Surface reconstruction using Delaunay triangulation for applications in life sciences

The Delaunay triangulation is an established method to define neighborhood relations in multi-particle systems. In particular, this method was employed for interacting multi-cellular systems in Biology. The extension of this method to a sub-cellular level that considers the membrane and the inner structure of cells is not straight forward and subject of this article. It is the objective to use a three-dimensional Delaunay-triangulation as a basis for the definition of a triangulation of a subset of particles that form a surface.An essential problem of this objective is the conservation of the number of particles belonging to the surface. This excludes established surface reconstruction algorithms. The presented algorithm allows the definition of a triangulation within a subset of particles attributed to a surface without the deletion of particles. A particular challenge is the deletion of connection that infer three-dimensional structures in the surface. The presented method is suitable for many configurations. Its performance and its limitations are analyzed and discussed.The developed algorithm for the reconstruction of connections in a surface is suitable to be used for simulations of biological cells because of the inherent conservation of the number of particles attributed to the membrane.     

Image reconstruction using data-dependent triangulation

Image reconstruction based on data-dependent triangulation with new cost functions and optimization can create higher quality images than traditional bilinear or bicubic spline reconstruction. The article presents a novel method for image reconstruction using a piecewise linear intensity surface whose elements don't generally align with the coordinate axes. This method is based on the technique of data-dependent triangulation (DDT) that N. Dyn et al. (1990) introduced and has proven capable of producing more pleasing reconstructions than axis-aligned methods     

Surface reconstruction by layer peeling

Given an input point cloud P in ?³, this paper proposes a novel algorithm to identify surface neighbors of each point p∈P respecting the underlying surface S and then to construct a piecewise linear surface for P. The algorithm utilizes the simple k-nearest neighborhood in constructing local surfaces. It makes use of two concepts: a local convexity criterion to extract a set of surface neighbors for each point, and a global projection test to determine an order for the reconstruction. Our algorithm not only produces a topologically correct surface for well-sampled point sets, but also adapts well to handle under-sampled point sets. Furthermore, the computational cost of the algorithm increases almost linearly in the size of the point cloud. It, thus, scales well to deal with large input point sets.     

On the choice of a cost function for the reconstruction of surfaces by triangulation between contours

Methods for the reconstruction of three-dimensional objects by triangulating between pairs of two-dimensional contours are discussed. Alternative cost functions for optimizing the triangulation are considered, and new cost functions are proposed that measure the narrowness of the triangles. These narrowness functions are particularly well suited to the generation of finite-element meshes.     

Modeling buckled developable surfaces by triangulation

In the first stage of sheet metal stamping, a binder ring, an annular surface surrounding the die cavity, clamps down on the flat blank, bending it to a developable binder wrap surface which may be smooth or buckled. Buckles generally appear in the binder wrap when the binder ring does not lie on a smooth developable surface that spans the die cavity. However, sometimes buckles can improve the formability of the stamped part, so the ability to design buckled developable surfaces becomes desirable. Designing buckled developable surfaces requires geometric modeling of creases and other singularities in the interior a flat sheet. In this paper we review the properties of such surfaces, show how to approximate buckled binder wrap surfaces by developable three-dimensional triangulations and discuss the insights gained from specific examples.     

Trajectory triangulation: 3D reconstruction of moving points from amonocular image sequence

We consider the problem of reconstructing the 3D coordinates of a moving point seen from a monocular moving camera, i.e., to reconstruct moving objects from line-of-sight measurements only. The task is feasible only when some constraints are placed on the shape of the trajectory of the moving point. We coin the family of such tasks as “trajectory triangulation.” We investigate the solutions for points moving along a straight-line and along conic-section trajectories, We show that if the point is moving along a straight line, then the parameters of the line (and, hence, the 3D position of the point at each time instant) can be uniquely recovered, and by linear methods, from at least five views. For the case of conic-shaped trajectory, we show that generally nine views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is of a known type (like a circle in 3D Euclidean space for which seven views are sufficient). The paradigm of trajectory triangulation, in general, pushes the envelope of processing dynamic scenes forward. Thus static scenes become a particular case of a more general task of reconstructing scenes rich with moving objects (where an object could be a single point)     

Surface reconstruction from scan paths

Given a finite set of points sampled from a surface, a particular important topic of surface reconstruction is to find a triangular mesh connecting the sampling points and approximating the surface. We introduce a new solution for this problem which takes into consideration hidden structural information in form of scan paths. The scan paths, which often are available in sampling data sets, allow us to cope with creases or ridges more reliably than algorithms assuming unstructured point clouds. Moreover, the consideration of scan paths leads to a better reconstruction of surface boundaries than other heuristics.     

