| Deformable models are geometric object models whose dynamic behaviors are governed by variational principles and/or partial differential equations (PDEs). They have proven to be valuable in an increasing number of applications spanning the fields of graphics, geometric modeling, vision, visualization, finite element simulation, and bio-medical imaging. Nevertheless, conventional parameterized deformable models are not amenable to arbitrarily complicated topology and geometry. Despite the recent advancement of the implicit level-set approach to overcome the topological deficiency of traditional deformable models, such a topological flexibility for level-set techniques is accompanied by a costly tradeoff in efficiency since all the computations must be conducted in a higher dimension.; In conjunction with rapidly improving data acquisition technologies for use in the physical, biological, and medical sciences, it is imperative to develop a new, complementary arsenal of deformable modeling techniques for analysis, simulation, manipulation, and visualization applications. In this dissertation, we will present three new deformable models that can overcome some limitations of the aforementioned techniques. Our new models are topology adaptive subdivision surfaces whose behaviors are governed by variational principles and/or PDEs. The new models can dynamically extract complicated geometry as well as arbitrary, unknown topology without a priori assumption on modeled datasets. They can process a large variety of data formats ranging from volumetric images, point clouds, to algebraic functions. More importantly, the new models can reconstruct shapes of disparate types (including open, closed, and even non-manifold geometry) and recover shape features.; Our new models prove to be very valuable to a wide range of applications in visual computing, including computer graphics, computer vision, visualization and bio-medical imaging. The new models have been successfully applied in areas such as surface reconstruction from 3D unorganized point clouds, volumetric image segmentation, iso-surface extraction, multiple-view images based computer vision, interactive mesh processing, etc. |
