A Framework for Exploring Multidimensional Data with 3D Projections

Visualization of high-dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e. g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high-dimensional data to 3D visual spaces, based on a generalization of the Least-Square Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the framework`s applicability for both visual exploration of multidimensional abstract (non-spatial) data as well as the feature space of multi-variate spatial data.

Building a Open Source Framework for Virtual Medical Training

This paper presents a framework to build medical training applications by using virtual reality and a tool that helps the class instantiation of this framework. The main purpose is to make easier the building of virtual reality applications in the medical training area, considering systems to simulate biopsy exams and make available deformation, collision detection, and stereoscopy functionalities. The instantiation of the classes allows quick implementation of the tools for such a purpose, thus reducing errors and offering low cost due to the use of open source tools. Using the instantiation tool, the process of building applications is fast and easy. Therefore, computer programmers can obtain an initial application and adapt it to their needs. This tool allows the user to include, delete, and edit parameters in the functionalities chosen as well as storing these parameters for future use. In order to verify the efficiency of the framework, some case studies are presented.

Modularity and robustness of bone networks

Cortical bones, essential for mechanical support and structure in many animals, involve a large number of canals organized in intricate fashion. By using state-of-the art image analysis and computer graphics, the 3D reconstruction of a whole bone (phalange) of a young chicken was obtained and represented in terms of a complex network where each canal was associated to an edge and every confluence of three or more canals yielded a respective node. The representation of the bone canal structure as a complex network has allowed several methods to be applied in order to characterize and analyze the canal system organization and the robustness. First, the distribution of the node degrees (i.e. the number of canals connected to each node) confirmed previous indications that bone canal networks follow a power law, and therefore present some highly connected nodes (hubs). The bone network was also found to be partitioned into communities or modules, i.e. groups of nodes which are more intensely connected to one another than with the rest of the network. We verified that each community exhibited distinct topological properties that are possibly linked with their specific function. In order to better understand the organization of the bone network, its resilience to two types of failures (random attack and cascaded failures) was also quantified comparatively to randomized and regular counterparts. The results indicate that the modular structure improves the robustness of the bone network when compared to a regular network with the same average degree and number of nodes. The effects of disease processes (e. g., osteoporosis) and mutations in genes (e.g., BMP4) that occur at the molecular level can now be investigated at the mesoscopic level by using network based approaches.

Three-Dimensional Stress Distribution in the Human Periodontal Ligament in Masticatory, Parafunctional, and Trauma Loads: Finite Element Analysis

Background: The presence of the periodontal ligament (PDL) makes it possible to absorb and distribute loads produced during masticatory function and other tooth contacts into the alveolar process via the alveolar bone proper. However, several factors affect the integrity of periodontal structures causing the destruction of the connective matrix and cells, the loss of fibrous attachment, and the resorption of alveolar bone. Methods: The purpose of this study was to evaluate the stress distribution by finite element analysis in a PDL in three-dimensional models of the upper central incisor under three different load conditions: 100 N occlusal loading at 45 degrees (model 1: masticatory load); 500 N at the incisal edge at 45 degrees (model 2: parafunctional habit); and 800 N at the buccal surface at 90 degrees (model 3: trauma case). The models were built from computed tomography scans. Results: The stress distribution was quite different among the models. The most significant values (harmful) of tensile and compressive stresses were observed in models 2 and 3, with similarly distinct patterns of stress distributions along the PDL. Tensile stresses were observed along the internal and external aspects of the PDL, mostly at the cervical and middle thirds. Conclusions: The stress generation in these models may affect the integrity of periodontal structures. A better understanding of the biomechanical behavior of the PDL under physiologic and traumatic loading conditions might enhance the understanding of the biologic reaction of the PDL in health and disease. J Periodontol 2009;80:1859-1867.

Improved detection of incipient vascular changes by a biotechnological platform combining post mortem MRI in situ with neuropathology

The histopathological counterpart of white matter hyperintensities is a matter of debate. Methodological and ethical limitations have prevented this question to be elucidated. We want to introduce a protocol applying state-of-the-art methods in order to solve fundamental questions regarding the neuroimaging-neuropathological uncertainties comprising the most common white matter hyperintensities [WMHs] seen in aging. By this protocol, the correlation between signal features in in situ, post mortem MRI-derived methods, including DTI and MTR and quantitative and qualitative histopathology can be investigated. We are mainly interested in determining the precise neuroanatomical substrate of incipient WMHs. A major issue in this protocol is the exact co-registration of small lesion in a tridimensional coordinate system that compensates tissue deformations after histological processing. The protocol is based on four principles: post mortem MRI in situ performed in a short post mortem interval, minimal brain deformation during processing, thick serial histological sections and computer-assisted 3D reconstruction of the histological sections. This protocol will greatly facilitate a systematic study of the location, pathogenesis, clinical impact, prognosis and prevention of WMHs. (C) 2009 Elsevier B.V. All rights reserved.

