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Stochastisch-geometrische Beschreibung, Filterung und Präsentation des Reliefs / Andrzej Borkowski (1994)
Titre : Stochastisch-geometrische Beschreibung, Filterung und Präsentation des Reliefs Titre original : [Description géométrique aléatoire, filtrage et présentation du relief] Type de document : Thèse/HDR Auteurs : Andrzej Borkowski, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1994 Collection : DGK - C Sous-collection : Dissertationen num. 431 Importance : 85 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 3-7696-9474-4 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Photogrammétrie numérique
[Termes IGN] discrétisation
[Termes IGN] entropie
[Termes IGN] filtrage linéaire
[Termes IGN] modèle numérique de terrain
[Termes IGN] représentation discrèteIndex. décimale : 33.30 Photogrammétrie numérique Résumé : (Auteur) This Doctoral thesis covers two main items: the linear relief filtering with restrictions and the discretization of relief without information loss. The modelling of the relief, which is assumed to be a realization of a two-dimensional normal, homogeneous, and bandlimited stochastic process, is based on the theory of stochastic processes. The adequacy of the model choice and its assumptions has been verified using some natural reliefs of the Earth's surface.
Concerning linear filtering the following quantity and quality restrictions were used: preservation of relief shape, of volume, of terrain inclination and finally, the reduction of relative extremums according to Toepfer's choice rule are expressed in stochastic process terminology. The above conditions are realized by the two-dimensional, non-recursive, digital linear filtering (e.g. for generalization purposes, for relief smoothing using digital data). In order to estimate the required parameters the complete knowledge of second order process quantities (autocovariance function or spectral density) is necessary. Numerical experiments with different relief types stored in digital terrain models (DTM) confirmed the possibility of practical realization of linear filtering with restrictions.
The conventional sampling theorem concerning bandlimited random signals is based on the discretization of the abscissa. In opposite to that, the contour line representation of the relief corresponds to a discretization on the ordinate. Sampling rules according to the ordinate, consistent with the original sampling theorem, are given for both one-dimensional and two-dimensional continuous stochastic processes and additionally for discrete signals (time series). Vertical and horizontal intervals of discretization relate to each other by the correlation coefficients of neighboured signal values for discrete signals or by the second order moment of terrain inclination for continuous processes. An estimation approach for optimum grid cell size of DTM interpolated from topographic maps is proposed. This grid ensures a complete as well as a non-redundant data capture from contour line information. The approach is based on the relation between vertical and horizontal intervals of discretization. The necessary parameter i.e. the variance of terrain inclination is estimated using measured lengths of contour lines at different height levels. The consistence of the discretization rules has been confirmed by numerical experiments.Numéro de notice : 28057 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63404 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 28057-01 33.30 Livre Centre de documentation Photogrammétrie - Lasergrammétrie Disponible 28057-02 33.30 Livre Centre de documentation Photogrammétrie - Lasergrammétrie Disponible Initiation géo-graphique / Eric Blin (1993)
Titre : Initiation géo-graphique : Comment visualiser son information Type de document : Guide/Manuel Auteurs : Eric Blin, Auteur ; Jean-Paul Bord, Auteur Editeur : Paris : SEDES Année de publication : 1993 Importance : 284 p. Format : 15 x 21 cm ISBN/ISSN/EAN : 978-2-7181-9326-7 Note générale : Bibliographie Langues : Français (fre) Descripteur : [Vedettes matières IGN] Cartographie
[Termes IGN] analyse multivariée
[Termes IGN] carte analytique
[Termes IGN] carte synthétique
[Termes IGN] cartographie thématique
[Termes IGN] diagramme
[Termes IGN] discrétisation
[Termes IGN] représentation graphique
[Termes IGN] sémiologie graphique
[Termes IGN] variable visuelle
