Three-dimensional scans and other volumetric data sources often result in representations that are more complex topologically than the original model. The extraneous critical points, handles, and components are called topological noise. Many algorithms in computer graphics require simple topology in order to work optimally, including texture mapping, surface parameterization, flows on surfaces, and conformal mappings. The topological noise disrupts these procedures by requiring each small handle to be dealt with individually. Furthermore, topological descriptions of volumetric data are useful for visualization and data queries. One such description is the contour tree (or Reeb graph), which depicts when the isosurfaces split and merge as the isovalue changes. In the presence of topological noise, the contour tree can be too large to be useful. For these reasons, an important goal in computer graphics is simplification of the topology of volumetric data. The key to this thesis is that the global topology of volumetric data sets is determined by local changes at individual points. Therefore, we march through the data one grid cell at a time, and for each cell, we use a local check to determine if the topology of an isosurface is changing. If so, we change the value of the cell so that the topology change is prevented. In this thesis we describe variations on the local topology check for use in different settings. We use the topology simplification procedure to extract a single component with controlled topology from an isosurface in volume data sets and partially-defined volume data sets. We also use it to remove critical points from three-dimensional volumes, as well as time-varying volumes. We have applied the technique to two-dimensional (plus time) data sets and three dimensional (plus time) data sets.

Thesis (M.S. in Computer Science)--Naval Postgraduate School, September 2003. / Thesis advisor(s): Don Brutzman, Curtis Blais. Includes bibliographical references (p. 103-104). Also available online.

Current trends indicate that the population explosion and invasion of information technology, particularly in developing nations, are likely to overwhelm education systems and policy makers, educators, researchers and therefore the community faces enormous challenges. Also, many graduates of various levels and disciplines appear unable to practically apply their knowledge in problem solving situations. In an attempt to achieve and maintain high educational standards, many nations are devoting substantial proportions of the gross domestic product toward educational endeavours. However, few systems are adopting modern education practices that intrinsically motivate and engage learners, and are at the same time flexible enough to consider students' aspirations and interests. It is argued that such systems would make learning more relevant, meaningful and enjoyable to the learners and are bound to improve exit performances. In such a system, the role of the teacher is that of a facilitator, and not instructor. Constructivism, a philosophy which holds that knowledge is actively constructed by learners through learning, is regarded as promising to provide a long-term solution to many educational problems since its underlying principles are argued to be holistic. It has become imperative that technology in general and the computer in particular should play a role as educational tools as these have capabilities that could be designed to make learning relevant and interesting to learners. It is argued that its use within constructivist approaches and curriculum considerations would increase learner abilities. An eclectic approach to curriculum design is advised for success in this endeavour. Since computers permeate most aspects of our lives (directly or indirectly) their inclusion in teaching and learning situations must become a reality. This project is focused on underscoring the fact that computer based education (CBE), under constructivist philosophy, can provide solutions to problems brought about by extreme interpretations of the deductive or traditional teaching approach. Particularly, it attempts to show that use of three-dimensional (3D) visualizations could significantly aid comprehension and perception of, among other units of discourse, cytoplasmic structure, geo-referenced graphical data, and the understanding of spatial relationships. This is a technique that has, in the recent past, received little attention and no extensive educational research has been carried out with the aim of perfecting it. Recent research carried out by members of the Biological Pedagogy (Bioped) research group identified conceptual problems in learners regarding biological processes such as photosynthesis and respiration. Having established that the misconceptions in learners were attributable to their lack of visualization ability, the first part of the project involved identifying some of the specific visual problems. A qualitative research approach was used to ascertain from university lecturers what convictions, beliefs and experiences they had had with their students that related to use of visualization skills. Skills most required included interpretation of 2D and 3D structures as well as their rotation in space. A survey was also carried out among Cell Biology first and second year students of the School of Life and Environmental Studies in order to precisely determine aspects of three-dimensionality and visual skills suspected to cause conceptual difficulties. Quantitative data analysis showed that the most deficient skills in the learners included pattern folding (projecting 2D material into 3D objects), orientation of form (identifying 3D objects that are oriented differently) and rotation (identifying 3D objects from top and front views). These findings corroborated qualitative analysis of lecturers opinions and convictions. An educational computer game was designed with the aim of ameliorating these problems. The game consisted of 3D scenes where puzzles related to the skills mentioned above needed to be solved. It was recommended that visualization skills should be incorporated into the biology curriculum for all undergraduate students within the first year of the course. / Thesis (M.Ed.)-University of Natal, 1999.

