Papers by Heinz-Otto Peitgen
Mathematische Annalen, 1977
Topological Methods in Nonlinear Analysis, 2002
The Lefschetz fixed point theorem for multivalued upper semicontinuous acyclic maps with multipli... more The Lefschetz fixed point theorem for multivalued upper semicontinuous acyclic maps with multiplicity with respect to (w.r.t.) a given field F of F-simplicial spaces is proved.
Mathematics and Biosciences in Interaction
We study various properties of constructive optimization in 3D vascular systems. After some remar... more We study various properties of constructive optimization in 3D vascular systems. After some remarks on existing approaches to vascular modeling and on the theory of vascular optimality, we briefly describe an algorithm called Global Constructive Optimization (GCO). Twenty-one vascular systems are modeled in three different groups: planar, spherical, and liver shaped. Based on the Strahler ordering scheme, these models are characterized and compared to data from liver corrosion casts. A good correspondence could be observed between modeled and real portal venous systems. The branching characteristics of the hepatic vein still pose open questions. Finally, a concept for the modeling of vascular interdigitation based on optimality principles is suggested.
Proceedings Visualization, 2001. VIS '01.
We describe a pipeline of image processing steps for deriving symbolic models of vascular structu... more We describe a pipeline of image processing steps for deriving symbolic models of vascular structures from radiological data which reflect the branching pattern and diameter of vessels. For the visualization of these symbolic models, concatenated truncated cones are smoothly blended at branching points. We put emphasis on the quality of the visualizations which is achieved by anti-aliasing operations in different stages of the visualization. The methods presented are referred to as HQVV (High Quality Vessel Visualization). Scalable techniques are provided to explore vascular structures of different orders of magnitude. The hierarchy as well as the diameter of the branches of vascular systems are used to restrict visualizations to relevant subtrees and to emphasize parts of vascular systems. Our research is inspired by clear visualizations in textbooks and is targeted toward medical education and therapy planning. We describe the application of vessel visualization techniques for liver surgery planning. For this application it is crucial to recognize the morphology and branching pattern of vascular systems as well as the basic spatial relations between vessels and other anatomic structures.
Chaos
Fractals for the Classroom: Strategic Activities Volume Two, 1992
IEEE Transactions on Visualization and Computer Graphics, 2006
Figure 1: Examples of vascular illustrations enhancing perception of properties important in surg... more Figure 1: Examples of vascular illustrations enhancing perception of properties important in surgery. Left and right image: Hatching indicates curvature and distances; middle image: Textures indicate distances to a generalized lesion (orange)
IEEE Transactions on Medical Imaging, 2008
Advanced Segmentation Techniques for Lung Nodules, Liver Metastases, and Enlarged Lymph Nodes in CT Scans
IEEE Journal of Selected Topics in Signal Processing, 2009
AbstractThis article presents advanced algorithms for seg-menting lung nodules, liver metastases... more AbstractThis article presents advanced algorithms for seg-menting lung nodules, liver metastases, and enlarged lymph nodes in CT scans. Segmentation and volumetry are essential tasks of a software assistant for oncological therapy monitoring. Our methods are based ...
Advances in Medical Sciences, 2012
Purpose: To evaluate the significance of the hypertrophy concept in patients requiring extended l... more Purpose: To evaluate the significance of the hypertrophy concept in patients requiring extended liver resections for colorectal metastasis in the time of computer assisted surgery. Methods: Retrospective analysis of patient collective undergoing major liver surgery. 2D CT, 3D CAS with Fraunhofer MeVis Sofware. Portal vein embolisation (PVE) with the Amplazer Plug, portal vein ligation (PVL) as 1. Stage operative procedure. Results: 2D CT data identified 29 patients out of 319 (2002-2009) to be at risk for liver failure after resection. After 3D CAS analysis and virtual operation planning, only 7/29 were at true risk and were submitted to portal vein occlusion (PVO). Another 5 patients were submitted to the hypertrophy concept for intraoperative finding of insufficient parenchyma quality. In total, 12 patients underwent PVO (6 PVE/6 PVL). 9/12 patients went to stage 2 and were successfully operated. There was no difference in future remnant liver volume (FRLV) gain or waiting time to step 2 between the groups, though survival was better in the PVE group. Conclusion: PVO is an effective approach if the patient's future remnant liver (FRL) is too small on 2D CT volumetry. 3D CAS has great impact on the analysis of FRL capacity and in augmenting resectability-in our experience only patients with insufficient FRLV on the virtual resection plan have to take the risk of PVO to maintain the chance of liver resection.
