Destructive diseases of the lung like lung cancer or fibrosis are still often lethal. Also in case of fibrosis in the liver, the only possible cure is transplantation. In this thesis, we investigate 3D micro computed synchrotron radiation (SR\( \mu \)CT) images of capillary blood vessels in mouse lungs and livers. The specimen show so-called compensatory lung growth as well as different states of pulmonary and hepatic fibrosis. During compensatory lung growth, after resecting part of the lung, the remaining part compensates for this loss by extending into the empty space. This process is accompanied by an active vessel growing. In general, the human lung can not compensate for such a loss. Thus, understanding this process in mice is important to improve treatment options in case of diseases like lung cancer. In case of fibrosis, the formation of scars within the organ's tissue forces the capillary vessels to grow to ensure blood supply. Thus, the process of fibrosis as well as compensatory lung growth can be accessed by considering the capillary architecture. As preparation of 2D microscopic images is faster, easier, and cheaper compared to SR\( \mu \)CT images, they currently form the basis of medical investigation. Yet, characteristics like direction and shape of objects can only properly be analyzed using 3D imaging techniques. Hence, analyzing SR\( \mu \)CT data provides valuable additional information. For the fibrotic specimen, we apply image analysis methods well-known from material science. We measure the vessel diameter using the granulometry distribution function and describe the inter-vessel distance by the spherical contact distribution. Moreover, we estimate the directional distribution of the capillary structure. All features turn out to be useful to characterize fibrosis based on the deformation of capillary vessels. It is already known that the most efficient mechanism of vessel growing forms small torus-shaped holes within the capillary structure, so-called intussusceptive pillars. Analyzing their location and number strongly contributes to the characterization of vessel growing. Hence, for all three applications, this is of great interest. This thesis provides the first algorithm to detect intussusceptive pillars in SR\( \mu \)CT images. After segmentation of raw image data, our algorithm works automatically and allows for a quantitative evaluation of a large amount of data. The analysis of SR\( \mu \)CT data using our pillar algorithm as well as the granulometry, spherical contact distribution, and directional analysis extends the current state-of-the-art in medical studies. Although it is not possible to replace certain 3D features by 2D features without losing information, our results could be used to examine 2D features approximating the 3D findings reasonably well.

Photolysiert man [{Cp R Ru(CO)2}2] (Cp R = Cp", Cp*) (1a,b), in Gegenwart von weißem Phosphor, so können keine phosphorhaltigen Produkte isoliert werden. Setzt man [{Cp"Ru(CO)2}2] (1a) mit weißem Phosphor bei 190 °C in Dekalin um, dann lassen sich als einzige Verbindungen das Pentaphospharuthenocen-Derivat [Cp"Ru(h 5 -P5)] (3a, 6 % Ausbeute) und [Cp"2Ru2P4] (4a, 17 % Ausbeute) säulenchromatographisch abtrennen. Für 4a wird auf Grund seiner spektroskopischen Eigenschaften eine den röntgenstruktur-analytisch charakterisierten pseudo-Tripeldecker-Komplexen [{Cp R Fe}2(micro-h 4:4 -P4)] (Cp R = Cp" [35] , Cp"' [11] ) analoge Struktur mit s-cis-Tetraphosphabutadiendiyl-"Mitteldeck" vorgeschlagen; es sind jedoch auch zwei micro-h 2:2 -P2-Liganden denkbar. Die Cothermolyse von [{Cp"Ru(CO)2}2] (1a) und [Cp*Fe(h 5 -P5)] (2b) ergibt ein breites Produktbild. Während [Cp"Ru(h 5 -P5)] (3a), das chromatographisch nicht von 2b abgetrennt werden konnte, und [Cp"2Ru2P4] (4a, 6 % Ausbeute) in vergleichsweise geringen Mengen entstehen, können [{Cp"Ru}3P5] (6) in 17 % Ausbeute, [{Cp"Ru}2{Cp*Fe}P5] (7) in 7 % Ausbeute, [{Cp*Fe}2{Cp"Ru}P5] (8) in 22 % Ausbeute