Resultados preliminares de um sistema de topografia de grande-ângulo usando videoceratógrafo com discos de Plácido

OBJETIVO: Desenvolver a instrumentação e o "software" para topografia de córnea de grande-ângulo usando o tradicional disco de Plácido. O objetivo é permitir o mapeamento de uma região maior da córnea para topógrafos de córnea que usem a técnica de Plácido, fazendo-se uma adaptação simples na mira. MÉTODOS: Utilizando o tradicional disco de Plácido de um topógrafo de córnea tradicional, 9 LEDs (Light Emitting Diodes) foram adaptados no anteparo cônico para que o paciente voluntário pudesse fixar o olhar em diferentes direções. Para cada direção imagens de Plácido foram digitalizadas e processadas para formar, por meio de algoritmo envolvendo elementos sofisticados de computação gráfica, um mapa tridimensional completo da córnea toda. RESULTADOS: Resultados apresentados neste trabalho mostram que uma região de até 100% maior pode ser mapeada usando esta técnica, permitindo que o clínico mapeie até próximo ao limbo da córnea. São apresentados aqui os resultados para uma superfície esférica de calibração e também para uma córnea in vivo com alto grau de astigmatismo, mostrando a curvatura e elevação. CONCLUSÃO: Acredita-se que esta nova técnica pode propiciar a melhoria de alguns processos, como por exemplo: adaptação de lentes de contato, algoritmos para ablações costumizadas para hipermetropia, entre outros.

HiPP: A Novel Hierarchical Point Placement Strategy and its Application to the Exploration of Document Collections

Point placement strategies aim at mapping data points represented in higher dimensions to bi-dimensional spaces and are frequently used to visualize relationships amongst data instances. They have been valuable tools for analysis and exploration of data sets of various kinds. Many conventional techniques, however, do not behave well when the number of dimensions is high, such as in the case of documents collections. Later approaches handle that shortcoming, but may cause too much clutter to allow flexible exploration to take place. In this work we present a novel hierarchical point placement technique that is capable of dealing with these problems. While good grouping and separation of data with high similarity is maintained without increasing computation cost, its hierarchical structure lends itself both to exploration in various levels of detail and to handling data in subsets, improving analysis capability and also allowing manipulation of larger data sets.

Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections ( LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.

PedVis: A Structured, Space-Efficient Technique for Pedigree Visualization

Public genealogical databases are becoming increasingly populated with historical data and records of the current population`s ancestors. As this increasing amount of available information is used to link individuals to their ancestors, the resulting trees become deeper and more dense, which justifies the need for using organized, space-efficient layouts to display the data. Existing layouts are often only able to show a small subset of the data at a time. As a result, it is easy to become lost when navigating through the data or to lose sight of the overall tree structure. On the contrary, leaving space for unknown ancestors allows one to better understand the tree`s structure, but leaving this space becomes expensive and allows fewer generations to be displayed at a time. In this work, we propose that the H-tree based layout be used in genealogical software to display ancestral trees. We will show that this layout presents an increase in the number of displayable generations, provides a nicely arranged, symmetrical, intuitive and organized fractal structure, increases the user`s ability to understand and navigate through the data, and accounts for the visualization requirements necessary for displaying such trees. Finally, user-study results indicate potential for user acceptance of the new layout.

Two-Phase Mapping for Projecting Massive Data Sets

Most multidimensional projection techniques rely on distance (dissimilarity) information between data instances to embed high-dimensional data into a visual space. When data are endowed with Cartesian coordinates, an extra computational effort is necessary to compute the needed distances, making multidimensional projection prohibitive in applications dealing with interactivity and massive data. The novel multidimensional projection technique proposed in this work, called Part-Linear Multidimensional Projection (PLMP), has been tailored to handle multivariate data represented in Cartesian high-dimensional spaces, requiring only distance information between pairs of representative samples. This characteristic renders PLMP faster than previous methods when processing large data sets while still being competitive in terms of precision. Moreover, knowing the range of variation for data instances in the high-dimensional space, we can make PLMP a truly streaming data projection technique, a trait absent in previous methods.