Thesis (MA)--University of Stellenbosch, 2005. / Bibliography. Also available via the Internet.

M.Sc. (Computer Science) / Please refer to full text to view abstract

La diffusion de données multimédia, et particulièrement les images, continuent à croitre de manière très significative. La recherche de schémas de codage efficaces des images reste donc un domaine de recherche très dynamique. Aujourd'hui, une des technologies innovantes les plus marquantes dans ce secteur est sans doute le passage à un affichage 3D. La technologie 3D est largement utilisée dans les domaines de divertissement, d'imagerie médicale, de l'éducation et même plus récemment dans les enquêtes criminelles. Il existe différentes manières de représenter l'information 3D. L'une des plus répandues consiste à associer à une image classique dite de texture, une image de profondeur de champs. Cette représentation conjointe permet ainsi une bonne reconstruction 3D dès lors que les deux images sont bien corrélées, et plus particulièrement sur les zones de contours de l'image de profondeur. En comparaison avec des images 2D classiques, la connaissance de la profondeur de champs pour les images 3D apporte donc une information sémantique importante quant à la composition de la scène. Dans cette thèse, nous proposons un schéma de codage scalable d'images 3D de type 2D + profondeur avec des fonctionnalités avancées, qui préserve toute la sémantique présente dans les images, tout en garantissant une efficacité de codage significative. La notion de préservation de la sémantique peut être traduite en termes de fonctionnalités telles que l'extraction automatique de zones d'intérêt, la capacité de coder plus finement des zones d'intérêt par rapport au fond, la recomposition de la scène et l'indexation. Ainsi, dans un premier temps, nous introduisons un schéma de codage scalable et joint texture/profondeur. La texture est codée conjointement avec la profondeur à basse résolution, et une méthode de compression de la profondeur adaptée aux caractéristiques des cartes de profondeur est proposée. Ensuite, nous présentons un schéma global de représentation fine et de codage basé contenu. Nous proposons ainsi schéma global de représentation et de codage de "Profondeur d'Intérêt", appelé "Autofocus 3D". Il consiste à extraire finement des objets en respectant les contours dans la carte de profondeur, et de se focaliser automatiquement sur une zone de profondeur pour une meilleure qualité de synthèse. Enfin, nous proposons un algorithme de segmentation en régions d'images 3D, fournissant une forte consistance entre la couleur, la profondeur et les régions de la scène. Basé sur une exploitation conjointe de l'information couleurs, et celle de profondeur, cet algorithme permet la segmentation de la scène avec un degré de granularité fonction de l'application visée. Basé sur cette représentation en régions, il est possible d'appliquer simplement le même principe d'Autofocus 3D précédent, pour une extraction et un codage de la profondeur d'Intérêt (DoI). L'élément le plus remarquable de ces deux approches est d'assurer une pleine cohérence spatiale entre texture, profondeur, et régions, se traduisant par une minimisation des problèmes de distorsions au niveau des contours et ainsi par une meilleure qualité dans les vues synthétisées. / Dissemination of multimedia data, in particular the images, continues to grow very significantly. Therefore, developing effective image coding schemes remains a very active research area. Today, one of the most innovative technologies in this area is the 3D technology. This 3D technology is widely used in many domains such as entertainment, medical imaging, education and very recently in criminal investigations. There are different ways of representing 3D information. One of the most common representations, is to associate a depth image to a classic colour image called texture. This joint representation allows a good 3D reconstruction, as the two images are well correlated, especially along the contours of the depth image. Therefore, in comparison with conventional 2D images, knowledge of the depth of field for 3D images provides an important semantic information about the composition of the scene. In this thesis, we propose a scalable 3D image coding scheme for 2D + depth representation with advanced functionalities, which preserves all the semantics present in the images, while maintaining a significant coding efficiency. The concept of preserving the semantics can be translated in terms of features such as an automatic extraction of regions of interest, the ability to encode the regions of interest with higher quality than the background, the post-production of the scene and the indexing. Thus, firstly we introduce a joint and scalable 2D plus depth coding scheme. First, texture is coded jointly with depth at low resolution, and a method of depth data compression well suited to the characteristics of the depth maps is proposed. This method exploits the strong correlation between the depth map and the texture to better encode the depth map. Then, a high resolution coding scheme is proposed in order to refine the texture quality. Next, we present a global fine representation and contentbased coding scheme. Therefore, we propose a representation and coding scheme based on "Depth of Interest", called "3D Autofocus". It consists in a fine extraction of objects, while preserving the contours in the depth map, and it allows to automatically focus on a particular depth zone, for a high rendering quality. Finally, we propose 3D image segmentation, providing a high consistency between colour, depth and regions of the scene. Based on a joint exploitation of the colour and depth information, this algorithm allows the segmentation of the scene with a level of granularity depending on the intended application. Based on such representation of the scene, it is possible to simply apply the same previous 3D Autofocus, for Depth of Interest extraction and coding. It is remarkable that both approaches ensure a high spatial coherence between texture, depth, and regions, allowing to minimize the distortions along object of interest's contours and then a higher quality in the synthesized views.

