Adaptive Cube Tessellation for Topologically Correct Isosurfaces

Three dimensional datasets representing scalar fields are frequently rendered using isosurfaces. For datasets arranged as a cubic lattice, the marching cubes algorithm is the most used isosurface extraction method. However, the marching cubes algorithm produces some ambiguities which have been solved using different approaches that normally imply a more complex process. One of them is to tessellate the cubes into tetrahedra, and by using a similar method (marching tetrahedra), to build the isosurface. The main drawback of other tessellations is that they do not produce the same isosurface topologies as those generated by improved marching cubes algorithms. We propose an adaptive tessellation that, being independent of the isovalue, preserves the topology. Moreover the tessellationallows the isosurface to evolve continuously when the isovalue is changed continuously.

Structural studies of decaying fluid turbulence: Effect of initial conditions

We present results from a systematic numerical study of structural properties of an unforced, incompressible, homogeneous, and isotropic three-dimensional turbulent fluid with an initial energy spectrum that develops a cascade of kinetic energy to large wave numbers. The results are compared with those from a recently studied set of power-law initial energy spectra [C. Kalelkar and R. Pandit, Phys. Rev. E 69, 046304 (2004)] which do not exhibit such a cascade. Differences are exhibited in plots of vorticity isosurfaces, the temporal evolution of the kinetic energy-dissipation rate, and the rates of production of the mean enstrophy along the principal axes of the strain-rate tensor. A crossover between "non-cascade-type" and "cascade-type" behavior is shown numerically for a specific set of initial energy spectra.

Relation-Aware Isosurface Extraction in Multifield Data

We introduce a variation density function that profiles the relationship between multiple scalar fields over isosurfaces of a given scalar field. This profile serves as a valuable tool for multifield data exploration because it provides the user with cues to identify interesting isovalues of scalar fields. Existing isosurface-based techniques for scalar data exploration like Reeb graphs, contour spectra, isosurface statistics, etc., study a scalar field in isolation. We argue that the identification of interesting isovalues in a multifield data set should necessarily be based on the interaction between the different fields. We demonstrate the effectiveness of our approach by applying it to explore data from a wide variety of applications.

Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence

We present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to 1024(3) collocation points, of incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number Pr-M over a large range, namely 0.01 <= Pr-M <= 10. We obtain data for a wide variety of statistical measures, such as probability distribution functions (PDFs) of the moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure functions, which we use to characterize intermittency, isosurfaces of quantities, such as the moduli of the vorticity and current density, and joint PDFs, such as those of fluid and magnetic dissipation rates. Our systematic study uncovers interesting results that have not been noted hitherto. In particular, we find a crossover from a larger intermittency in the magnetic field than in the velocity field, at large Pr-M, to a smaller intermittency in the magnetic field than in the velocity field, at low Pr-M. Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of Pr-M, multiscaling exponent ratios agree, at least within our error bars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.

Halogen Bonding in 2,5-Dichloro-1,4-benzoquinone: Insights from Experimental and Theoretical Charge Density Analysis

Experimental charge density distribution in 2, 5-dichloro-1, 4-benzoquinone has been carried out using high resolution X-ray diffraction data at 90 K to quantitatively evaluate the nature of C-Cl center dot center dot center dot O=C halogen bond in molecular crystals. Additionally, the halogen bond is studied from geometrical point of view and the same has been visualized using Hirshfeld surface analysis. The obtained results from experimental charge density analysis are compared with periodic quantum calculations using B3LYP 6-31G(d,p) level of theory. The topological values at bond critical point, three-dimensional static deformation density features and electrostatic potential isosurfaces unequivocally establish the attractive nature of C-Cl center dot center dot center dot O=C halogen bond in crystalline lattice.

Charge Density Analysis of a Pentaborate Ion in an Ammonium Borate: Toward the Understanding of Topological Features in Borate Minerals

Structural and charge density distribution studies have been carried out on a single crystal data of an ammonium borate, [C(10)H(26)N(4)][B(5)O(6)(OH)(4)](2), synthesized by solvothermal method. Further, the experimentally observed geometry is used for the theoretical charge density calculations using the B3LYP/6-31G** level of theory, and the results are compared with the experimental values. Topological analysis of charge density based on the Atoms in Molecules approach for B-O bonds exhibit mixed covalent/ionic character. Detailed analysis of the hydrogen bonds in the crystal structure in the ammonium borate provides insights into the understanding of the reaction pathways that net atomic charges and electrostatic potential isosurfaces also give additional such systems. could result in the formation of borate minerals. The input to evaluate chemical and physical properties in such systems.