IEEE Transactions on Medical Imaging, 2006
Volumetric growth assessment of pulmonary lesions is crucial to both lung cancer screening and on... more Volumetric growth assessment of pulmonary lesions is crucial to both lung cancer screening and oncological therapy monitoring. While several methods for small pulmonary nodules have previously been presented, the segmentation of larger tumors that appear frequently in oncological patients and are more likely to be complexly interconnected with lung morphology has not yet received much attention. We present a fast, automated segmentation method that is based on morphological processing and is suitable for both small and large lesions. In addition, the proposed approach addresses clinical challenges to volume assessment such as variations in imaging protocol or inspiration state by introducing a method of segmentation-based partial volume analysis (SPVA) that follows on the segmentation procedure. Accuracy and reproducibility studies were performed to evaluate the new algorithms. In vivo interobserver and interscan studies on low-dose data from eight clinical metastasis patients revealed that clinically significant volume change can be detected reliably and with negligible computation time by the presented methods. In addition, phantom studies were conducted. Based on the segmentation performed with the proposed method, the performance of the SPVA volumetry method was compared with the conventional technique on a phantom that was scanned with different dosages and reconstructed with varying parameters. Both systematic and absolute errors were shown to be reduced substantially by the SPVA method. The method was especially successful in accounting for slice thickness and reconstruction kernel variations, where the median error was more than halved in comparison to the conventional approach. Index Terms-Chest imaging, computer aided analysis, image segmentation, volume measurement, X-ray tomography. I. INTRODUCTION A. Clinical Background Since the entire cardiac output flows through the lungs, the risk of hematogenous lung metastases is very high. Apart from primary lung cancer, the most common tumors metastasizing
Deterministic Chaos: Sensitivity, Mixing, and Periodic Points
Mathematical research in chaos can be traced back at least to 1890, when Henri Poincare studied t... more Mathematical research in chaos can be traced back at least to 1890, when Henri Poincare studied the stability of the solar system. He asked if the planets would continue on indefinitely in roughly their present orbits, or might one of them wander off into eternal darkness or crash into the sun. He did not find an answer to his question, but he did create a new analytical method, the geometry of dynamics. Today his ideas have grown into the subject called topology, which is the geometry of continuous deformation. Poincare made the first discovery of chaos in the orbital motion of three bodies which mutually exert gravitational forces on each other.
Surgical procedures for the resection of pathologic lesions are often risky interventions. The ri... more Surgical procedures for the resection of pathologic lesions are often risky interventions. The risk concerns postoperative complications as well as the success of the operation in terms of its long-term effect. Postoperative complications may result if too much tissue is removed. The long-term effect depends on whether all lesions are detected and are removed entirely together with a saftey margin. Risk analysis is an important aspect in preoperative surgery planning. Currently, preoperative planning considers the general state of the patient as well as special images resulting e.g. from computer tomography (CT). The currently prevailing techniques for preoperative planning are highly subjective and error-prone as no reliable methods exist to evaluate the extent of anatomic and pathologic structures and to quantitatively analyze these structures.
IEEE Visualization, 2002. VIS 2002.
We discuss 3d interaction techniques for the quantitative analysis of spatial relations in medica... more We discuss 3d interaction techniques for the quantitative analysis of spatial relations in medical visualizations. We describe the design and implementation of measurement tools to measure distances, angles and volumes in 3d visualizations. The visualization of measurement tools as recognizable 3d objects and a 3d interaction, which is both intuitive and precise, determines the usability of such facilities. Measurements may be carried out in 2d visualizations of the original radiological data and in 3d visualizations. The result of a measurement carried out in one view is also displayed in the other view appropriately. We discuss the validation of the obtained measures. Finally, we describe how some important measurement tasks may be solved automatically.
Evaluation of Image Registration Using a Mass-Spring Model of the Breast
IFMBE Proceedings
ABSTRACT Deformable motion correction has become a fundamental image processing task for the quan... more ABSTRACT Deformable motion correction has become a fundamental image processing task for the quantitative analysis of dynamic contrast-enhanced breast magnetic-resonance imaging (MRI). However, although various non-linear image registration techniques are available, objective evaluation remains challenging. In this paper, we propose a biomechanical model of the breast based on a mass-spring system and an internal tetrahedron structure. We demonstrate how this model can be applied to clinical datasets to generate plausible breast deformations for the evaluation. For this purpose, we integrate a thin-plate spline image transformation into the model. Furthermore, we show how the specific model can be used to quantitatively evaluate breast MRI motion correction, and present preliminary registration results achieved with the proposed method.
