Shape Recovery From Medical Image Data Using Extended Superquadrics

Rapid and representative reconstruction of geometric shape models from surface measurements has applications in diverse arenas ranging from industrial product design to biomedical organ/tissue modeling. However, despite the large body of work, most shape models have had limited success in bridging the gap between reconstruction, recognition, and analysis due to conflicting requirements. On one hand, large numbers of shape parameters are necessary to obtain meaningful information from noisy sensor data. On the other hand, search and recognition techniques require shape parameterizations/abstractions employing few robust shape descriptors. The extension of such shape models to encompass various analysis modalities (in the form of kinematics, dynamics and FEA) now necessitates the inclusion of the appropriate physics (preferably in parametric form) to support the simulation based refinement process. Thus, in this paper we discuss development of a class of parametric shape abstraction models termed as extended superquadrics. The underlying geometric and computational data structure intimately ties together implicit-, explicit- and parametric- surface representation together with a volumetric solid representation that makes them well suited for shape representation. Furthermore, such models are well suited for transitioning to analysis, as for example, in model-based non rigid structure and motion recovery or for mesh generation and simplified volumetric-FEA applications. However, the development of the concomitant methods and benchmarking is necessary prior to widespread acceptance. We will explore some of these aspects further in this paper supported with case studies of shape abstraction from image data in the biomedical/life-sciences arena whose diversity and irregularities pose difficulties for more traditional models.