[Termes IGN] visualisation cartographiqueIndex. décimale : 39.00 Cartographie - généralités - Cartologie Résumé : (Editeur) Cet ouvrage pratique, avec exercices, s'adresse plus particulièrement à des étudiants de premier et second cycles, mais aussi à tous ceux (enseignants, chercheurs, chargés d'étude, décideurs...) qui désirent visualiser au mieux leur information. Il se veut un guide utile, indispensable même, pour produire des cartes, mais pas n'importe quelles cartes, et aussi pour s'interroger sur la carte, image, représentation du réel. Note de contenu : Initiation à la graphique
Qu'est-ce qu'une carte ? Et pourquoi parler de géo-graphique ? Image et communication
Les moyens et les règles du système graphique
Comment utiliser les variables visuelles ? Quelles sont les grandes règles à respecter ? Les cartes à un caractère ou cartes analytiques
Un caractère géographique, un caractère différentiel, en implantation ponctuelle, linéaire et zonale
La discrétisation
Un caractère géographique, un caractère quantitatif, en implantation ponctuelle et linéaire
Un caractère géographique, un caractère quantitatif, en implantation zonale
Réseaux, courbes et diagrammes
Les réseaux
Les courbes
Comment construire un diagramme ? Pondération
Echelle propre
Echelle commune
Les principaux types de diagrammes
Les cartes à plusieurs caractères ou cartes de synthèse
Collection de cartes et (ou) carte de synthèse
Les cartes de superposition
Les cartes par bandes
La matrice ordonnable
Le fichier-image et le fichier-matrice
Nouvelles approches, nouvelles représentations
Le traitement statistique multivarié
Transformations cartographiques
Les modèles graphiques en géographie
L'espace manipulé par les cartesNuméro de notice : 34760 Affiliation des auteurs : non IGN Thématique : GEOMATIQUE Nature : Manuel de cours Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=47407 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 34760-01 39.00 Livre Centre de documentation Cartographie Disponible 34760-02 39.00 Livre Centre de documentation Cartographie Disponible 34760-03 DEP-ELD Livre Marne-la-Vallée Dépôt en unité Exclu du prêt Lösung des fixen geodätischen Randwertproblems mit Hilfe der Randelementmethode / R. Klees (1992)
Titre : Lösung des fixen geodätischen Randwertproblems mit Hilfe der Randelementmethode Titre original : [Solution du problème géodésique de valeurs aux limites à l'aide de la méthode des éléments résiduels] Type de document : Thèse/HDR Auteurs : R. Klees, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1992 Collection : DGK - C Sous-collection : Dissertationen num. 382 Importance : 314 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9428-4 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Géodésie physique
[Termes IGN] discrétisation
[Termes IGN] équation intégrale
[Termes IGN] linéarisation
[Termes IGN] problème des valeurs limitesIndex. décimale : 30.40 Géodésie physique Résumé : (Auteur)The présent study deals with thé numerical solution of thé fixed geodetic boundary value problem (bvp) using thé boundary élément method. Assuming a continuous covering of thé Earth's surface with gravity values thé mathematical formulation leads to a nonlinear outer bvp for thé Laplace-operator in three dimensional euclidean space.
The theoretical part starts in section 1 with some of thé most important mathematical foundations we need such as properties of boundary surfaces embedded in R3, strongly singular surface intégrais, some aspects of thé theory of pseudodifferential operators and singular intégral operators forming thé theoretical frame for thé whole convergence analysis and finally some détails from thé theory of (bivariate) spline functions. Section 2 contains thé mathematical formulation of thé fixed geodetic bvp and gives a short overview over known geodetic literatures concerning this problem. Local existence and uniqueness assertions both in Hôlder and Sobolev spaces are given based on thé implicit function theorem of Hildebrandt and Graves. Besides, thé convergence of a perturbation expansion is shown based on an idea of Jorge (1987) leading to a constructive method for thé solution of thé nonlinear problem in Hôlder spaces. In both cases thé nonlinear problem is transformed into a séries of linear ones which can be classified as oblique bvps. Under thé assumption of their regularity thé Fredholm alternative is valid not only in thé case of Hôlder spaces but also in Sobolev spaces so that uniqueness implies existence. The uniqueness can be proved in both cases using thé generalized maximum principle of Hopf. The very restrictive requirement F e C3 in thé case of Sobolev spaces can be weakened under some suppositions so that F e G1*" is sufficient to apply thé maximum principle. Therefore thé nonlinear fixed bvp can be solved iteratively where in each step a classi-cal oblique bvp arises being thé subject of thé next sections.
