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.     

不确定非线性系统的高阶滑模控制器设计

针对一类不确定非线性SISO系统,结合系统有限时间稳定理论与积分滑模控制理论,提出了一种新的高阶滑模控制器设计方法,改善了现有高阶滑模控制中存在的缺陷.积分滑模保证了系统初始时刻就具有抗扰能力,同时采用有限时间稳定观测器实现了高阶滑模的输出反馈控制.仿真结果表明该控制器可使系统在有限时间内收敛,并有效地减小了系统抖振.     

Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation

The generalized nonlinear Schrödinger (GNLS) equation is solved numerically by a split-step Fourier method. The first, second and fourth-order versions of the method are presented. A classical problem concerning the motion of a single solitary wave is used to compare the first, second and fourth-order schemes in terms of the accuracy and the computational cost. This numerical experiment shows that the split-step Fourier method provides highly accurate solutions for the GNLS equation and that the fourth-order scheme is computationally more efficient than the first-order and second-order schemes. Furthermore, two test problems concerning the interaction of two solitary waves and an exact solution that blows up in finite time, respectively, are investigated by using the fourth-order split-step scheme and particular attention is paid to the conserved quantities as an indicator of the accuracy. The question how the present numerical results are related to those obtained in the literature is discussed.     

Implicit meshes for surface reconstruction

Deformable 3D models can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surfaces are widely accepted because they are simple to deform and render, but fitting them involves minimizing a nondifferentiable distance function. By contrast, implicit surfaces allow fitting by minimizing a differentiate algebraic distance, but are harder to meaningfully deform and render. Here, we propose a method that combines the strength of both approaches. It relies on a technique that can turn a completely arbitrary triangulated mesh, such as one taken from the Web, into an implicit surface that closely approximates it and can deform in tandem with it. This allows both automated algorithms to take advantage of the attractive properties of implicit surfaces for fitting purposes and people to use standard deformation tools they feel comfortable for interaction and animation purposes. We demonstrate the applicability of our technique to modeling the human upper-body, including face, neck, shoulders, and ears, from noisy stereo and silhouette data.     

高阶连续的形状可调三角多项式曲线曲面

目的目前使用的B样条曲线曲面存在着高连续阶与高局部调整性两者无法兼而有之的不足,且B样条曲线曲面的形状被控制顶点和节点向量唯一确定,这些因素影响着B样条方法的几何设计效果与方便性。本文旨在克服这种局限,以期构造具有高次B样条方法的高连续阶,低次B样条方法的高局部调整性,以及有理B样条方法权因子决定的形状调整性的曲线曲面。方法在三角函数空间上构造了一组含参数的调配函数,进而定义具有与3次B样条曲线曲面相同结构的新曲线与张量积曲面。结果新曲线曲面继承了B样条方法的凸包性、对称性、几何不变性等诸多性质。不同的是,同样是基于4点分段,3次均匀B样条曲线C2连续,而对于等距节点,在一般情况下,新曲线C5连续,当参数取特殊值时可达C7连续。新曲线在C5连续的情况下存在1个形状参数,能较好地调整曲线的形状同时又无须改变控制顶点。另外,将形状参数设为特定值,新曲线可以自动插值给定点列。新曲面具有与新曲线相应的优点。结论在强局部性下实现高阶连续性的形状可调分段组合曲线曲面,为高阶光滑曲线曲面的设计提供了可能,并且新曲线实现了逼近与插值的统一表示,能较好地应用于工程实际。调配函数的构造方法具有一般性,可用相同方式构造其他具有类似性质的调配函数。     

On stochastic methods for surface reconstruction

In this article, we present and discuss three statistical methods for surface reconstruction. A typical input to a surface reconstruction technique consists of a large set of points that has been sampled from a smooth surface and contains uncertain data in the form of noise and outliers. We first present a method that filters out uncertain and redundant information yielding a more accurate and economical surface representation. Then we present two methods, each of which converts the input point data to a standard shape representation; the first produces an implicit representation while the second yields a triangle mesh.     

Ordered subsets Bayesian tomographic reconstruction using 2-D smoothing splines as priors

The ordered subsets expectation maximization (OS-EM) algorithm has enjoyed considerable interest for accelerating the well-known EM algorithm for emission tomography. The OS principle has also been applied to several regularized EM algorithms, such as nonquadratic convex minimization-based maximum a posteriori (MAP) algorithms. However, most of these methods have not been as practical as OS-EM due to their complex optimization methods and difficulties in hyperparameter estimation. We note here that, by relaxing the requirement of imposing sharp edges and using instead useful quadratic spline priors, solutions are much easier to compute, and hyperparameter calculation becomes less of a problem. In this work, we use two-dimensional smoothing splines as priors and apply a method of iterated conditional modes for the optimization. In this case, step sizes or line-search algorithms necessary for gradient-based descent methods are avoided. We also accelerate the resulting algorithm using the OS approach and propose a principled way of scaling smoothing parameters to retain the strength of smoothing for different subset numbers. Our experimental results show that the OS approach applied to our quadratic MAP algorithms provides a considerable acceleration while retaining the advantages of quadratic spline priors.     