Law Tsui Ying. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 64-70). / Abstracts in English and Chinese. / Acknowledgments --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Structure of Bronchus --- p.3 / Chapter 1.2 --- Existing Systems --- p.4 / Chapter 1.2.1 --- Virtual Endoscope System (VES) --- p.4 / Chapter 1.2.2 --- Virtual Reality Surgical Simulator --- p.4 / Chapter 1.2.3 --- Automated Virtual Colonoscopy (AVC) --- p.5 / Chapter 1.2.4 --- QUICKSEE --- p.5 / Chapter 1.3 --- Organization of Thesis --- p.6 / Chapter 2 --- Three Dimensional Visualization in Medicine --- p.7 / Chapter 2.1 --- Acquisition --- p.8 / Chapter 2.1.1 --- Computed Tomography --- p.8 / Chapter 2.2 --- Resampling --- p.9 / Chapter 2.3 --- Segmentation and Classification --- p.9 / Chapter 2.3.1 --- Segmentation by Thresholding --- p.10 / Chapter 2.3.2 --- Segmentation by Texture Analysis --- p.10 / Chapter 2.3.3 --- Segmentation by Region Growing --- p.10 / Chapter 2.3.4 --- Segmentation by Edge Detection --- p.11 / Chapter 2.4 --- Rendering --- p.12 / Chapter 2.5 --- Display --- p.13 / Chapter 2.6 --- Hazards of Visualization --- p.13 / Chapter 2.6.1 --- Adding Visual Richness and Obscuring Important Detail --- p.14 / Chapter 2.6.2 --- Enhancing Details Incorrectly --- p.14 / Chapter 2.6.3 --- The Picture is not the Patient --- p.14 / Chapter 2.6.4 --- Pictures-'R'-Us --- p.14 / Chapter 3 --- Overview of Advanced Segmentation Methodologies --- p.15 / Chapter 3.1 --- Mathematical Morphology --- p.15 / Chapter 3.2 --- Recursive Region Search --- p.16 / Chapter 3.3 --- Active Region Models --- p.17 / Chapter 4 --- Overview of Centerline Methodologies --- p.18 / Chapter 4.1 --- Thinning Approach --- p.18 / Chapter 4.2 --- Volume Growing Approach --- p.21 / Chapter 4.3 --- Combination of Mathematical Morphology and Region Growing Schemes --- p.22 / Chapter 4.4 --- Simultaneous Borders Identification Approach --- p.23 / Chapter 4.5 --- Tracking Approach --- p.24 / Chapter 4.6 --- Distance Transform Approach --- p.25 / Chapter 5 --- Automated Extraction of Bronchus Area --- p.27 / Chapter 5.1 --- Basic Idea --- p.27 / Chapter 5.2 --- Outline of the Automated Extraction Algorithm --- p.28 / Chapter 5.2.1 --- Selection of a Start Point --- p.28 / Chapter 5.2.2 --- Three Dimensional Region Growing Method --- p.29 / Chapter 5.2.3 --- Optimization of the Threshold Value --- p.29 / Chapter 5.3 --- Retrieval of Start Point Algorithm Using Genetic Algorithm --- p.29 / Chapter 5.3.1 --- Introduction to Genetic Algorithm --- p.30 / Chapter 5.3.2 --- Problem Modeling --- p.31 / Chapter 5.3.3 --- Algorithm for Determining a Start Point --- p.33 / Chapter 5.3.4 --- Genetic Operators --- p.33 / Chapter 5.4 --- Three Dimensional Painting Algorithm --- p.34 / Chapter 5.4.1 --- Outline of the Three Dimensional Painting Algorithm --- p.34 / Chapter 5.5 --- Optimization of the Threshold Value --- p.36 / Chapter 6 --- Automatic Centerline Determination Algorithm --- p.38 / Chapter 6.1 --- Distance Transformations --- p.38 / Chapter 6.2 --- End Points Retrieval --- p.41 / Chapter 6.3 --- Graph Based Centerline Algorithm --- p.44 / Chapter 7 --- Experiments and Discussion --- p.48 / Chapter 7.1 --- Experiment of Automated Determination of Bronchus Algorithm --- p.48 / Chapter 7.2 --- Experiment of Automatic Centerline Determination Algorithm --- p.54 / Chapter 8 --- Conclusion --- p.62 / Bibliography --- p.63