und [{Cp"Ru}3{Cp*Fe}(P2)2] (9) in 14 % Ausbeute isoliert werden. Für 9 wird, basierend auf den NMR-spektroskopischen Befunden, eine zu [{CpFe}4(P2)2] (10) [24] analoge Struktur mit einem hier verzerrten Dreiecksdodekaedergerüst vorge-schlagen, dessen vier Ecken der Konnektivität fünf von drei Rutheniumatomen und einem Eisenatom besetzt sind und dessen vier Ecken der Konnektivität vier zwei micro-h 2:2:1:1 -P2-Einheiten einnehmen. Es handelt sich bei 9 wie bei 10 um Cluster vom hypercloso-Typ (n+1 = 8 GEP). [30,31] Röntgenstrukturanalysen zeigen, daß 6, 7 und 8 ebenfalls verzerrt dreiecksdodekaedrische Gerüststrukturen besitzen. Damit ist auch die Struktur der bereits früher synthetisierten und spektroskopisch charakterisierten Komplexe [{Cp R Fe}3P5] (Cp R = Cp*, Cp*') (11b,c) [8] geklärt, deren NMR-Daten auf eine enge Verwandtschaft insbesondere mit 6 hinweisen. Gegenüber 9 bzw. 10 [24] mit einem M4P4-Gerüst (M = allgem. Übergangsmetallatom) ist in den Clustern 6, 7, 8 und 11b,c [8] mit M3P5-Gerüst formal ein 13 VE-Metallkomplex-fragment (Konnektivität fünf; 1 GE) durch ein Phosphoratom (3 GE) ersetzt, wodurch der Übergang zum closo-Strukturtyp des Dreiecksdodekaeders (n+1 = 9 GEP) [30,31] vollzogen wird. Die Cluster 6, 7, 8 und 11b,c [8] enthalten eine bisher unbekannte Koordinationsform der P5-Einheit. Bei der thermischen Umsetzung von [{Cp*Ru(CO)2}2] (1b) mit [Cp*Ru(h 5 -P5)] (3b) erhält man als Hauptprodukt den Dreikernkomplex [{Cp*Ru}3(P4)(P)] (17b, 62 % Ausbeute). Als einziges Nebenprodukt kann [Cp*2Ru2P4] (4b, 5 % Ausbeute) säulen-chromatographisch isoliert werden. Die NMR-Daten von 17b lassen in Analogie zum röntgenstrukturanalytisch charakterisierten [{Cp*'Fe}3(P4)(P){Mo(CO)5}] (18c) [8] auf eine cubanartige Struktur schließen, in der die fünf Phosphoratome in Form einer Isotetraphosphid-Einheit und eines einzelnen Phosphoratoms vorliegen. Die Gesamtzahl von 64 Valenzelektronen ist im Einklang mit drei Metall-Metall-Bindungen [31] . Für 4b ist wie für das voranstehend besprochene Cp"-Derivat 4a eine Pseudo- Tripeldecker-Struktur mit s-cis-Tetraphosphabutadiendiyl-"Mitteldeck" oder mit zwei micro-h 2:2 -P2-Liganden zu diskutieren. Thermolysiert man [{Cp* Ru(CO)2}2] (1c) mit 3b, so erhält man die Komplexe [Cp*'nCp*2-nRu2P4] (n = 0,1,2) (4b,d,c) und [{Cp*'Ru}n{Cp*Ru}3-n(P4)(P)] (n = 1,2,3) (17e,d,c) jeweils als nicht auftrennbare Gemische von analog aufgebauten Verbindungen, die sich nur im Zahlenverhältnis der verschiedenen Cyclopentadienyl-Liganden Cp*' und Cp* unterscheiden. In geringem Umfang beobachtet man dabei auch eine cyclo-P5-Übertragung unter Bildung des literaturbekannten [Cp*'Ru(h 5 -P5)] [7,10] , das im Gemisch mit nicht abreagiertem 3b anfällt. Durch Umsetzung mit [W(CO)5(thf)] gelingt die Komplexierung des dreiecks-dodekaedrischen Clusters [{Cp*Fe}2{Cp"Ru}P5] (8) zum Monoaddukt [{Cp*Fe}2{Cp"Ru}P5{W(CO)5}] (19), während beim Komplexierungsversuch des ebenfalls dreiecksdodekaedrischen Clusters [{Cp*'Fe}3P5] (11c) mit [Mo(CO)5(thf)] [8] eine Gerüstumlagerung zur cubanartig aufgebauten Verbindung [{Cp*'Fe}3(P4)(P){Mo(CO)5}] (18c) erfolgt. Der Strukturvorschlag für 19 basiert auf dem 31 P-NMR-Spektrum. Versuche zur Oxidation von 8 mit gelbem Schwefel bei Raumtemperatur führen zu unspezifischer Zersetzung bzw. Folgereaktionen von 8. Orientierende Versuche mit grauem Selen als milderem Oxidationsmittel deuten darauf hin, daß unter geeigneten Reaktionsbedingungen eine einfache Selenierung am endständigen Phosphoratom des P5-Liganden von 8 erfolgt. Bei der Umsetzung von [{Cp"Ru}3{Cp*Fe}(P2)2] (9) mit gelbem Schwefel können je nach Reaktionsbedingungen bis zu drei Phosphoratome oxidiert werden. Vollständige Sulfurierung wie im Falle von [{CpFe}4(P2S2)2] [24] wird nicht beobachtet. Die Sulfurierung ist regioselektiv. Für einen bestimmten Sulfurierungsgrad wird jeweils nur ein Produkt erhalten. Die Strukturvorschläge für die Cluster 21 23 werden anhand ihrer 31 P-NMR-spektroskopischen Daten abgeleitet.

