where the second part consists of three steps: In a first step the unknown potential density is replaced by a linear combination of exponentially decreasing basis functions concentrated near the boundary points. In a second step, integration over the boundary partial G is replaced by integration over the tangents at the boundary points such that even analytical expressions for the potential approximations can be obtained. In a third step, finally, the linear algebraic system is solved to determine an approximate density function and the resulting solution of the Stokes boundary value problem. Even not convergent the method leads to an efficient approximation of the form O(h^2) + epsilon, where epsilon can be chosen arbitrarily small.

An attempt on the calculation of relativistic potential energy curves: noble gas difluorides

Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr - F and Xe - F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF_2 may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF_2 and XeF_2 to within 2 eV.

Relativistic Dirac-Fock-Slater program to calculate potential-energy curves for diatomic molecules

A LCAO-MO (linear combination of atomic orbitals - molecular orbitals) relativistic Dirac-Fock-Slater program is presented, which allows one to calculate accurate total energies for diatomic molecules. Numerical atomic Dirac-Fock-Slater wave functions are used as basis functions. All integrations as well as the solution of the Poisson equation are done fully numerical, with a relative accuracy of 10{^-5} - 10{^-6}. The details of the method as well as first results are presented here.