by Chi-Min Pang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 110-[115]). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Range Images --- p.1 / Chapter 1.2 --- Rigid Body Model --- p.3 / Chapter 1.3 --- Motivation --- p.4 / Chapter 1.4 --- Thesis Outline --- p.6 / Chapter 2 --- Object Recognition by Relaxation Processes --- p.7 / Chapter 2.1 --- An Overview of Probabilistic Relaxation Labelling --- p.8 / Chapter 2.2 --- Formulation of Model-matching Problem Solvable by Probabilistic Relaxation --- p.10 / Chapter 2.2.1 --- Compatibility Coefficient --- p.11 / Chapter 2.2.2 --- Match Score --- p.13 / Chapter 2.2.3 --- Iterative Algorithm --- p.14 / Chapter 2.2.4 --- A Probabilistic Concurrent Matching Scheme --- p.15 / Chapter 2.3 --- Formulation of Model-merging Problem Solvable by Fuzzy Relaxation --- p.17 / Chapter 2.3.1 --- Updating Mechanism --- p.17 / Chapter 2.3.2 --- Iterative Algorithm --- p.19 / Chapter 2.3.3 --- Merging Sub-Rigid Body Models --- p.20 / Chapter 2.4 --- Simulation Results --- p.21 / Chapter 2.4.1 --- Experiments in Model-matching Using Probabilistic Relaxation --- p.22 / Chapter 2.4.2 --- Experiments in Model-matching Using Probabilistic Concur- rent Matching Scheme --- p.26 / Chapter 2.4.3 --- Experiments in Model-merging Using Fuzzy Relaxation --- p.33 / Chapter 2.5 --- Summary --- p.36 / Chapter 3 --- Object Recognition by Hopfield Network --- p.37 / Chapter 3.1 --- An Overview of Hopfield Network --- p.38 / Chapter 3.2 --- Model-matching Problem Solved by Hopfield Network --- p.41 / Chapter 3.2.1 --- Representation of the Solution --- p.41 / Chapter 3.2.2 --- Energy Function --- p.42 / Chapter 3.2.3 --- Equations of Motion --- p.46 / Chapter 3.2.4 --- Interpretation of Solution --- p.49 / Chapter 3.2.5 --- Convergence of the Hopfield Network --- p.50 / Chapter 3.2.6 --- Iterative Algorithm --- p.51 / Chapter 3.3 --- Estimation of Distance Threshold Value --- p.53 / Chapter 3.4 --- Cooperative Concurrent Matching Scheme --- p.55 / Chapter 3.4.1 --- Scheme for Recognizing a Single Object --- p.56 / Chapter 3.4.2 --- Scheme for Recognizing Multiple Objects --- p.60 / Chapter 3.5 --- Simulation Results --- p.60 / Chapter 3.5.1 --- Experiments in the Model-matching Problem Using a Hopfield Network --- p.61 / Chapter 3.5.2 --- Experiments in Model-matching Problem Using Cooperative Concurrent Matching --- p.69 / Chapter 3.5.3 --- Experiments in Model-merging Problem Using Hopfield Network --- p.77 / Chapter 3.6 --- Summary --- p.80 / Chapter 4 --- Genetic Generation of Weighting Parameters for Hopfield Network --- p.83 / Chapter 4.1 --- An Overview of Genetic Algorithms --- p.84 / Chapter 4.2 --- Determination of Weighting Parameters for Hopfield Network --- p.86 / Chapter 4.2.1 --- Chromosomal Representation --- p.87 / Chapter 4.2.2 --- Initial Population --- p.88 / Chapter 4.2.3 --- Evaluation Function --- p.88 / Chapter 4.2.4 --- Genetic Operators --- p.89 / Chapter 4.2.5 --- Control Parameters --- p.91 / Chapter 4.2.6 --- Iterative Algorithm --- p.94 / Chapter 4.3 --- Simulation Results --- p.95 / Chapter 4.3.1 --- Experiments in Model-matching Problem using Hopfield Net- work with Genetic Generated Parameters --- p.95 / Chapter 4.3.2 --- Experiments in Model-merging Problem Using Hopfield Network --- p.101 / Chapter 4.4 --- Summary --- p.104 / Chapter 5 --- Conclusions --- p.106 / Chapter 5.1 --- Conclusions --- p.106 / Chapter 5.2 --- Suggestions for Future Research --- p.109 / Bibliography --- p.110 / Chapter A --- Proof of Convergence of Fuzzy Relaxation Process --- p.116

