Physically Interacting With Four Dimensions

Thesis (Ph.D.) - Indiana University, Computer Sciences, 2009People have long been fascinated with understanding the fourth dimension. While making pictures of 4D objects by projecting them to 3D can help reveal basic geometric features, 3D graphics images by themselves are of limited value. For example, just as 2D shadows of 3D curves may have lines crossing one another in the shadow, 3D graphics projections of smooth 4D topological surfaces can be interrupted where one surface intersects another. The research presented here creates physically realistic models for simple interactions with objects and materials in a virtual 4D world. We provide methods for the construction, multimodal exploration, and interactive manipulation of a wide variety of 4D objects. One basic achievement of this research is to exploit the free motion of a computer-based haptic probe to support a continuous motion that follows the \emph{local continuity\/} of a 4D surface, allowing collision-free exploration in the 3D projection. In 3D, this interactive probe follows the full local continuity of the surface as though we were in fact \emph{physically touching\/} the actual static 4D object. Our next contribution is to support dynamic 4D objects that can move, deform, and collide with other objects as well as with themselves. By combining graphics, haptics, and collision-sensing physical modeling, we can thus enhance our 4D visualization experience. Since we cannot actually place interaction devices in 4D, we develop fluid methods for interacting with a 4D object in its 3D shadow image using adapted reduced-dimension 3D tools for manipulating objects embedded in 4D. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D interactive or haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the real-world experience accessible to human beings

Identifying Phase Space Boundaries with Voronoi Tessellations

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.Comment: 48 pages, 23 figures, Journal-submitted versio

Accurate geometry reconstruction of vascular structures using implicit splines

3-D visualization of blood vessel from standard medical datasets (e.g. CT or MRI) play an important role in many clinical situations, including the diagnosis of vessel stenosis, virtual angioscopy, vascular surgery planning and computer aided vascular surgery. However, unlike other human organs, the vasculature system is a very complex network of vessel, which makes it a very challenging task to perform its 3-D visualization. Conventional techniques of medical volume data visualization are in general not well-suited for the above-mentioned tasks. This problem can be solved by reconstructing vascular geometry. Although various methods have been proposed for reconstructing vascular structures, most of these approaches are model-based, and are usually too ideal to correctly represent the actual variation presented by the cross-sections of a vascular structure. In addition, the underlying shape is usually expressed as polygonal meshes or in parametric forms, which is very inconvenient for implementing ramification of branching. As a result, the reconstructed geometries are not suitable for computer aided diagnosis and computer guided minimally invasive vascular surgery. In this research, we develop a set of techniques associated with the geometry reconstruction of vasculatures, including segmentation, modelling, reconstruction, exploration and rendering of vascular structures. The reconstructed geometry can not only help to greatly enhance the visual quality of 3-D vascular structures, but also provide an actual geometric representation of vasculatures, which can provide various benefits. The key findings of this research are as follows: 1. A localized hybrid level-set method of segmentation has been developed to extract the vascular structures from 3-D medical datasets. 2. A skeleton-based implicit modelling technique has been proposed and applied to the reconstruction of vasculatures, which can achieve an accurate geometric reconstruction of the vascular structures as implicit surfaces in an analytical form. 3. An accelerating technique using modern GPU (Graphics Processing Unit) is devised and applied to rendering the implicitly represented vasculatures. 4. The implicitly modelled vasculature is investigated for the application of virtual angioscopy

Matching and compressing sequences of visual hulls

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 61-63).In this thesis, we implement the polyhedral visual hull (PVH) algorithm in a modular software system to reconstruct 3D meshes from 2D images and camera poses. We also introduce the new idea of visual hull graphs. For data, using an eight camera synchronous system after multi-camera calibration, we collect video sequences to study the pose and motion of people. For efficiency in VH processing, we compress 2D input contours to reduce te number of triangles in the output mesh and demonstrate how subdivision surfaces smoothly approximate the irregular output mesh in 3D. After generating sequences of visual hulls from source video, to define a visual hull graph, we use a simple distance metric for pose by calculating Chamfer distances between 2D shape contours. At each frame of our graph, we store a view independent 3D pose and calculate the transition probability to any other frame based on similarity of pose. To test our approach, we synthesize new realistic motion by walking through cycles in the graph. Our results are new videos of arbitrary length and viewing direction based on a sample source video.by Naveen Goela.M.Eng