S center dot center dot center dot O chalcogen bonding in sulfa drugs: insights from multipole charge density and X-ray wavefunction of acetazolamide

Experimental charge density analysis combined with the quantum crystallographic technique of X-ray wavefunction refinement (XWR) provides quantitative insights into the intra-and intermolecular interactions formed by acetazolamide, a diuretic drug. Firstly, the analysis of charge density topology at the intermolecular level shows the presence of exceptionally strong interaction motifs such as a DDAA-AADD (D-donor, A-acceptor) type quadruple hydrogen bond motif and a sulfonamide dimer synthon. The nature and strength of intra-molecular S center dot center dot center dot O chalcogen bonding have been characterized using descriptors from the multipole model (MM) and XWR. Although pure geometrical criteria suggest the possibility of two intra-molecular S center dot center dot center dot O chalcogen bonded ring motifs, only one of them satisfies the ``orbital geometry'' so as to exhibit an interaction in terms of an electron density bond path and a bond critical point. The presence of `s-holes' on the sulfur atom leading to the S center dot center dot center dot O chalcogen bond has been visualized on the electrostatic potential surface and Laplacian isosurfaces close to the `reactive surface'. The electron localizability indicator (ELI) and Roby bond orders derived from the `experimental wave function' provide insights into the nature of S center dot center dot center dot O chalcogen bonding.

Verifiable Visualization for Isosurface Extraction

Visual representations of isosurfaces are ubiquitous in the scientific and engineering literature. In this paper, we present techniques to assess the behavior of isosurface extraction codes. Where applicable, these techniques allow us to distinguish whether anomalies in isosurface features can be attributed to the underlying physical process or to artifacts from the extraction process. Such scientific scrutiny is at the heart of verifiable visualization - subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. More concretely, we derive formulas for the expected order of accuracy (or convergence rate) of several isosurface features, and compare them to experimentally observed results in the selected codes. This technique is practical: in two cases, it exposed actual problems in implementations. We provide the reader with the range of responses they can expect to encounter with isosurface techniques, both under ""normal operating conditions"" and also under adverse conditions. Armed with this information - the results of the verification process - practitioners can judiciously select the isosurface extraction technique appropriate for their problem of interest, and have confidence in its behavior.

Extração de isosuperfícies a partir de dados meteorológicos

This work aims viewing weather information, by building isosurfaces enabling enjoy the advantages of three-dimensional geometric models, to communicate the meaning of the data used in a clear and efficient way. The evolving technology of data processing makes possible the interpretation of masses of data increasing, through robust algorithms. In meteorology, in particular, we can benefit from this fact, due to the large amount of data required for analysis and statistics. The manipulation of data, by users from other areas, is facilitated by the choice of algorithm and the tools involved in this work. The project was further developed into distinct modules, increasing their flexibility and reusability for future studies

Topologically Accurate Dual Isosurfacing Using Ray Intersection

“Dual contouring” approaches provide an alternative to standard Marching Cubes (MC) method to extract and approximate an isosurface from trivariate data given on a volumetric mesh. These dual approaches solve some of the problems encountered by the MC methods. We present a simple method based on the MC method and the ray intersection technique to compute isosurface points in the cell interior. One of the advantages of our method is that it does not require us to use Hermite interpolation scheme, unlike other dual contouring methods. We perform a complete analysis of all possible configurations to generate a look-up table for all configurations. We use the look-up table to optimize the ray-intersection method to obtain minimum number of points necessarily sufficient for defining topologically correct isosurfaces in all possible configurations. Isosurface points are connected using a simple strategy.