Medical Image Computing and Computer-Assisted Intervention – MICCAI 2000
A robust method for the removal of non-cerebral tissue in T1-weighted magnetic resonance (MR) bra... more A robust method for the removal of non-cerebral tissue in T1-weighted magnetic resonance (MR) brain images is presented. This procedure, often referred to as skull stripping, is an important step in neuroimaging. Our novel approach consists of a single morphological operation, namely a modified three-dimensional fast watershed transform that is perfectly suited to locate the brain, including the cerebellum and the spinal cord. The main advantages of our method lie in its simplicity and robustness. It is simple since neither preprocessing of the MRI data nor contour refinement is required. Furthermore, the skull stripping solely relies on one basic anatomical fact, i.e. the three-dimensional connectivity of white matter. As long as this feature is observed in the image data, a robust segmentation can be guaranteed independently from image orientation and slicing, even in presence of severe intensity non-uniformity and noise. For that purpose, the watershed algorithm has been modified by the concept of pre-flooding, which helps to prevent oversegmentation, depending on a single parameter. The automatic selection of the optimal parameter as well as the applicability are discussed based on the results of phantom and clinical brain studies.
it - Information Technology
ZusammenfassungDie medizinische Visualisierung befasst sich mit der Darstellung und Exploration r... more ZusammenfassungDie medizinische Visualisierung befasst sich mit der Darstellung und Exploration radiologischer Bilddatensätze. Zu den grundlegenden Aufgaben gehören die Exploration der patientenindividuellen Bilddaten, die Visualisierung baumartiger Strukturen, die Hervorhebung von Objekten, die quantitative Analyse sowie die virtuelle Resektion. Lösungsmöglichkeiten für diese Aufgaben werden anhand konkreter Fallbeispiele beschrieben.
Self-Affine Curves and Sequential Machines
Real Analysis Exchange
Our paper was motivated by the desire to understand to what extend the notion of sequential funct... more Our paper was motivated by the desire to understand to what extend the notion of sequential functions is capable to construct self-affine functions and curves. We shall prove that each self-affine curve is generated by a sequential machine. This includes not only the curves obtained by the method of M. F. Dekking but also curves produced by iterated function systems. In order to expose the relations between the construction using sequential functions and the previous established methods we introduce several types of self-affine curves. Many classical examples will be discussed to illustrate the different types of self-affinity. In the general case, the realization of the curves by means of sequential functions is based on the classical Cantor representation of the real numbers in the unit interval. The combinatorial part of Dekking’s construction, the substitution, will appear as an ingredient of the sequential machine. The geometrical part can be recovered in the consistency condition for sequential machines, which assures that a sequential machine leads to a continuous function.
Pacific Journal of Mathematics
The fixed point theory for mappings of compact attraction type is used to obtain some new asympto... more The fixed point theory for mappings of compact attraction type is used to obtain some new asymptotic fixed point theorems. These investigations have been motivated by the properties of ejective and attractive fixed points. Special emphasis is given to those situations where the fixed points are of zero index. The generality of the approach admits the useful formula ind(X,/, F) = Λ(/,X)-Λ(/,X\F) which allows the computation of the index of FC Fix (/: X-> X) in terms of Lefschetz numbers.
Simulation und Visualisierung, 2001
Zusammenfassung. Wir pr?sentieren Methoden zur Bema?u ng segmentierter Objekte in medizinischen 3... more Zusammenfassung. Wir pr?sentieren Methoden zur Bema?u ng segmentierter Objekte in medizinischen 3d-Visualisierungen. Im Vordergrund steht die Distanzbe-stimmung, die Beurteilung von Gr??enverh?ltnissen und die Vermessung von Win-keln. Dabei wird die Visualisierung von Messwerkzeugen und die 3d-Interaktion bei der Anwendung dieser Werkzeuge erl?utert. Darüber hinaus werden wich tige Ver-messungsaufgaben identifiziert, die einer weitestgehenden Automatisierung bedür-fen. Dazu z?hlt die Bestimmung minimaler Abst?nde und
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Papers by Heinz-Otto Peitgen