Publikationen

The study and analysis of relationships in a complex and multi-scale data set is a challenge of information and scientific visualization. This work proposes an integrated visualization to capture all the important aspects of multi-scale data into the same view by leveraging the multi-scale biomedical knowledge encoded into an underly- ing ontology. Ontology supports visualization by providing semantic means to identify relevant items that must be presented to the user. The study and analysis of relationships across the scales are presented as results of queries to the multi-scale biomedical knowledge space. We demonstrate the prototype of the graphical interface of an integrated visualization framework and the knowledge formalization support in an example scenario related to the musculoskeletal diseases.

Pathologies which simultaneously involve different spatial scales are often difficult to understand. Biomedical data from different modalities and spatio-temporal scales needs to be combined to obtain an understandable representation for its examination. Despite of requests to improve the exploration of multi-scale biomedical data, no major progress has been made in terms of a common strategy combining the state of art in visualization and interaction. This work presents a multimodal approach for a natural biomedical multi-scale exploration. The synergy of a multi-layered visualization environment based on spatial scales with hand gestures and haptic interfaces opens new perspectives for a natural data manipulation.

Lecture given at Massachusetts Institute of Technology (september 11, 2014) by Prof. F.-E. Wolter. More information: 

http://sandlab.mit.edu/index.php/seminars/95-seminar-by-prof-franz-erich-wolter-sept-11-12-00pm-33-116

We shall describe how concepts from differential geometry have been providing powerful tools creating major advances in geometric modeling, geometry processing and image analysis dealing with the topics presented in the title of this address. This talk includes a retrospective compiling contributions of the author's works showing how concepts from local and global differential geometry have introduced new methods into geometric modeling and shape interrogation and classification finally ending with modern state of the art research on geometry processing and image processing. A major part of this seminar starting with works in the late nineties at the author's laboratory is dedicated to discussing how "efficient finger prints" useful for indexing and clustering digital data collections can be derived from spectra of Laplace operators being naturally associated with geometric objects such as surfaces and solids as well as (colored) images including medical 2d- and 3d-images. Recently the latter works obtained particular attention in the area of medical imaging. Geometric aspects of the Laplacian operator lead to generalizations of the Laplacian operating on line bundles allowing to compute eigen-functions whose iso-surfaces yield smooth non-orientable Seifert surfaces spanning knot complements in three-dimensional manifolds. Next we focus on cut loci, the medial axis and its inverse in Euclidean and Riemannian worlds.

This work starts with basic medial axis results presented by the the author in the early nineties. Those results state: The Medial Axis Transform can be used to reconstruct, modify and design a given shape ("Shape Reconstruction Theorem"). Under some weak assumptions the medial axis contains the essence of the topological shape of the geometric object as it is a deformation retract of the given shape ("Topological Shape Theorem"). Therefore the medial axis contains the homotopy type of the given shape. We present recent results showing how geodesic Voronoi diagrams, geodesic medial axis and its inverse can be computed in 3d- or higher-dimensional Riemannian spaces. The "medial axis inverse" allows to construct a medial modeler providing efficient features for shape optimization with respect to shape dependent mechanical properties.