The growing computational power enables the establishment of the Population Balance Equation (PBE) to model the steady state and dynamic behavior of multiphase flow unit operations. Accordingly, the twophase flow behavior inside liquid-liquid extraction equipment is characterized by different factors. These factors include: interactions among droplets (breakage and coalescence), different time scales due to the size distribution of the dispersed phase, and micro time scales of the interphase diffusional mass transfer process. As a result of this, the general PBE has no well known analytical solution and therefore robust numerical solution methods with low computational cost are highly admired. In this work, the Sectional Quadrature Method of Moments (SQMOM) (Attarakih, M. M., Drumm, C., Bart, H.-J. (2009). Solution of the population balance equation using the Sectional Quadrature Method of Moments (SQMOM). Chem. Eng. Sci. 64, 742-752) is extended to take into account the continuous flow systems in spatial domain. In this regard, the SQMOM is extended to solve the spatially distributed nonhomogeneous bivariate PBE to model the hydrodynamics and physical/reactive mass transfer behavior of liquid-liquid extraction equipment. Based on the extended SQMOM, two different steady state and dynamic simulation algorithms for hydrodynamics and mass transfer behavior of liquid-liquid extraction equipment are developed and efficiently implemented. At the steady state modeling level, a Spatially-Mixed SQMOM (SM-SQMOM) algorithm is developed and successfully implemented in a onedimensional physical spatial domain. The integral spatial numerical flux is closed using the mean mass droplet diameter based on the One Primary and One Secondary Particle Method (OPOSPM which is the simplest case of the SQMOM). On the other hand the hydrodynamics integral source terms are closed using the analytical Two-Equal Weight Quadrature (TEqWQ). To avoid the numerical solution of the droplet rise velocity, an analytical solution based on the algebraic velocity model is derived for the particular case of unit velocity exponent appearing in the droplet swarm model. In addition to this, the source term due to mass transport is closed using OPOSPM. The resulting system of ordinary differential equations with respect to space is solved using the MATLAB adaptive Runge–Kutta method (ODE45). At the dynamic modeling level, the SQMOM is extended to a one-dimensional physical spatial domain and resolved using the finite volume method. To close the mathematical model, the required quadrature nodes and weights are calculated using the analytical solution based on the Two Unequal Weights Quadrature (TUEWQ) formula. By applying the finite volume method to the spatial domain, a semi-discreet ordinary differential equation system is obtained and solved. Both steady state and dynamic algorithms are extensively validated at analytical, numerical, and experimental levels. At the numerical level, the predictions of both algorithms are validated using the extended fixed pivot technique as implemented in PPBLab software (Attarakih, M., Alzyod, S., Abu-Khader, M., Bart, H.-J. (2012). PPBLAB: A new multivariate population balance environment for particulate system modeling and simulation. Procedia Eng. 42, pp. 144-562). At the experimental validation level, the extended SQMOM is successfully used to model the steady state hydrodynamics and physical and reactive mass transfer behavior of agitated liquid-liquid extraction columns under different operating conditions. In this regard, both models are found efficient and able to follow liquid extraction column behavior during column scale-up, where three column diameters were investigated (DN32, DN80, and DN150). To shed more light on the local interactions among the contacted phases, a reduced coupled PBE and CFD framework is used to model the hydrodynamic behavior of pulsed sieve plate columns. In this regard, OPOSPM is utilized and implemented in FLUENT 18.2 commercial software as a special case of the SQMOM. The dropletdroplet interactions (breakage and coalescence) are taken into account using OPOSPM, while the required information about the velocity field and energy dissipation is calculated by the CFD model. In addition to this, the proposed coupled OPOSPM-CFD framework is extended to include the mass transfer. The proposed framework is numerically tested and the results are compared with the published experimental data. The required breakage and coalescence parameters to perform the 2D-CFD simulation are estimated using PPBLab software, where a 1D-CFD simulation using a multi-sectional gird is performed. A very good agreement is obtained at the experimental and the numerical validation levels.