Functional networks for B-spline surface reconstruction

Recently, a new extension of the standard neural networks, the so-called functional networks, has been described [E. Castillo, Functional networks, Neural Process. Lett. 7 (1998) 151–159]. This approach has been successfully applied to the reconstruction of a surface from a given set of 3D data points assumed to lie on unknown Bézier [A. Iglesias, A. Gálvez, Applying functional networks to CAGD: the tensor-product surface problem, in: D. Plemenos (Ed.), Proceedings of the International Conference on Computer Graphics and Artificial Intelligence, 3IA’2000, 2000, pp. 105–115; A. Iglesias, A. Gálvez, A new artificial intelligence paradigm for computer-aided geometric design, in: Artificial Intelligence and Symbolic Computation, J.A. Campbell, E. Roanes-Lozano (Eds.), Lectures Notes in Artificial Intelligence, Berlin, Heidelberg, Springer-Verlag, vol. 1930, 2001, pp. 200–213] and B-spline tensor-product surfaces [A. Iglesias, A. Gálvez, Applying functional networks to fit data points from B-spline surfaces, in: H.H.S. Ip, N. Magnenat-Thalmann, R.W.H. Lau, T.S. Chua (Eds.), Proceedings of the Computer Graphics International, CGI’2001, IEEE Computer Society Press, Los Alamitos, CA, 2001, pp. 329–332]. In both cases the sets of data were fitted using Bézier surfaces. However, in general, the Bézier scheme is no longer used for practical applications. In this paper, the use of B-spline surfaces (by far the most common family of surfaces in surface modeling and industry) for the surface reconstruction problem is proposed instead. The performance of this method is discussed by means of several illustrative examples. A careful analysis of the errors makes it possible to determine the number of B-spline surface fitting control points that best fit the data points. This analysis also includes the use of two sets of data (the training and the testing data) to check for overfitting, which does not occur here.     

Computational topology for isotopic surface reconstruction

New computational topology techniques are presented for surface reconstruction of 2-manifolds with boundary, while rigorous proofs have previously been limited to surfaces without boundary. This is done by an intermediate construction of the envelope   (as defined herein) of the original surface. For any compact C²$C^2$-manifold M$M$ embedded in R³${\mathbf{R}}^3$, it is shown that its envelope is C^1,1$C^{1,1}$. Then it is shown that there exists a piecewise linear (PL) subset of the reconstruction of the envelope that is ambient isotopic to M$M$, whenever M$M$ is orientable. The emphasis of this paper is upon the formal mathematical proofs needed for these extensions. (Practical application examples have already been published in a companion paper.) Possible extensions to non-orientable manifolds are also discussed. The mathematical exposition relies heavily on known techniques from differential geometry and topology, but the specific new proofs are intended to be sufficiently specialized to prompt further algorithmic discoveries.     

The ball-pivoting algorithm for surface reconstruction

The Ball-Pivoting Algorithm (BPA) computes a triangle mesh interpolating a given point cloud. Typically, the points are surface samples acquired with multiple range scans of an object. The principle of the BPA is very simple: Three points form a triangle if a ball of a user-specified radius p touches them without containing any other point. Starting with a seed triangle, the ball pivots around an edge (i.e., it revolves around the edge while keeping in contact with the edge's endpoints) until it touches another point, forming another triangle. The process continues until all reachable edges have been tried, and then starts from another seed triangle, until all points have been considered. The process can then be repeated with a ball of larger radius to handle uneven sampling densities. We applied the BPA to datasets of millions of points representing actual scans of complex 3D objects. The relatively small amount of memory required by the BPA, its time efficiency, and the quality of the results obtained compare favorably with existing techniques     

基于属性散射信息的随机梯度最小方差追踪SAR超分辨重建算法

无论军事还是民用合成孔径雷达（SAR）应用领域,对实现目标更高分辨、更精细描述的期望和需求都十分迫切。在稀疏表示框架下,构建了基于属性散射中心模型（ASC）部件级局部散射模型的SAR重建观测模型;提出一种基于信号域的散射中心属性参数空间分类策略,并联合频域外推,提出一种基于随机梯度最小方差追踪的部件级超分辨SAR重建算法。该算法最终的超分辨SAR图像由FFT获得,提高了算法效率;并且该算法实现了在重建超分辨SAR图像的同时获取高精度的目标散射中心属性级特征。仿真合成数据和电磁计算数据验证了算法的超分辨能力,并利用ASC属性的克拉美罗界对算法属性估计性能进行了评估。     