Surface reconstruction with higher-order smoothness

This work proposes a method to reconstruct surfaces with higher-order smoothness from noisy 3D measurements. The reconstructed surface is implicitly represented by the zero-level set of a continuous valued embedding function. The key idea is to find a function whose higher-order derivatives are regularized and whose gradient is best aligned with a vector field defined by the input point set. In contrast to methods based on the first-order variation of the function that are biased toward the constant functions and treat the extraction of the isosurface without aliasing artifacts as an afterthought, we impose a higher-order smoothness directly on the embedding function. After solving a convex optimization problem with a multiscale iterative scheme, a triangulated surface can be extracted using the marching cubes algorithm. We demonstrated the proposed method on several data sets obtained from raw laser-scanners and multiview stereo approaches. Experimental results confirm that our approach allows us to reconstruct smooth surfaces from points in the presence of noise, outliers, large missing parts, and very coarse orientation information.     

Vision-based localization algorithm based on landmark matching, triangulation, reconstruction, and comparison

Many generic position-estimation algorithms are vulnerable to ambiguity introduced by nonunique landmarks. Also, the available high-dimensional image data is not fully used when these techniques are extended to vision-based localization. This paper presents the landmark matching, triangulation, reconstruction, and comparison (LTRQ global localization algorithm, which is reasonably immune to ambiguous landmark matches. It extracts natural landmarks for the (rough) matching stage before generating the list of possible position estimates through triangulation. Reconstruction and comparison then rank the possible estimates. The LTRC algorithm has been implemented using an interpreted language, onto a robot equipped with a panoramic vision system. Empirical data shows remarkable improvement in accuracy when compared with the established random sample consensus method. LTRC is also robust against inaccurate map data.     

Surface reconstruction techniques: a review

Surface reconstruction means that retrieve the data by scanning an object using a device such as laser scanner and construct it using the computer to gain back the soft copy of data on that particular object. It is a reverse process and is very useful especially when that particular object original data is missing without doing any backup. Hence, by doing so, the data can be recollected and can be stored for future purposes. The type of data can be in the form of structure or unstructured points. The accuracy of the reconstructed result should be concerned because if the result is incorrect, hence it will not exactly same like the original shape of the object. Therefore, suitable methods should be chosen based on the data used. Soft computing methods also have been used in the reconstruction field. This papers highlights the previous researches and methods that has been used in the surface reconstruction field.     

Surface reconstruction with data-driven exemplar priors

In this paper, we propose a framework to reconstruct 3D models from raw scanned points by learning the prior knowledge of a specific class of objects. Unlike previous work that heuristically specifies particular regularities and defines parametric models, our shape priors are learned directly from existing 3D models under a framework based on affinity propagation. Given a database of 3D models within the same class of objects, we build a comprehensive library of 3D local shape priors. We then formulate the problem to select as-few-as-possible priors from the library, referred to as exemplar priors. These priors are sufficient to represent the 3D shapes of the whole class of objects from where they are generated. By manipulating these priors, we are able to reconstruct geometrically faithful models with the same class of objects from raw point clouds. Our framework can be easily generalized to reconstruct various categories of 3D objects that have more geometrically or topologically complex structures. Comprehensive experiments exhibit the power of our exemplar priors for gracefully solving several problems in 3D shape reconstruction such as preserving sharp features, recovering fine details and so on.     

Surface remeshing with robust high-order reconstruction

Remeshing is an important problem in variety of applications, such as finite element methods and geometry processing. Surface remeshing poses some unique challenges, as it must deliver not only good mesh quality but also good geometric accuracy. For applications such as finite elements with high-order elements (quadratic or cubic elements), the geometry must be preserved to high-order (third-order or higher) accuracy, since low-order accuracy may undermine the convergence of numerical computations. The problem is particularly challenging if the CAD model is not available for the underlying geometry, and is even more so if the surface meshes contain some inverted elements. We describe remeshing strategies that can simultaneously produce high-quality triangular meshes, untangling mildly folded triangles and preserve the geometry to high-order of accuracy. Our approach extends our earlier works on high-order surface reconstruction and mesh optimization by enhancing its robustness with a geometric limiter for under-resolved geometries. We also integrate high-order surface reconstruction with surface mesh adaptation techniques, which alter the number of triangles and nodes. We demonstrate the utilization of our method to meshes for high-order finite elements, biomedical image-based surface meshes, and complex interface meshes in fluid simulations.     

