Shape Recovery Using Extended Superquadrics

Reverse engineering of accurate 3D models and 2D contours of real objects from surface measurements is recognized as an important research goal in various communities. Currently the application domains include industrial product design and computer generated imagery for film and multimedia and potential application now also extends to the life sciences realm. Despite the large body of work on 3D modeling, most models of shape lack the descriptive power to bridge the gap between reconstruction, recognition, and analysis due, mostly, to conflicting requirements. To obtain meaningful information from noisy sensor data reconstruction models, researchers have traditionally used large numbers of parameters. In contrast searching and recognition techniques use shape abstractions, which drastically reduce information. Analysis models require the inclusion of physics, in the form of kinematics, dynamics and FEA, preferably in parametric form to support simulation-based refinement processes. Thus the goal of our effort is to develop a class of hybrid models whose underlying geometric and computational data structure intimately combines implicit, explicit and parameterized surface representations with volumetric solid representations that are well suited for transitioning to analysis and at the same time enjoy a low order parameterization. This thesis proposes a new shape parameterization for smoothly deformable two and three dimensional objects, such as those found in biomedical images, whose diversity and irregularity make them difficult to represent in terms of fixed features or high fidelity models which are capable for any analysis. iii The proposed representation strategy can then represent 3D medical data obtained as point clouds from sources such range imaging devices. To achieve this we have utilized extended-superquadric models which are well-suited for shape representation but require the development of the concomitant methods and benchmarking prior to widespread acceptance. 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.