Both direct and indirect methods are discussed in section 4 to transform thé oblique boundary value prob-lem into an intégral équation leading to équations of différent types like strongly singular or hypersingular équations of thé second kind depending on thé methods used. It is shown that thé strongly singular intégral équation resulting from thé représentation of thé unknown disturbing potential as single layer potential is thé most appropriate one especially from thé numerical point of view. The principal symbol of this intégral operator is determined and it is proved that our intégral operator is strongly elliptic if and only if thé oblique direction is never tangential to thé Earth's surface, i.e. thé strong ellipticity is not automatically fulfilled by our intégral operator but has to be demanded explicitly.
For thé transformation of thé intégral équation into a finite dimensional lirfear System différent discreti-zation methods are disussed in section 5 like allocation, Galerkin and least squares. It is shown that GalerkinBubnov discretization is thé best compromise between thé numerical effort, thé properties of thé boundary intégral operator to assure thé convergence of thé discretization procédure and thé order of convergence. For thé convergence of thé GalerkinBubnov method we need thé strong ellipticity of thé boundary intégral operator bringing on thé coerciveness in thé form of a Garding's inequality being thé starting point for thé whole convergence analysis. Section 6 contains thé définition of thé boundary élément method including thé pros and cons in relation to finite élément methods, thé définition of thé test and trial functions consisting of polynomial finite élément functions on thé boundary. Besides, thé coefficients of thé linear System for GalerkinBubnov discretization using piecewise constant test and trial functions are derived. In section 7 a nearly complète error analysis in Sobolev spaces is given, considering both discreti-zation and numerical cubature errors and giving thé state of thé art in estimating thé influence of surface approximation errors. Under thé assumption of strong ellipticity, being équivalent to thé positive definiteness of thé principal symbol of thé boundary intégral operator, it is shown that ail Galerkin methods are stable and converge. The asymptotic order of convergence is quasioptimal i.e. it has thé same order as thé best approximation of thé theoretical solution by our boundary élément trial functions. For piecewise constant functions a convergence of thé order 0(h2) for h-iO is proved if we measure thé error in thé Sobolev norm H''(F). This implies convergence of thé same order for thé potential in points away from thé boundary surface in any norm.
The numerical part mainly deals with thé development of efficient methods for thé approximation and représentation of parts of thé Earth's surface and of cubature formulas for calculating thé coefficients of thé linear System and thé potential in thé Earth's outer space. It is shown in section 9 that Overhauser splines and bicubic BSplines are very suitable for thé approximation and représentation of thé boundary surface and superior to many other methods. For 1 1 km2 boundary éléments this leads to mean approximation errors of approximately 810 m where larger errors are possible depending on thé roughness of thé real topography. For thé représentation of thé surface normal field it is also shown that Overhauser splines are thé most appropriate approximation especially for finer grids.
In Section 10 thé problem of efficient cubatures is considered for calculating thé coefficients of thé linear System defined by single and double intégrais over boundary éléments where both regular, weakly singular, strongly singular and quasisingular intégrais arise. Several cubature formulas for thé différent types of intégrais are considered. Extensive analytical and numerical developments show their efficiency compared with other cubature formulas used in engineering sciences. A detailed analysis shows that thé highly prob-
lematic strongly singular intégrais can be calculated analytically and that thé resulting kernel has a loga-rithmic singularity over thé whole boundary of thé fini te élément.
