TY - JOUR A1 - Zaikin, Alexei A1 - Kurths, Jürgen A1 - Saparin, Peter A1 - Gowin, W. A1 - Prohaska, Steffen T1 - Modeling bone resorption in 2D CT and 3D mu CT images N2 - We study several algorithms to simulate bone mass loss in two-dimensional and three-dimensional computed tomography bone images. The aim is to extrapolate and predict the bone loss, to provide test objects for newly developed structural measures, and to understand the physical mechanisms behind the bone alteration. Our bone model approach differs from those already reported in the literature by two features. First, we work with original bone images, obtained by computed tomography (CT); second, we use structural measures of complexity to evaluate bone resorption and to compare it with the data provided by CT. This gives us the possibility to test algorithms of bone resorption by comparing their results with experimentally found dependencies of structural measures of complexity, as well as to show efficiency of the complexity measures in the analysis of bone models. For two-dimensional images we suggest two algorithms, a threshold algorithm and a virtual slicing algorithm. The threshold algorithm simulates bone resorption on a boundary between bone and marrow, representing an activity of osteoclasts. The virtual slicing algorithm uses a distribution of the bone material between several virtually created slices to achieve statistically correct results, when the bone-marrow transition is not clearly defined. These algorithms have been tested for original CT 10 mm thick vertebral slices and for simulated 10 mm thick slices constructed from ten I mm thick slices. For three-dimensional data, we suggest a variation of the threshold algorithm and apply it to bone images. The results of modeling have been compared with CT images using structural measures of complexity in two- and three-dimensions. This comparison has confirmed credibility of a virtual slicing modeling algorithm for two-dimensional data and a threshold algorithm for three-dimensional data Y1 - 2005 SN - 0218-1274 ER - TY - JOUR A1 - Saparin, P. I. A1 - Thomsen, J. S. A1 - Prohaska, Steffen A1 - Zaikin, Alexei A1 - Kurths, Jürgen A1 - Hege, H. C. A1 - Gowin, W. T1 - Quantification of spatial structure of human proximal tibial bone biopsies using 3D measures of complexity N2 - Changes in trabecular bone composition during development of osteoporosis are used as a model for bone loss in microgravity conditions during a space flight. Symbolic dynamics and measures of complexity are proposed and applied to assess quantitatively the structural composition of bone tissue from 3D data sets of human tibia bone biopsies acquired by a micro-CT scanner. In order to justify the newly proposed approach, the measures of complexity of the bone architecture were compared with the results of traditional 2D bone histomorphometry. The proposed technique is able to quantify the structural loss of the bone tissue and may help to diagnose and to monitor changes in bone structure of patients on Earth as well as of the space-flying personnel. © 2005 Elsevier Ltd. All rights reserved Y1 - 2005 SN - 0094-5765 ER - TY - THES A1 - Prohaska, Steffen T1 - Skeleton-based visualization of massive voxel objects with network-like architecture T1 - Skelettbasierte Visualisierung großer Voxel-Objekte mit netzwerkartiger Architektur N2 - This work introduces novel internal and external memory algorithms for computing voxel skeletons of massive voxel objects with complex network-like architecture and for converting these voxel skeletons to piecewise linear geometry, that is triangle meshes and piecewise straight lines. The presented techniques help to tackle the challenge of visualizing and analyzing 3d images of increasing size and complexity, which are becoming more and more important in, for example, biological and medical research. Section 2.3.1 contributes to the theoretical foundations of thinning algorithms with a discussion of homotopic thinning in the grid cell model. The grid cell model explicitly represents a cell complex built of faces, edges, and vertices shared between voxels. A characterization of pairs of cells to be deleted is much simpler than characterizations of simple voxels were before. The grid cell model resolves topologically unclear voxel configurations at junctions and locked voxel configurations causing, for example, interior voxels in sets of non-simple voxels. A general conclusion is that the grid cell model is superior to indecomposable voxels for algorithms that need detailed control of topology. Section 2.3.2 introduces a noise-insensitive measure based on the geodesic distance along the boundary to compute two-dimensional skeletons. The measure is able to retain thin object structures if they are geometrically important while ignoring noise on the object's boundary. This combination of properties is not known of other measures. The measure is also used to guide erosion in a thinning process from the boundary towards lines centered within plate-like structures. Geodesic distance based quantities