Dynamical systems flow computation by adaptive triangulation methods

The behavior of a dynamical system can be studied by investigating the system’s flow. This paper presents new methods that are capable to reveal the evolution of points, curves, or surfaces in time. Adaptive triangulation methods and linear vertex splines are used for the numerical computation of flow approximations. The article provides a comparison between classical domain methods, which are convenient in finite element methods, and new approaches called image methods. Theoretical background and algorithms as well as illustrative examples for the Lorenz equation are included. Received: 3 September 1998 / Revised version: 12 May 1999     

一种改进的用于三维DT剖分的三角网生长算法

三角网生长法具有独特的优势,但将其扩展到三维的研究远远少于逐点插入法、分治法以及二者的合成算法,研究扩展三角网生长法实现三维DT剖分的算法。引入k近邻思想优化了原始算法,时间复杂度可达O(NlogN),且改进对二维、三维算法都有效。通过AE二次开发完成了数据操作、算法实现和二维、三维显示等功能,后续能够较方便地添加和扩展ArcGIS相关功能以及其他数据挖掘算法模块。用两组6个点集数据进行实验分析,网格构建时间对比验证了算法性能。     

Surface and normal ensembles for surface reconstruction

The majority of the existing techniques for surface reconstruction and the closely related problem of normal reconstruction are deterministic. Their main advantages are the speed and, given a reasonably good initial input, the high quality of the reconstructed surfaces. Nevertheless, their deterministic nature may hinder them from effectively handling incomplete data with noise and outliers. An ensemble is a statistical technique which can improve the performance of deterministic algorithms by putting them into a statistics based probabilistic setting. In this paper, we study the suitability of ensembles in normal and surface reconstruction. We experimented with a widely used normal reconstruction technique [Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W. Surface reconstruction from unorganized points. Computer Graphics 1992;71-8] and Multi-level Partitions of Unity implicits for surface reconstruction [Ohtake Y, Belyaev A, Alexa M, Turk G, Seidel H-P. Multi-level partition of unity implicits. ACM Transactions on Graphics 2003;22(3):463-70], showing that normal and surface ensembles can successfully be combined to handle noisy point sets.     

Surface reconstruction based on extreme learning machine

In this paper, extreme learning machine (ELM) is used to reconstruct a surface with a high speed. It is shown that an improved ELM, called polyharmonic extreme learning machine (P-ELM), is proposed to reconstruct a smoother surface with a high accuracy and robust stability. The proposed P-ELM improves ELM in the sense of adding a polynomial in the single-hidden-layer feedforward networks to approximate the unknown function of the surface. The proposed P-ELM can not only retain the advantages of ELM with an extremely high learning speed and a good generalization performance but also reflect the intrinsic properties of the reconstructed surface. The detailed comparisons of the P-ELM, RBF algorithm, and ELM are carried out in the simulation to show the good performances and the effectiveness of the proposed algorithm.     

可控的高度规整三角网格生成算法

本文提出了一种新的用户可控的高度规整三角网格生成算法.通过在网格表面上构造3个标量场,利用其等值线相交生成高度规整的三角网格.算法借助N-对称方向场来指导生成网格的边方向,在网格表面指定密度场来控制采样密度,同时还提供了特征对齐和对带边界模型的处理能力.所有的控制需求都被纳入标量场求解框架中统一优化.实验表明,本文的方法能够满足多种用户控制需求,生成高度规整的三角网格.     

Controllable highly regular triangulation

This paper presents a novel algorithm for generating a highly regular triangle mesh under various user requirements. Three scalar fields are first computed on the input mesh. Then, the intersections of their isocontours with one another are used to construct the highly regular mesh result. The proposed algorithm uses the N-symmetry direction field to guide the edge orientation. Size control is achieved by using a density function on the surface. All user requirements are incorporated into an energy optimiza...