Volume Haptics and Dendritic Spine Editing

Esta tesis se ha desarrollado en el contexto del proyecto Cajal Blue Brain, una iniciativa europea dedicada al estudio del cerebro. Uno de los objetivos de esta iniciativa es desarrollar nuevos métodos y nuevas tecnologías que simplifiquen el análisis de datos en el campo neurocientífico. El presente trabajo se ha centrado en diseñar herramientas que combinen información proveniente de distintos canales sensoriales con el fin de acelerar la interacción y análisis de imágenes neurocientíficas. En concreto se estudiará la posibilidad de combinar información visual con información háptica. Las espinas dendríticas son pequeñas protuberancias que recubren la superficie dendrítica de muchas neuronas del cerebro. A día de hoy, se cree que tienen un papel clave en la transmisión de señales neuronales. Motivo por el cual, el interés por parte de la comunidad científica por estas estructuras ha ido en aumento a medida que las técnicas de adquisición de imágenes mejoraban hasta alcanzar una calidad suficiente para analizar dichas estructuras. A menudo, los neurocientíficos utilizan técnicas de microscopía con luz para obtener los datos que les permitan analizar estructuras neuronales tales como neuronas, dendritas y espinas dendríticas. A pesar de que estas técnicas ofrezcan ciertas ventajas frente a su equivalente electrónico, las técnicas basadas en luz permiten una menor resolución. En particular, estructuras pequeñas como las espinas dendríticas pueden capturarse de forma incorrecta en las imágenes obtenidas, impidiendo su análisis. En este trabajo, se presenta una nueva técnica, que permite editar imágenes volumétricas, mediante un dispositivo háptico, con el fin de reconstruir de los cuellos de las espinas dendríticas. Con este objetivo, en un primer momento se desarrolló un algoritmo que proporciona retroalimentación háptica en datos volumétricos, completando la información que provine del canal visual. Dicho algoritmo de renderizado háptico permite a los usuarios tocar y percibir una isosuperficie en el volumen de datos. El algoritmo asegura un renderizado robusto y eficiente. Se utiliza un método basado en las técnicas de “marching tetrahedra” para la extracción local de una isosuperficie continua, lineal y definida por intervalos. La robustez deriva tanto de una etapa de detección de colisiones continua de la isosuperficie extraída, como del uso de técnicas eficientes de renderizado basadas en un proxy puntual. El método de “marching tetrahedra” propuesto garantiza que la topología de la isosuperficie extraída coincida con la topología de una isosuperficie equivalente determinada utilizando una interpolación trilineal. Además, con el objetivo de mejorar la coherencia entre la información háptica y la información visual, el algoritmo de renderizado háptico calcula un segundo proxy en la isosuperficie pintada en la pantalla. En este trabajo se demuestra experimentalmente las mejoras en, primero, la etapa de extracción de isosuperficie, segundo, la robustez a la hora de mantener el proxy en la isosuperficie deseada y finalmente la eficiencia del algoritmo. En segundo lugar, a partir del algoritmo de renderizado háptico propuesto, se desarrolló un procedimiento, en cuatro etapas, para la reconstrucción de espinas dendríticas. Este procedimiento, se puede integrar en los cauces de segmentación automática y semiautomática existentes como una etapa de pre-proceso previa. El procedimiento está diseñando para que tanto la navegación como el proceso de edición en sí mismo estén controlados utilizando un dispositivo háptico. Se han diseñado dos experimentos para evaluar esta técnica. El primero evalúa la aportación de la retroalimentación háptica y el segundo se centra en evaluar la idoneidad del uso de un háptico como dispositivo de entrada. En ambos casos, los resultados demuestran que nuestro procedimiento mejora la precisión de la reconstrucción. En este trabajo se describen también dos casos de uso de nuestro procedimiento en el ámbito de la neurociencia: el primero aplicado a neuronas situadas en la corteza cerebral humana y el segundo aplicado a espinas dendríticas situadas a lo largo de neuronas piramidales de la corteza del cerebro de una rata. Por último, presentamos el programa, Neuro Haptic Editor, desarrollado a lo largo de esta tesis junto con los diferentes algoritmos ya mencionados. ABSTRACT This thesis took place within the Cajal Blue Brain project, a European initiative dedicated to the study of the brain. One of the main goals of this project is the development of new methods and technologies simplifying data analysis in neuroscience. This thesis focused on the development of tools combining information originating from distinct sensory channels with the aim of accelerating both the interaction with neuroscience images and their analysis. In concrete terms, the objective is to study the possibility of combining visual information with haptic information. Dendritic spines are thin protrusions that cover the dendritic surface of numerous neurons in the brain and whose function seems to play a key role in neural circuits. The interest of the neuroscience community toward those structures kept increasing as and when acquisition methods improved, eventually to the point that the produced datasets enabled their analysis. Quite often, neuroscientists use light microscopy techniques to produce the dataset that will allow them to analyse neuronal structures such as neurons, dendrites and dendritic spines. While offering some advantages compared to their electronic counterpart, light microscopy techniques achieve lower resolutions. Particularly, small structures such as dendritic spines might suffer from a very low level of fluorescence in the final dataset, preventing further analysis. This thesis introduces a new technique enabling the edition of volumetric datasets in order to recreate dendritic spine necks using a haptic device. In order to fulfil this objective, we first presented an algorithm to provide haptic feedback directly from volumetric datasets, as an aid to regular visualization. The haptic rendering algorithm lets users perceive isosurfaces in volumetric datasets, and it relies on several design features that ensure a robust and efficient rendering. A marching tetrahedra approach enables the dynamic extraction of a piecewise linear continuous isosurface. Robustness is derived using a Continuous Collision Detection step coupled with acknowledged proxy-based rendering methods over the extracted isosurface. The introduced marching tetrahedra approach guarantees that the extracted isosurface will match the topology of an equivalent isosurface computed using trilinear interpolation. The proposed haptic rendering algorithm improves the coherence between haptic and visual cues computing a second proxy on the isosurface displayed on screen. Three experiments demonstrate the improvements on the isosurface extraction stage as well as the robustness and the efficiency of the complete algorithm. We then introduce our four-steps procedure for the complete reconstruction of dendritic spines. Based on our haptic rendering algorithm, this procedure is intended to work as an image processing stage before the automatic segmentation step giving the final representation of the dendritic spines. The procedure is designed to allow both the navigation and the volume image editing to be carried out using a haptic device. We evaluated our procedure through two experiments. The first experiment concerns the benefits of the force feedback and the second checks the suitability of the use of a haptic device as input. In both cases, the results shows that the procedure improves the editing accuracy. We also report two concrete cases where our procedure was employed in the neuroscience field, the first one concerning dendritic spines in the human cortex, the second one referring to an ongoing experiment studying dendritic spines along dendrites of mouse cortical pyramidal neurons. Finally, we present the software program, Neuro Haptic Editor, that was built along the development of the different algorithms implemented during this thesis, and used by neuroscientists to use our procedure.