A local solution is calculated for a région of size 100-100 km2 using 10000 boundary éléments. The GalerkinBubnov discretization with piecewise constant trial functions leads to a dense unsymmetric linear System of thé order 10000-10000 with approximately 108 coefficients. In order to achieve a relative accuracy of at least 10'3 - 10'4 for each coefficient setting up thé linear System takes about 1 CPU-hour. In section 11.2 an efficient direct équation solver is developed based on a LUfactorization using a spécial Gaussian élimination well adapted to thé architecture of thé pipeline computer Siemens/Fujitsu VP 400-EX resp. S400/10. It is shown that thé time for thé I/O opérations can be reduced by minimizing thé amount of data to be transferred and by speeding up thé I/Oopérations using spécial runtime options of thé operational System and asynchronous I/O so that CPUusage and I/O opérations are done in parallel. The test compu-tations show that thé linear System mentioned before can be solved in approximately 10.5 resp. 7 minutes corresponding to a performance of 1.1 resp. 1.6 GFLOPS. In section 11.4 thé well-conditioning of thé linear System is proved leading to a very small sensitivity against errors of thé input data; thé influence of round off errors is proved to be below 10-". The local solution is based on thé use of a degree and order 360 spherical harmonie expansion of thé gravitational potential as référence potential and thé neglect of thé outer zone. As a detailed analysis shows, this leads to large errors only near by thé boundary of thé local région and a drastic decrease of thé layer density errors with increasing distance from thé boundary so that only relative différences of thé order 10'3 10'5 occur in most parts of our local région.
In section 12 thé calculation of thé gravitational potential in points of thé Earth's outer space is considered. Efficient cubatures for thé numerical calculation of thé single layer potential are developed especially for points near by thé Earth's surface, and they are compared with other cubatures used in engineering sciences. The results show that such formulas can be found based on spécial parameter transformations smoothing out thé strong variation of thé integrand in points near by both thé Earth's surface and thé boundary of thé fmite élément. '
Section 13 contains some proposais for future work which has to be done in relation to thé numerical sol-ution of thé fixed geodetic bvp and thé boundary élément method.Numéro de notice : 28089 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63436 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 28089-01 30.40 Livre Centre de documentation Géodésie Disponible 28089-02 30.40 Livre Centre de documentation Géodésie Disponible Fundamentals of pattern recognition / Monique Pavel (1989)
Titre : Fundamentals of pattern recognition Type de document : Guide/Manuel Auteurs : Monique Pavel, Auteur Mention d'édition : 1ère édition Editeur : New York : Marcel Dekker, Inc. Année de publication : 1989 Collection : Pure and applied mathematics Importance : 183 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-0-8247-8025-8 Langues : Français (fre) Descripteur : [Vedettes matières IGN] Traitement d'image
[Termes IGN] classification
[Termes IGN] discrétisation
[Termes IGN] reconnaissance de formes
[Termes IGN] topologieIndex. décimale : 35.20 Traitement d'image Numéro de notice : 58588 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Manuel de cours Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=60391 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 58588-01 35.20 Livre Centre de documentation Télédétection Disponible Analyse und Optimierung geodätischer Netze nach spektralen Kriterien und mechanische Analogien / R. Jäger (1988)
Titre : Analyse und Optimierung geodätischer Netze nach spektralen Kriterien und mechanische Analogien Titre original : [Analyse et optimisation des réseaux géodésiques d'après des critères spectraux et des analogies mécaniques] Type de document : Thèse/HDR Auteurs : R. Jäger, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1988 Collection : DGK - C Sous-collection : Dissertationen num. 342 Importance : 135 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-9390-4 Note générale : Bibliographie Langues : Allemand (ger) Descripteur : [Vedettes matières IGN] Systèmes de référence et réseaux
[Termes IGN] élasticité
[Termes IGN] matrice
[Termes IGN] méthode des éléments finis
[Termes IGN] optimisation (mathématiques)
[Termes IGN] quantité discrète
[Termes IGN] réseau géodésique
[Termes IGN] valeur propreIndex. décimale : 30.10 Systèmes de référence et réseaux géodésiques Résumé : (Auteur) According to the expression 'spectral criterions' this thesis is dealing - within the analysis and optimisation of geodetic networks - with mathematical models describable as eigenvalue problems connected with the variance-covariance matrix of network-coordinates. The eigenvalues and eigenvectors serve as spectral criterions for network analysis and as spectral target functions for network optimisation respectively.