Interactive Vector Field Feature Identification

We introduce a flexible technique for interactive exploration of vector field data through classification derived from user-specified feature templates. Our method is founded on the observation that, while similar features within the vector field may be spatially disparate, they share similar neighborhood characteristics. Users generate feature-based visualizations by interactively highlighting well-accepted and domain specific representative feature points. Feature exploration begins with the computation of attributes that describe the neighborhood of each sample within the input vector field. Compilation of these attributes forms a representation of the vector field samples in the attribute space. We project the attribute points onto the canonical 2D plane to enable interactive exploration of the vector field using a painting interface. The projection encodes the similarities between vector field points within the distances computed between their associated attribute points. The proposed method is performed at interactive rates for enhanced user experience and is completely flexible as showcased by the simultaneous identification of diverse feature types.

Resampling Strategies for Deforming MLS Surfaces

Moving-least-squares (MLS) surfaces undergoing large deformations need periodic regeneration of the point set (point-set resampling) so as to keep the point-set density quasi-uniform. Previous work by the authors dealt with algebraic MLS surfaces, and proposed a resampling strategy based on defining the new points at the intersections of the MLS surface with a suitable set of rays. That strategy has very low memory requirements and is easy to parallelize. In this article new resampling strategies with reduced CPU-time cost are explored. The basic idea is to choose as set of rays the lines of a regular, Cartesian grid, and to fully exploit this grid: as data structure for search queries, as spatial structure for traversing the surface in a continuation-like algorithm, and also as approximation grid for an interpolated version of the MLS surface. It is shown that in this way a very simple and compact resampling technique is obtained, which cuts the resampling cost by half with affordable memory requirements.

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.

Front tracking with moving-least-squares surfaces

The representation of interfaces by means of the algebraic moving-least-squares (AMLS) technique is addressed. This technique, in which the interface is represented by an unconnected set of points, is interesting for evolving fluid interfaces since there is]to surface connectivity. The position of the surface points can thus be updated without concerns about the quality of any surface triangulation. We introduce a novel AMLS technique especially designed for evolving-interfaces applications that we denote RAMLS (for Robust AMLS). The main advantages with respect to previous AMLS techniques are: increased robustness, computational efficiency, and being free of user-tuned parameters. Further, we propose a new front-tracking method based on the Lagrangian advection of the unconnected point set that defines the RAMLS surface. We assume that a background Eulerian grid is defined with some grid spacing h. The advection of the point set makes the surface evolve in time. The point cloud can be regenerated at any time (in particular, we regenerate it each time step) by intersecting the gridlines with the evolved surface, which guarantees that the density of points on the surface is always well balanced. The intersection algorithm is essentially a ray-tracing algorithm, well-studied in computer graphics, in which a line (ray) is traced so as to detect all intersections with a surface. Also, the tracing of each gridline is independent and can thus be performed in parallel. Several tests are reported assessing first the accuracy of the proposed RAMLS technique, and then of the front-tracking method based on it. Comparison with previous Eulerian, Lagrangian and hybrid techniques encourage further development of the proposed method for fluid mechanics applications. (C) 2008 Elsevier Inc. All rights reserved.

A solid-like FEM for geometrically non-linear 3D frames

This study presents a solid-like finite element formulation to solve geometric non-linear three-dimensional inhomogeneous frames. To achieve the desired representation, unconstrained vectors are used instead of the classic rigid director triad; as a consequence, the resulting formulation does not use finite rotation schemes. High order curved elements with any cross section are developed using a full three-dimensional constitutive elastic relation. Warping and variable thickness strain modes are introduced to avoid locking. The warping mode is solved numerically in FEM pre-processing computational code, which is coupled to the main program. The extra calculations are relatively small when the number of finite elements. with the same cross section, increases. The warping mode is based on a 2D free torsion (Saint-Venant) problem that considers inhomogeneous material. A scheme that automatically generates shape functions and its derivatives allow the use of any degree of approximation for the developed frame element. General examples are solved to check the objectivity, path independence, locking free behavior, generality and accuracy of the proposed formulation. (C) 2009 Elsevier B.V. All rights reserved.