We report on the design and implementation of a number type called Real_algebraic. This number type allows us to compute the sign of arithmetic expressions involving the operations +, −, ·, /, d √ . The sign computation is always correct and, in this sense, not subject to rounding errors. We focus on modularity and use generic programming techniques to make key parts of the implementation exchangeable. Thus, our design allows for easily performing experiments with different implementations or thereby tailoring the number type for specific tasks. For many problems in computational geometry, instantiations of our number type Real_algebraic are a user-friendly alternative for implementing the exact geometric computation paradigm in order to abandon numerical robustness problems.

The presented technique is both, fast and flexible. It can be used to interactively derive automatic distance measures for arbitrary mesh-based segmentations. Due to the geometrically exact measurements, it is possible to reliably estimate safety margins, assess possible infiltrations and other clinically relevant measures. To exploit this benefit, the method requires precise segmentations as input data.

Clinically relevant lymph nodes were detected within a few minutes and provided sufficient accuracy to demonstrate the feasibility of a new segmentation method. The test data were diverse, and the robust results suggest potential applicability to many kinds of lymph node abnormalities, except for extremely degenerated lymph nodes.

The evaluation of spatial relationships between anatomic structures is a major task in surgical planning. Surface models generated from medical image data (intensity, binary) are often used for visualization and 3D measurement of extents and distances between neighboring structures. In applications for intervention or radiation treatment planning, the surface models need to exhibit a natural look (referring to smoothness of the surface), but also to be accurate. Smoothing algorithms allow to reduce artifacts from mesh generation, but the result is always a tradeoff between smoothness and accuracy. Required features will be removed and distances between adjacent structures get changed. Thus, we present a modification to common mesh smoothing algorithms, which allows to generate smooth surfaces models while distances of neighboring structures are preserved. We compared our distance-aware approach to conventional uniform smoothing methods and evaluated the resulting surfac e models regarding smoothness and accuracy for their application within the context of surgical planning

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