This thesis presents a novel, generic framework for information segmentation in document images. A document image contains different types of information, for instance, text (machine printed/handwritten), graphics, signatures, and stamps. It is necessary to segment information in documents so that to process such segmented information only when required in automatic document processing workflows. The main contribution of this thesis is the conceptualization and implementation of an information segmentation framework that is based on part-based features. The generic nature of the presented framework makes it applicable to a variety of documents (technical drawings, magazines, administrative, scientific, and academic documents) digitized using different methods (scanners, RGB cameras, and hyper-spectral imaging (HSI) devices). A highlight of the presented framework is that it does not require large training sets, rather a few training samples (for instance, four pages) lead to high performance, i.e., better than previously existing methods. In addition, the presented framework is simple and can be adapted quickly to new problem domains. This thesis is divided into three major parts on the basis of document digitization method (scanned, hyper-spectral imaging, and camera captured) used. In the area of scanned document images, three specific contributions have been realized. The first of them is in the domain of signature segmentation in administrative documents. In some workflows, it is very important to check the document authenticity before processing the actual content. This can be done based on the available seal of authenticity, e.g., signatures. However, signature verification systems expect pre-segmented signature image, while signatures are usually a part of document. To use signature verification systems on document images, it is necessary to first segment signatures in documents. This thesis shows that the presented framework can be used to segment signatures in administrative documents. The system based on the presented framework is tested on a publicly available dataset where it outperforms the state-of-the-art methods and successfully segmented all signatures, while less than half of the found signatures are false positives. This shows that it can be applied for practical use. The second contribution in the area of scanned document images is segmentation of stamps in administrative documents. A stamp also serves as a seal for documents authenticity. However, the location of stamp on the document can be more arbitrary than a signature depending on the person sealing the document. This thesis shows that a system based on our generic framework is able to extract stamps of any arbitrary shape and color. The evaluation of the presented system on a publicly available dataset shows that it is also able to segment black stamps (that were not addressed in the past) with a recall and precision of 83% and 73%, respectively. %Furthermore, to segment colored stamps, this thesis presents a novel feature set which is based on intensity gradient, is able to extract unseen, colored, arbitrary shaped, textual as well as graphical stamps, and outperforms the state-of-the-art methods. The third contribution in the scanned document images is in the domain of information segmentation in technical drawings (architectural floorplans, maps, circuit diagrams, etc.) containing usually a large amount of graphics and comparatively less textual components. Further, as in technical drawings, text is overlapping with graphics. Thus, automatic analysis of technical drawings uses text/graphics segmentation as a pre-processing step. This thesis presents a method based on our generic information segmentation framework that is able to detect the text, which is touching graphical components in architectural floorplans and maps. Evaluation of the method on a publicly available dataset of architectural floorplans shows that it is able to extract almost all touching text components with precision and recall of 71% and 95%, respectively. This means that almost all of the touching text components are successfully extracted. In the area of hyper-spectral document images, two contributions have been realized. Unlike normal three channels RGB images, hyper-spectral images usually have multiple channels that range from ultraviolet to infrared regions including the visible region. First, this thesis presents a novel automatic method for signature segmentation from hyper-spectral document images (240 spectral bands between 400 - 900 nm). The presented method is based on a part-based key point detection technique, which does not use any structural information, but relies only on the spectral response of the document regardless of ink color and intensity. The presented method is capable of segmenting (overlapping and non-overlapping) signatures from varying backgrounds like, printed text, tables, stamps, logos, etc. Importantly, the presented method can extract signature pixels and not just the bounding boxes. This is substantial when signatures are overlapping with text and/or other objects in image. Second, this thesis presents