Dynamic Multivariate Simplex Splines For Volume Representation And Modeling

Volume representation and modeling of heterogeneous objects acquired from real world are very challenging research tasks and playing fundamental roles in many potential applications, e.g., volume reconstruction, volume simulation and volume registration. In order to accurately and efficiently represent and model the real-world objects, this dissertation proposes an integrated computational framework based on dynamic multivariate simplex splines (DMSS) that can greatly improve the accuracy and efficacy of modeling and simulation of heterogenous objects. The framework can not only reconstruct with high accuracy geometric, material, and other quantities associated with heterogeneous real-world models, but also simulate the complicated dynamics precisely by tightly coupling these physical properties into simulation. The integration of geometric modeling and material modeling is the key to the success of representation and modeling of real-world objects. The proposed framework has been successfully applied to multiple research areas, such as volume reconstruction and visualization, nonrigid volume registration, and physically based modeling and simulation

Functional representation and manipulation of shapes with applications in surface and solid modeling

Real-valued functions have wide applications in various areas within computer graphics. In this work, we examine three representation of shapes using functions. In particular, we study the classical B-spline representation of piece-wise polynomials in the univariate domain. We provide a generalization of B-spline to the bivariate domain using intuition gained from the univariate construction. We also study the popular scheme of representing 3D density distribution using a uniform, rectilinear grid, where we provide a novel contouring scheme that culls occluded inner geometries. Lastly, we examine a ray-based representation for 3D indicator functions called ray-rep, for which we present a novel meshing scheme with multi-material extensions

Almost-C1C^1 splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems

Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from Computer-Aided Design models, which is in general a non-trivial and time-consuming task. In this article, we present a novel spline construction, that enables model reconstruction as well as simulation of high-order PDEs on the reconstructed models. The proposed almost-$C^1$ are biquadratic splines on fully unstructured quadrilateral meshes (without restrictions on placements or number of extraordinary vertices). They are $C^1$ smooth almost everywhere, that is, at all vertices and across most edges, and in addition almost (i.e. approximately) $C^1$ smooth across all other edges. Thus, the splines form $H^2$-nonconforming analysis-suitable discretization spaces. This is the lowest-degree unstructured spline construction that can be used to solve fourth-order problems. The associated spline basis is non-singular and has several B-spline-like properties (e.g., partition of unity, non-negativity, local support), the almost-$C^1$ splines are described in an explicit B\'ezier-extraction-based framework that can be easily implemented. Numerical tests suggest that the basis is well-conditioned and exhibits optimal approximation behavior

Active modelling of virtual humans

This thesis provides a complete framework that enables the creation of photorealistic 3D human models in real-world environments. The approach allows a non-expert user to use any digital capture device to obtain four images of an individual and create a personalised 3D model, for multimedia applications. To achieve this, it is necessary that the system is automatic and that the reconstruction process is flexible to account for information that is not available or incorrectly captured. In this approach the individual is automatically extracted from the environment using constrained active B-spline templates that are scaled and automatically initialised using only image information. These templates incorporate the energy minimising framework for Active Contour Models, providing a suitable and flexible method to deal with the adjustments in pose an individual can adopt. The final states of the templates describe the individual’s shape. The contours in each view are combined to form a 3D B-spline surface that characterises an individual’s maximal silhouette equivalent. The surface provides a mould that contains sufficient information to allow for the active deformation of an underlying generic human model. This modelling approach is performed using a novel technique that evolves active-meshes to 3D for deforming the underlying human model, while adaptively constraining it to preserve its existing structure. The active-mesh approach incorporates internal constraints that maintain the structural relationship of the vertices of the human model, while external forces deform the model congruous to the 3D surface mould. The strength of the internal constraints can be reduced to allow the model to adopt the exact shape of the bounding volume or strengthened to preserve the internal structure, particularly in areas of high detail. This novel implementation provides a uniform framework that can be simply and automatically applied to the entire human model

Approximation with interval B-splines for robust reverse engineering

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1997.Includes bibliographical references (leaves 132-136).by Guoling Shen.M.S

Blending techniques in Curve and Surface constructions

Source at https://www.geofo.no/geofoN.html. <p

Feature-Based Models for Three-Dimensional Data Fitting.

There are numerous techniques available for fitting a surface to any supplied data set. The feature-based modeling technique takes advantage of the known, geometric shape of the data by deforming a model having this generic shape to approximate the data. The model is constructed as a rational B-spline surface with characteristic features superimposed on its definition. The first step in the fitting process is to align the model with a data set using the center of mass, principal axes and/or landmarks. Using this initial orientation, the position, rotation and scale parameters are optimized using a Newton-type optimization of a least squares cost function. Once aligned, features embedded within the model, corresponding to pertinent characteristics of the shape, are used to improve the fit of the model to the data. Finally, the control vertex weights and positions of the rational B-spline model are optimized to approximate the data to within a specified tolerance. Since the characteristic features are defined within the model a creation, important measures are easily extracted from a data set, once fit. The feature-based modeling approach is demonstrated in two-dimensions by the fitting of five facial, silhouette profiles and in three-dimensions by the fitting of eleven human foot scans. The algorithm is tested for sensitivity to data distribution and structure and the extracted measures are tested for repeatability and accuracy. Limitations within the current implementation, future work and potential applications are also provided

An Investigation of NURBS-Based Deformable Image Registration

Deformable image registration (DIR) is an essential tool in medical image processing. It provides a means to combine image datasets, allowing for intra-subject, inter-subject, multi-modality, and multi-instance analysis, as well as motion detection and compensation. One of the most popular DIR algorithms models the displacement vector field (DVF) as B-splines, a sum of piecewise polynomials with coefficients that enable local shape control. B-splines have many advantageous properties in the context of DIR, but they often struggle to adequately model steep local gradients and discontinuities. This dissertation addresses that limitation by proposing the replacement of conventional B-splines with a generalized formulation known as a Non-Uniform Rational B-Splines (NURBS). Beginning with the 1D fitting, heuristic rules are developed to determine the values of the additional free parameters introduced by NURBS. These rules are subsequently modified and extended to the 2D and 3D fitting of anonymized and publicly available patient DVFs. Based on the lessons learned from these increasingly complex test cases, a 2D DIR scheme is developed and tested on slices from a thoracic computed tomography (CT) scan. Finally, an automatic, non-uniform scheme is presented, and its registration performance is compared to the conventional uniform methods

3D reconstruction using a spherical spiral scan camera

Thesis (Master)--Izmir Institute of Technology, Computer Engineering, Izmir, 2006Includes bibliographical references (leaves: 48-49)Text in English; Abstract: Turkish and Englishviii, 50 leavesConstruction of 3D models representing industrial products/objects is commonly used as a preliminary step of production process. These models are represented by a set of points which can be combined by planar patches (i.e. triangulation) or by smooth surface approximtions. In some cases, we may need to construct the 3D models of real objects. This problem is known as the 3D reconstruction problem which is one of the most important problems in the field of computer vision. In this thesis, a sytem has been developed to transform images of real objects into their 3D models automatically. The system consists of a PC, an inexpensive camera and an electromechanical component. The camera attached to this component moves around the object over a spiral trajectory and observes it from different view angles. At the same time, feature points of object surface are tracked using a tracking algorithm over object images. Then tracked points are reconstructed in 3D space using a stereo vision technique. A surface approximation is fitted to this 3D point set as a last step in the process. Open source .Intel®-OpenCV. C library is used both in image capturing and in image processing