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A recently developed topological mesh modeling approach allows users to change topology of orientable 2-manifold meshes and to create unusual faces. Handle-faces are one of such faces that are commonly created during topology changes. This paper shows that vertex insertion and corner cutting subdivision schemes can effectively be used to reconstruct handle-faces. These reconstructions effectively show the structure of these unusual faces. The paper has three contributions. First, we develop a new corner cutting scheme, which provides a tension parameter to control the shape of subdivided surface. Second, we develop careful and efficient remeshing algorithms for our comer cutting scheme that use only the basic operations provided by our topological mesh modeling approach. This implementation ensures that our new corner cutting scheme preserves topological robustness. Finally, a comparative study shows that the corner cutting schemes create better handles and holes than the well-known Catmull-Clark scheme.

We present a novel medial-based, multi-scale approach to shape representation and controlled deformation. We use medial-based profiles for shape representation, which follow the geometry of the structure and describe general, intuitive, and independent shape measures (length, orientation, and thickness). Controlled shape deformations (stretch, bend, and bulge) are obtained either as a result of applying deformation operators at certain locations and scales on the medial profiles, or by varying the weights of the main variation modes obtained from a new hierarchical (multi-scale) and regional (multi-location) principal component analysis of the medial profiles. We demonstrate the ability to produce controlled shape deformations on a medial-based representation of the corpus callosum. We show how this control of shape deformations facilitates the design of a layered framework for image segmentation and present results of segmenting the corpus callosum from 2D mid-sagittal magnetic resonance images of the human brain. Furthermore we show how the medial-based representation facilitates hierarchical, deformation-specific statistical shape analysis of segmented corpora callosa.

Meshes, which generalize polyhedra by using non-planar faces, are the most commonly used objects in computer graphics. Modeling 2-dimensional manifold meshes with a simple user interface is an important problem in computer graphics and computer aided geometric design. In this paper, we propose a conceptual framework to model meshes. Our framework guarantees topologically correct 2-dimensional manifolds and provides a new user interface paradigm for mesh modeling systems.

Bio structural and functional research and education is playing an increasingly important role in today's post-genome era. Protein geometry and shape modeling is thus a fundamental issue for protein visualization. The number of protein structures determined by X-ray crystallography or Nuclear Magnetic Resonance (NMR) is expanding in an exponential rate. Recent technology advancement has also made it possible for the determination of larger and more complicated proteins structure. A generic and automatic shape modeling for protein structures is therefore highly desired for effective and efficient protein visualization. We propose a bio-native geometric modeling technique in this paper for constructing protein secondary structure. Our emphasis is placed on the shape compatibility with the protein conformation property. Efforts are also made to handle smooth sweeping for complex protein structures. We describe as well a Virtual Reality (VR) application for protein structure education based on our Bio-native shape modeling and visualization techniques developed in this work.

In a research context in which multiple and well-behaved Surface Reconstruction algorithms already exist, the main goal is not to implement a visualization toolkit able render complex object, but the implementation of methods which can improve our knowledge on the observed world. This work presents a general Surface Reconstruction framework which encapsulates the uncertainty of the sampled data, making no assumption on the shape of the surface to be reconstructed. Starting from the input points (either points clouds or multiple range images), an Estimated Existence Function (EEF) is built which models the space in which the desired surface could exist and, by the extraction of EEF critical points, the surface is reconstructed. The final goal is the development of a generic framework that is able to adapt the result to different kinds of additional information coming that is from multiple sensors.

Touch is an important modality to recover object shape. We present a method for a robot to complete a partial shape model by local tactile exploration. In local tactile exploration, the finger is constrained to follow the local surface. This is useful for recovering information about a contiguous portion of the object and is frequently employed by humans. There are three contributions. First, we show how to segment an initial point cloud of a grasped, unknown object into hand and object. Second, we present a local tactile exploration planner. This combines a Gaussian Process (GP) model of the object surface with an AtlasRRT planner. The GP predicts the unexplored surface and the uncertainty of that prediction. The AtlasRRT creates a tactile exploration path across this predicted surface, driving it towards the region of greatest uncertainty. Finally, we experimentally compare the planner with alternatives in simulation, and demonstrate the complete approach on a real robot. We show that our planner successfully traverses the object, and that the full object shape can be recovered with a good degree of accuracy.