a new dataset comprising of 300 documents scanned using a high-resolution hyper-spectral scanner. Evaluation of the presented signature segmentation method on this hyper-spectral dataset shows that it is able to extract signature pixels with the precision and recall of 100% and 79%, respectively. Further contributions have been made in the area of camera captured document images. A major problem in the development of Optical Character Recognition (OCR) systems for camera captured document images is the lack of labeled camera captured document images datasets. In the first place, this thesis presents a novel, generic, method for automatic ground truth generation/labeling of document images. The presented method builds large-scale (i.e., millions of images) datasets of labeled camera captured / scanned documents without any human intervention. The method is generic and can be used for automatic ground truth generation of (scanned and/or camera captured) documents in any language, e.g., English, Russian, Arabic, Urdu. The evaluation of the presented method, on two different datasets in English and Russian, shows that 99.98% of the images are correctly labeled in every case. Another important contribution in the area of camera captured document images is the compilation of a large dataset comprising 1 million word images (10 million character images), captured in a real camera-based acquisition environment, along with the word and character level ground truth. The dataset can be used for training as well as testing of character recognition systems for camera-captured documents. Various benchmark tests are performed to analyze the behavior of different open source OCR systems on camera captured document images. Evaluation results show that the existing OCRs, which already get very high accuracies on scanned documents, fail on camera captured document images. Using the presented camera-captured dataset, a novel character recognition system is developed which is based on a variant of recurrent neural networks, i.e., Long Short Term Memory (LSTM) that outperforms all of the existing OCR engines on camera captured document images with an accuracy of more than 95%. Finally, this thesis provides details on various tasks that have been performed in the area closely related to information segmentation. This includes automatic analysis and sketch based retrieval of architectural floor plan images, a novel scheme for online signature verification, and a part-based approach for signature verification. With these contributions, it has been shown that part-based methods can be successfully applied to document image analysis.

Numerical Godeaux surfaces are minimal surfaces of general type with the smallest possible numerical invariants. It is known that the torsion group of a numerical Godeaux surface is cyclic of order \(m\leq 5\). A full classification has been given for the cases \(m=3,4,5\) by the work of Reid and Miyaoka. In each case, the corresponding moduli space is 8-dimensional and irreducible. There exist explicit examples of numerical Godeaux surfaces for the orders \(m=1,2\), but a complete classification for these surfaces is still missing. In this thesis we present a construction method for numerical Godeaux surfaces which is based on homological algebra and computer algebra and which arises from an experimental approach by Schreyer. The main idea is to consider the canonical ring \(R(X)\) of a numerical Godeaux surface \(X\) as a module over some graded polynomial ring \(S\). The ring \(S\) is chosen so that \(R(X)\) is finitely generated as an \(S\)-module and a Gorenstein \(S\)-algebra of codimension 3. We prove that the canonical ring of any numerical Godeaux surface, considered as an \(S\)-module, admits a minimal free resolution whose middle map is alternating. Moreover, we show that a partial converse of this statement is true under some additional conditions. Afterwards we use these results to construct (canonical rings of) numerical Godeaux surfaces. Hereby, we restrict our study to surfaces whose bicanonical system has no fixed component but 4 distinct base points, in the following referred to as marked numerical Godeaux surfaces. The particular interest of this thesis lies on marked numerical Godeaux surfaces whose torsion group is trivial. For these surfaces we study the fibration of genus 4 over \(\mathbb{P}^1\) induced by the bicanonical system. Catanese and Pignatelli showed that the general fibre is non-hyperelliptic and that the number \(\tilde{h}\) of hyperelliptic fibres is bounded by 3. The two explicit constructions of numerical Godeaux surfaces with a trivial torsion group due to Barlow and Craighero-Gattazzo, respectively, satisfy \(\tilde{h} = 2\). With the method from this thesis, we construct an 8-dimensional family of numerical Godeaux surfaces with a trivial torsion group and whose general element satisfy \(\tilde{h}=0\). Furthermore, we establish a criterion for the existence of hyperelliptic fibres in terms of a minimal free resolution of \(R(X)\). Using this criterion, we verify experimentally the existence of a numerical Godeaux surface with \(\tilde{h}=1\).