AbstractÐThis paper introduces a refined general definition of a skeleton that is based on a penalized-distance function and cannot create any of the degenerate cases of the earlier CEASAR and TEASAR algorithms. Additionally, we provide an algorithm that finds the skeleton accurately and rapidly. Our solution is fully automatic, which frees the user from having to engage in manual data preprocessing. We present the accurate skeletons computed on a number of test datasets. The algorithm is very efficient as demonstrated by the running times which were all below seven minutes. Index TermsÐSkeleton, centerline, medial axis, automatic preprocessing, modeling. 1

AbstractÐVirtual endoscopy is a computerized, noninvasive procedure for detecting anomalies inside human organs. Several preliminary studies have demonstrated the benefits and effectiveness of this modality. Unfortunately, previous work cannot guarantee that an existing anomaly will be detected, especially for complex organs with multiple branches. In this paper, we introduce the concept of reliable navigation, which ensures the interior organ surface is fully examined by the physician performing the virtual endoscopy procedure. To achieve this, we propose computing a reliable fly-through path that ensures no blind area during the navigation. Theoretically, we discuss the criteria of evaluating a reliable path and prove that the problem of generating an optimal reliable path for virtual endoscopy is NP-complete. In practice, we develop an efficient method for the calculation of an effective reliable path. First, a small set of center observation points are automatically located inside the hollow organ. For each observation point, there exists at least one patch of interior surface visible to it, but that cannot be seen from any of the other observation points. These chosen points are then linked with a path that stays in the center of the organ. Finally, new points inside the organ are recursively selected and connected into the path until the entire organ surface is visible from the path. We present encouraging results from experiments on several data sets. For a medium size volumetric model with several hundred thousand inner voxels, an effective reliable path can be generated in several minutes. Index TermsÐVirtual endscopy, reliable path, reliable navigation, camera control, NP-complete, visibility. 1

AbstractÐWe propose a novel conservative visibility culling technique based on the Prioritized-Layered Projection (PLP) algorithm. PLP is a time-critical rendering technique that computes, for a given viewpoint, a partially correct image by rendering only a subset of the geometric primitives, those that PLP determines to be most likely visible.Our new algorithm builds on PLP and provides an efficient way of finding the remaining visible primitives.We do this by adding a second phase to PLP which uses image-space techniques for determining the visibility status of the remaining geometry.Another contribution of our work is to show how to efficiently implement such image-space visibility queries using currently available OpenGL hardware and extensions.We report on the implementation of our techniques on several graphics architectures, analyze their complexity, and discuss a possible hardware extension that has the potential to further increase performance. Index TermsÐConservative visibility, occlusion culling, interactive rendering. æ