A first network analysis model consists in the comparison of the appropriate variance-covariance matrix with an ideal criterion-matrix, and is based on the general eigenvalue problem of these matrices. Theoretical investigations concerning thereby the problem of choice of datum lead to a unification of hitherto existing approaches in form of a datum-invariant substitutive eigenvalue problem. A second consideration is due to the simple eigenvalue-problem of the variance-covariance matrix of the network-coordinates itself. A therefore developed filter model includes the influence of a weak datum on the spectral criterions as well as a separation between the inner geometry of the regarded network and its absolute foundation. The theoretical studies are completed and further extended by network examples.
The analysis of geodetic networks by means of the simple eigenvalue problem of its variance-covariance matrix of coordinates is closely linked to the kinetics, especially to the eigen-vibrations of elastic mechanical structures. Proceeding from the elastic continuum, the complete foundation of analogies between elastomechanics and geodetic network-compensation by least squares can be carried out in the step of its finite-element-discretisation, being based fundamentally ('fundamental analogies') on equivalent principles, of variations. The well-known analogies between particular corresponding finite elements and geodetic observational types are thereby included and resulting as a special case (denoted as 'direct analogies') of the so cal-led 'principal analogies', which are not at all depending on special types of elements. The principal analogies are forming the central kernel of the treated concept of analogy-foundation. In the sense of a complete analogy-foundation the very principal analogies at the same time represent the link to the way back to the differential equations of the adjoint continuum structures. The differential equations are traced back to their dependence to network-design (pattern), the observational types/elements and their weight-parameterisation). For the purpose of a general derivation of differential equations of regularly designed geodetic networks, there is developed a procedure with an algorithmic nature which is also be applicable to mechanical structures. The mechanical analogies in the matrix equations and differential equations turn out to be useful for the interpretation of the eigenvector-shapes and the eigenvalue-spectrum within the above mentioned geodetic network analysis. For geodetic networks of high density the spectral analysis can advantageously be performed directly by the solution of the differential equations of the (elastic) continuum. The theoretical parts of this chapter are underpinned by appropriate examples.
As inversion of the network analysis with spectral criterions this thesis is (to its second main part) further on dealing with the optimisation on spectral target functions. The chapters of optimisation are introduced by preliminary theoretical research concerning the influence of single observations on the spectral characteristics of a network and with the possibilities of modifying the eigenvalue-spectrum and the eigenvectors by changing observation-weights, design (graph) and nodal point-positions respectively within the network. As for the spectral optimisation concerning 2nd/3rd Order Design and 1st Order Design of point observations, this theoretical framework turns out that the aims of these optimisation-designs can be achieved by target functions limited to the eigenvalues of the above-mentioned eigenvalue problems. The concept of optimisation leads - mathematically spoken - to the problem of solving different associated inverse eigenvalue problems with respect to prescribed target-spectra. For all interesting eigenvalue problems and intended optimisation problems of the above-mentioned designs there can be found a unified iterative solution procedure referring to the normal equations as kernel. The particular eigenvalue problem of optimisation as well as partly required datum-changes are realized by specific transformations within this iteration procedure.
As concerns the final representation of some results of the spectral estimation method, a first attention is - above mechanical aspects - paid to the theoretically founded accordance between the results obtained by classical optimisation and those of spectral optimisation in 2nd/3rd Order Design of classical observation types (applying thereby the corresponding model of the general eigenvalue problem due to a criterion matrix). The second point of interest is mainly dedicated to the results and network examples concerning 1st Order Design appearing as the problem of determining optimum supporting-point observations in geodetic networks; this is quite a dual problem between pure 1st Order Design (optimum positions of these points) and 2nd/3rd Order Design (optimum weights of these point-observations).
The optimisation concerning point observations is representing a new component within geodetic network optimisation. Besides the problem of ideal positions for linking free networks (for ex-ample railway network-chains) to points of the superior network, this kind of optimisation is actually getting more and more important with regard to the quest/ion of finding out best positions for supporting classical terrestrial networks by GPS-point-positioning.Numéro de notice : 28104 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Thèse étrangère Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=63451 Réservation
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