Analysis and Manipulation of Repetitive Structures of Varying Shape

Self-similarity and repetitions are ubiquitous in man-made and natural objects. Such structural regularities often relate to form, function, aesthetics, and design considerations. Discovering structural redundancies along with their dominant variations from 3D geometry not only allows us to better understand the underlying objects, but is also beneficial for several geometry processing tasks including compact representation, shape completion, and intuitive shape manipulation. To identify these repetitions, we present a novel detection algorithm based on analyzing a graph of surface features. We combine general feature detection schemes with a RANSAC-based randomized subgraph searching algorithm in order to reliably detect recurring patterns of locally unique structures. A subsequent segmentation step based on a simultaneous region growing is applied to verify that the actual data supports the patterns detected in the feature graphs. We introduce our graph based detection algorithm on the example of rigid repetitive structure detection. Then we extend the approach to allow more general deformations between the detected parts. We introduce subspace symmetries whereby we characterize similarity by requiring the set of repeating structures to form a low dimensional shape space. We discover these structures based on detecting linearly correlated correspondences among graphs of invariant features. The found symmetries along with the modeled variations are useful for a variety of applications including non-local and non-rigid denoising. Employing subspace symmetries for shape editing, we introduce a morphable part model for smart shape manipulation. The input geometry is converted to an assembly of deformable parts with appropriate boundary conditions. Our method uses self-similarities from a single model or corresponding parts of shape collections as training input and allows the user also to reassemble the identified parts in new configurations, thus exploiting both the discrete and continuous learned variations while ensuring appropriate boundary conditions across part boundaries. We obtain an interactive yet intuitive shape deformation framework producing realistic deformations on classes of objects that are difficult to edit using repetition-unaware deformation techniques

Three dimensional flame reconstruction towards the study of fire-induced transmission line flashovers.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, 2007.The work presented in this thesis focuses on the problem of reconstructing threedimensional models of fire from real images. The intended application of the reconstructions is for use in research into the phenomenon of fire-induced high voltage flashover, which, while a common problem, is not fully understood. As such the reconstruction must estimate not only the geometry of the flame but also the internal density structure, using only a set of a few synchronised images. Current flame reconstruction techniques are investigated, revealing that relatively little work has been done on the subject, and that most techniques follow either an exclusively geometric or tomographic direction. A novel method, termed the 3D Fuzzy Hull method, is proposed, incorporating aspects of tomography, statistical image segmentation and traditional object reconstruction techniques. By using physically based principles the flame images are related to the relative flame density, allowing the problem to be tackled from a tomographic perspective. A variation of algebraic tomography is then used to estimate the internal density field of the flame. This is done within a geometric framework by integrating the fuzzy c-means image segmentation technique and the visual hull concept into the process. Results are presented using synthetic and real flame image sets

Model driven segmentation and the detection of bone fractures

Bibliography: leaves 83-90.The introduction of lower dosage image acquisition devices and the increase in computational power means that there is an increased focus on producing diagnostic aids for the medical trauma environment. The focus of this research is to explore whether geometric criteria can be used to detect bone fractures from Computed Tomography data. Conventional image processing of CT data is aimed at the production of simple iso-surfaces for surgical planning or diagnosis - such methods are not suitable for the automated detection of fractures. Our hypothesis is that through a model-based technique a triangulated surface representing the bone can be speedily and accurately produced. And, that there is sufficient structural information present that by examining the geometric structure of this representation we can accurately detect bone fractures. In this dissertation we describe the algorithms and framework that we built to facilitate the detection of bone fractures and evaluate the validity of our approach