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An intuitive and sparse representation of the void space of porous materials supports the efficient analysis and visualization of interesting qualitative and quantitative parameters of such materials. We introduce definitions of the elements of this void space, here called pore space, based on its distance function, and present methods to extract these elements using the extremal structures of the distance function. The presented methods are implemented by an image processing pipeline that determines pore centers, pore paths and pore constrictions. These pore space elements build a graph that represents the topology of the pore space in a compact way. The representations we derive from μCT image data of realistic soil specimens enable the computation of many statistical parameters and, thus, provide a basis for further visual analysis and application-specific developments. We introduced parts of our pipeline in previous work. In this chapter, we present additional details and compare our results with the analytic computation of the pore space elements for a sphere packing in order to show the correctness of our graph computation.
Purpose/Aims of the Study: Bone’s hierarchical structure can be visualized using a variety of methods. Many techniques, such as light and electron microscopy generate two-dimensional (2D) images, while micro computed tomography (μCT) allows a direct representation of the three-dimensional (3D) structure. In addition, different methods provide complementary structural information, such as the arrangement of organic or inorganic compounds. The overall aim of the present study is to answer bone research questions by linking information of different 2D and 3D imaging techniques. A great challenge in combining different methods arises from the fact that they usually reflect different characteristics of the real structure.
Materials and Methods: We investigated bone during healing by means of μCT and a couple of 2D methods. Backscattered electron images were used to qualitatively evaluate the tissue’s calcium content and served as a position map for other experimental data. Nanoindentation and X-ray scattering experiments were performed to visualize mechanical and structural properties. Results: We present an approach for the registration of 2D data in a 3D μCT reference frame, where scanning electron microscopies serve as a methodic link. Backscattered electron images are perfectly suited for registration into μCT reference frames, since both show structures based on the same physical principles. We introduce specific registration tools that have been developed to perform the registration process in a semi-automatic way.
Conclusions: By applying this routine, we were able to exactly locate structural information (e.g. mineral particle properties) in the 3D bone volume. In bone healing studies this will help to better understand basic formation, remodeling and mineralization processes.
Efficient implementations of irregular problems on vector and parallel architectures are generally hard to realize. An important class of problems are Gauß-Seidel iteration schemes applied to irregular data sets. The unstructured data dependences arising there prevent restructuring compilers from generating efficient code for vector or parallel machines. It is shown, how to structure the data dependences by decomposing the underlying data set using graph coloring techniques and by specifying a particular execution order already on the algorithm level. Methods to master the irregularities originating from different types of tasks are proposed. An application is given and some open issues and future developments are discussed.
Traditionally, Lagrangian fields such as finite-time Lyapunov exponents (FTLE)
are precomputed on a discrete grid and are ray casted afterwards. This, however,
introduces both grid discretization errors and sampling errors during ray marching.
In this work, we apply a progressive, view-dependent Monte Carlo-based approach
for the visualization of such Lagrangian fields in time-dependent flows. Our ap-
proach avoids grid discretization and ray marching errors completely, is consistent,
and has a low memory consumption. The system provides noisy previews that con-
verge over time to an accurate high-quality visualization. Compared to traditional
approaches, the proposed system avoids explicitly predefined fieldline seeding
structures, and uses a Monte Carlo sampling strategy named Woodcock tracking
to distribute samples along the view ray. An acceleration of this sampling strategy
requires local upper bounds for the FTLE values, which we progressively acquire
during the rendering. Our approach is tailored for high-quality visualizations of
complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface
structures as indicators for Lagrangian coherent structures (LCS). We demonstrate
the effectiveness of our approach by using a set of analytic test cases and real-world numerical simulations.
Sparse LU factorization offers some potential for parallelism, but at a level of very fine granularity. However, most current distributed memory MIMD architectures have too high communication latencies for exploiting all parallelism available. To cope with this, latencies must be avoided by coarsening the granularity and by message fusion. However, both techniques limit the concurrency, thereby reducing the scalability. In this paper, an implementation of a parallel LU decomposition algorithm for linear programming bases is presented for distributed memory parallel computers with noticable communication latencies. Several design decisions due to latencies, including data distribution and load balancing techniques, are discussed. An approximate performance model is set up for the algorithm, which allows to quantify the impact of latencies on its performance. Finally, experimental results for an Intel iPSC/860 parallel computer are reported and discussed.
We propose a novel GPU-based approach to render virtual X-ray projections of deformable tetrahedral meshes. These meshes represent the shape and the internal density distribution of a particular anatomical structure and are derived from statistical shape and intensity models (SSIMs). We apply our method to improve the geometric reconstruction of 3D anatomy (e.g.\ pelvic bone) from 2D X-ray images. For that purpose, shape and density of a tetrahedral mesh are varied and virtual X-ray projections are generated within an optimization process until the similarity between the computed virtual X-ray and the respective anatomy depicted in a given clinical X-ray is maximized. The OpenGL implementation presented in this work deforms and projects tetrahedral meshes of high resolution (200.000+ tetrahedra) at interactive rates. It generates virtual X-rays that accurately depict the density distribution of an anatomy of interest. Compared to existing methods that accumulate X-ray attenuation in deformable meshes, our novel approach significantly boosts the deformation/projection performance. The proposed projection algorithm scales better with respect to mesh resolution and complexity of the density distribution, and the combined deformation and projection on the GPU scales better with respect to the number of deformation parameters. The gain in performance allows for a larger number of cycles in the optimization process. Consequently, it reduces the risk of being stuck in a local optimum. We believe that our approach contributes in orthopedic surgery, where 3D anatomy information needs to be extracted from 2D X-rays to support surgeons in better planning joint replacements.