Digital Clay is a next generation human-machine communication interface based on a tangible haptic surface. This thesis embraces this revolutionary concept and seeks to give it a physical embodiment that will confirm its feasibility and enable experimentation relating to its utility and possible improvements. Per the approach adopted in work, Digital Clay could be described as a 3D monitor whose pixels can move perpendicularly to the screen to form a morphing surface. Users can view, touch and modify the shape of the working surface formed by these pixels. In reality, the pixels are the tips of micro hydraulic actuators or Hapcel (i.e. haptic cell, since the Digital Clay supports the haptic interface). The user can get a feel of the desired material properties when he/she touches the working surface. The potential applications of Digital Clay cover a wide range from computer aided engineering design to scientific research to medical diagnoses, 3D dynamic mapping and entertainment. One could predict a future in which, by using Digital Clay, not only could the user watch an actor in a movie, but also touch the face of the actor! This research starts from the review of the background of virtual reality. Then the concept and features of the proposed Digital Clay is provided. Research stages and a 5x5 cell array prototype are presented in this thesis on the structural design and control of Digital Clay. The first stage of the research focuses on the design and control of a single cell system of Digital Clay. Control issues of a single cell system constructed using conventional and off-the-shelf components are discussed first in detail followed by experimental results. Then practical designs of micro actuators and sensors are presented. The second stage of the research deals with the cell array system of Digital Clay. Practical structural design and control methods are discussed which are suitable for a 100x 100 (even 1000X 1000) cell array. Conceptual design and detailed implementations are presented. Finally, a 5 x 5 cell array prototype constructed using the discussed design solutions for testing is presented.

A formable surface is part of an effort to create a haptic device that allows for a three dimensional human-computer interface called digital clay. As with real clay, digital clay allows a user to physically manipulate the surface into some form or orientation that is sensed and directly represented in a computer model. Furthermore, digital clay will allow a user to change the computer model by manipulating the inputs that are directly represented in the physical model. The digital clay device being researched involves a computer-interfaced array of vertically displacing actuators that is bound by a formable surface. The surface is composed of an array of unit cells that are constructed of compliant spherical joints and translational joints. As part of this thesis, a series of unit cells were developed and planar surfaces were fabricated utilizing the additive manufacturing process of stereolithography. The process of computing the resultant shape of a manipulated surface was modeled mathematically through energy minimization algorithms that utilized least squares analysis to compute the positions of the unit cells of the surface. Simulation results were computed and analyzed against the movement of a fabricated planar surface. Once the mathematical models were validated against the manufactured surface, a method for attaching the surface to an array of actuators was recommended.