seem to be well suited to robustly identify one- and two-dimensional skeletons. Chapter 6 applies the method to visualization of bone micro-architecture. Chapter 3 describes a novel geometry generation scheme for representing voxel skeletons, which retracts voxel skeletons to piecewise linear geometry per dual cube. The generated triangle meshes and graphs provide a link to geometry processing and efficient rendering of voxel skeletons. The scheme creates non-closed surfaces with boundaries, which contain fewer triangles than a representation of voxel skeletons using closed surfaces like small cubes or iso-surfaces. A conclusion is that thinking specifically about voxel skeleton configurations instead of generic voxel configurations helps to deal with the topological implications. The geometry generation is one foundation of the applications presented in Chapter 6. Chapter 5 presents a novel external memory algorithm for distance ordered homotopic thinning. The presented method extends known algorithms for computing chamfer distance transformations and thinning to execute I/O-efficiently when input is larger than the available main memory. The applied block-wise decomposition schemes are quite simple. Yet it was necessary to carefully analyze effects of block boundaries to devise globally correct external memory variants of known algorithms. In general, doing so is superior to naive block-wise processing ignoring boundary effects. Chapter 6 applies the algorithms in a novel method based on confocal microscopy for quantitative study of micro-vascular networks in the field of microcirculation. N2 - Die vorliegende Arbeit führt I/O-effiziente Algorithmen und Standard-Algorithmen zur Berechnung von Voxel-Skeletten aus großen Voxel-Objekten mit komplexer, netzwerkartiger Struktur und zur Umwandlung solcher Voxel-Skelette in stückweise-lineare Geometrie ein. Die vorgestellten Techniken werden zur Visualisierung und Analyse komplexer drei-dimensionaler Bilddaten, beispielsweise aus Biologie und Medizin, eingesetzt. Abschnitt 2.3.1 leistet mit der Diskussion von topologischem Thinning im Grid-Cell-Modell einen Beitrag zu den theoretischen Grundlagen von Thinning-Algorithmen. Im Grid-Cell-Modell wird ein Voxel-Objekt als Zellkomplex dargestellt, der aus den Ecken, Kanten, Flächen und den eingeschlossenen Volumina der Voxel gebildet wird. Topologisch unklare Situationen an Verzweigungen und blockierte Voxel-Kombinationen werden aufgelöst. Die Charakterisierung von Zellpaaren, die im Thinning-Prozess entfernt werden dürfen, ist einfacher als bekannte Charakterisierungen von so genannten "Simple Voxels". Eine wesentliche Schlussfolgerung ist, dass das Grid-Cell-Modell atomaren Voxeln überlegen ist, wenn Algorithmen detaillierte Kontrolle über Topologie benötigen. Abschnitt 2.3.2 präsentiert ein rauschunempfindliches Maß, das den geodätischen Abstand entlang der Oberfläche verwendet, um zweidimensionale Skelette zu berechnen, welche dünne, aber geometrisch bedeutsame, Strukturen des Objekts rauschunempfindlich abbilden. Das Maß wird im weiteren mit Thinning kombiniert, um die Erosion von Voxeln auf Linien zuzusteuern, die zentriert in plattenförmigen Strukturen liegen. Maße, die auf dem geodätischen Abstand aufbauen, scheinen sehr geeignet zu sein, um ein- und zwei-dimensionale Skelette bei vorhandenem Rauschen zu identifizieren. Eine theoretische Begründung für diese Beobachtung steht noch aus. In Abschnitt 6 werden die diskutierten Methoden zur Visualisierung von Knochenfeinstruktur eingesetzt. Abschnitt 3 beschreibt eine Methode, um Voxel-Skelette durch kontrollierte Retraktion in eine stückweise-lineare geometrische Darstellung umzuwandeln, die als Eingabe für Geometrieverarbeitung und effizientes Rendering von Voxel-Skeletten dient. Es zeigt sich, dass eine detaillierte Betrachtung der topologischen Eigenschaften eines Voxel-Skeletts einer Betrachtung von allgemeinen Voxel-Konfigurationen für die Umwandlung zu einer geometrischen Darstellung überlegen ist. Die diskutierte Methode bildet die Grundlage für die Anwendungen, die in Abschnitt 6 diskutiert werden. Abschnitt 5 führt einen I/O-effizienten Algorithmus für Thinning ein. Die vorgestellte Methode erweitert bekannte Algorithmen zur Berechung von Chamfer-Distanztransformationen und Thinning so, dass diese effizient ausführbar sind, wenn die Eingabedaten den verfügbaren Hauptspeicher übersteigen. Der Einfluss der Blockgrenzen auf die Algorithmen wurde analysiert, um global korrekte Ergebnisse sicherzustellen. Eine detaillierte Analyse ist einer naiven Zerlegung, die die Einflüsse von Blockgrenzen vernachlässigt, überlegen. In Abschnitt 6 wird, aufbauend auf den I/O-effizienten Algorithmen, ein Verfahren zur quantitativen Analyse von Mikrogefäßnetzwerken diskutiert. KW - Visualisierung KW - Bilddatenanalyse KW - Skelettberechnung KW - Geometrieerzeugung KW - I/O-effiziente Algorithmen KW - visualization KW - image data analysis KW - skeletonization KW - geometry generation KW - external memory algorithms Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14888 ER -