Sensory-evoked signal flow, at cellular and network levels, is primarily determined by the synaptic wiring of the underlying neuronal circuitry. Measurements of synaptic innervation, connection probabilities and sub-cellular organization of synaptic inputs are thus among the most active fields of research in contemporary neuroscience. Methods to measure these quantities range from electrophysiological recordings over reconstructions
of dendrite-axon overlap at light-microscopic levels to dense circuit reconstructions of small volumes at electron-microscopic resolution. However, quantitative and complete measurements at subcellular resolution and mesoscopic scales to obtain all local and long-range synaptic in/outputs for any neuron within an entire brain region are beyond present methodological limits. Here, we present a novel concept, implemented within an interactive software environment called NeuroNet, which allows (i) integration of sparsely sampled (sub)cellular morphological data into an accurate anatomical reference frame of the brain region(s) of interest, (ii) up-scaling to generate an average dense model of the neuronal circuitry within the respective brain region(s) and (iii) statistical measurements of synaptic innervation between all neurons within the model. We illustrate our approach by generating a dense average model of the entire rat vibrissal cortex, providing the required anatomical data, and illustrate how to measure synaptic innervation statistically. Comparing our results with data from paired recordings in vitro and in vivo, as well as with reconstructions of synaptic contact sites at light- and electron-microscopic levels, we find that our in silico measurements are in line with previous results.
Neuroanatomical analysis, such as classification of cell types, depends on reliable reconstruction of large numbers of complete 3D dendrite and axon morphologies. At present, the majority of neuron reconstructions are obtained from preparations in a single tissue slice in vitro, thus suffering from cut off dendrites and, more dramatically, cut off axons. In general, axons can innervate volumes of several cubic millimeters and may reach path lengths of tens of centimeters. Thus, their complete reconstruction requires in vivo labeling, histological sectioning and imaging of large fields of view. Unfortunately, anisotropic background conditions across such large tissue volumes, as well as faintly labeled thin neurites, result in incomplete or erroneous automated tracings and even lead experts to make annotation errors during manual reconstructions. Consequently, tracing reliability renders the major bottleneck for reconstructing complete 3D neuron morphologies. Here, we present a novel set of tools, integrated into a software environment named ‘Filament Editor’, for creating reliable neuron tracings from sparsely labeled in vivo datasets. The Filament Editor allows for simultaneous visualization of complex neuronal tracings and image data in a 3D viewer, proof-editing of neuronal tracings, alignment and interconnection across sections, and morphometric analysis in relation to 3D anatomical reference structures. We illustrate the functionality of the Filament Editor on the example of in vivo labeled axons and demonstrate that for the exemplary dataset the final tracing results after proof-editing are independent of the expertise of the human operator.
Ancient Egyptian papyri are often folded, rolled up or kept as small packages, sometimes even sealed. Physically unrolling or unfolding these packages might severely damage them. We demonstrate a way to get access to the hidden script without physical unfolding by employing computed tomography and mathematical algorithms for virtual unrolling and unfolding. Our algorithmic approaches are combined with manual interaction. This provides the necessary flexibility to enable the unfolding of even complicated and partly damaged papyrus packages. In addition, it allows us to cope with challenges posed by the structure of ancient papyrus, which is rather irregular, compared to other writing substrates like metallic foils or parchment. Unfolding of packages is done in two stages. In the first stage, we virtually invert the physical folding process step by step until the partially unfolded package is topologically equivalent to a scroll or a papyrus sheet folded only along one fold line. To minimize distortions at this stage, we apply the method of moving least squares. In the second stage, the papyrus is simply flattened, which requires the definition of a medial surface. We have applied our software framework to several papyri. In this work, we present the results of applying our approaches to mockup papyri that were either rolled or folded along perpendicular fold lines. In the case of the folded papyrus, our approach represents the first attempt to address the unfolding of such complicated folds.
A great amount of material properties is strongly influenced by dislocations, the carriers of plastic deformation. It is therefore paramount to have appropriate tools to quantify dislocation substructures with regard to their features, e.g., dislocation density, Burgers vectors or line direction. While the transmission electron microscope (TEM) has been the most widely-used equipment implemented to investigate dislocations, it usually is limited to the two-dimensional (2D) observation of three-dimensional (3D) structures. We reconstruct, visualize and quantify 3D dislocation substructure models from only two TEM images (stereo-pairs) and assess the results. The reconstruction is based on the manual interactive tracing of filiform objects on both images of the stereo-pair. The reconstruction and quantification method are demonstrated on dark field (DF) scanning (S)TEM micrographs of dislocation substructures imaged under diffraction contrast conditions. For this purpose, thick regions (> 300 nm) of TEM foils are analyzed, which are extracted from a Ni-base superalloy single crystal after high temperature creep deformation. It is shown how the method allows 3D quantification from stereo-pairs in a wide range of tilt conditions, achieving line length and orientation uncertainties of 3 % and 7°, respectively. Parameters that affect the quality of such reconstructions are discussed.