Virtual reconstruction of archeological vessels using expert priors and intrinsic differential geometry information

This paper presents a method to assist in the tedious task of reconstructing ceramic vessels from unearthed archeological shards (fragments) using 3D computer vision-enabling technologies. The method exploits the shards surface intrinsic differential geometry information (one of many possible tools) coupled with a series of generic models to produce a virtual reconstruction and rendition of what the original vessel may have looked like. Generic models are constructed based on a host of factors including expert historical knowledge of the period, provenance of the artifact, and site location. The generic models need not to be identical to the original vessel, but they must be within a geometric transformation of it in most of its parts. The method is suited for ceramic vessels with some relief (i.e., surface with molding, carving, or stamping), as this method exploits surface intrinsic features for alignment. The alignment of the shards against the generic model uses a novel set of 3D weighted curve moments. The transformation is computed from corresponding parabolic contours on the shard and the generic model. A distance error metric is used to access the accuracy of alignment of a fragment to a given generic vessel model. The method is also extendable to surface markings. For a vessel that has no relief, color information or surface breaks can be used for the alignment. The method is tested on a subset of 3D scanned Independence National Historical Park (INDE) ceramic artifacts and the generic models created by experts. This work is part of an ongoing research activity in computational archeology that exploits many different tools and features to help in the mending process. Only the use of surface differential geometry information is reported here. This aspect is complementary to various other tools reported elsewhere by us and others, such as surface breaks, texture, color, etc.     

A surface reconstruction algorithm for topology optimization

For mechanical structural design, topology optimization is often utilized. During this process, a topologically optimized model must be converted into a parametric CAD solid model. The key point of conversion is that a discretized shape of a topologically optimized model must be smoothed, but features such as creases and corners must be retained. Thus, a surface reconstruction algorithm to produce the parametric CAD solid model from a topologically optimized model is proposed in this paper. Our presented algorithm consists of three parts: (1) an enclosed isosurface geometry from which the topologically optimized model is generated, (2) features detected and (3) the parametric CAD solid model reconstructed as biquartic surface splines. In order to generate an enclosed isosurface model effectively, we propose an algorithm based upon the marching cubes method to detect elements intersected by an isosurface. After generating an enclosed isosurface model, we produce biquartic surface splines. By applying our algorithm to an enclosed isosurface model, it is possible to produce smoothed biquartic surface splines with features retained. Some examples are shown and the effectiveness of our algorithm is discussed in this paper.     

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.     

Efficient surface reconstruction method for distributed CAD

This paper describes a new fast Reverse Engineering (RE) method for creating a 3D computerized model from an unorganized cloud of points. The proposed method is derived directly from the problems and difficulties currently associated with remote design over the Internet, such as accuracy, transmission time and representation at different levels of abstraction. With the proposed method, 3D models suitable for distributed design systems can be reconstructed in real time. The mesh reconstruction approach is based on aggregating very large scale 3D scanned data into a Hierarchical Space Decomposition Model (HSDM), realized by the Octree data structure. Then, a Connectivity Graph (CG) is extracted and filled with facets. The HSDM can represent both the boundary surface and the interior volume of an object. Based on the proposed volumetric model, the surface reconstruction process becomes robust and stable with respect to sampling noise. Moreover, the data received from different surface/volume sampling devices can be handled naturally. The hierarchical structure of the proposed volumetric model enables data reduction, while preserving significant geometrical features and object topology. As a result, reconstruction and transmission over the network are efficient. Furthermore, the hierarchical representation provides a capability for extracting models at desired levels of detail, thus enabling designers to collaborate at any product development stage: draft or detailed design.     

Optimization-based approach for curve and surface reconstruction

This paper introduces an optimization-based approach for the curve reconstruction problem, where piecewise linear approximations are computed from sets of points sampled from target curves. In this approach, the problem is formulated as an optimization problem. To be more concrete, at first the Delaunay triangulation for the sample points is computed, and a weight is assigned with each Delaunay edge. Then the problem becomes minimization or maximization of the total weights of the edges that constitute the reconstruction. This paper proposes one exact method and two approximate methods, and shows that the obtained results are improved both theoretically and empirically. In addition, the optimization-based approach is further extended to three dimensions, where surfaces are to be reconstructed, and the quality of the reconstructions is examined.     

Progressive surface reconstruction for heart mapping procedure

The composite imaging of measured cardiac properties like electrical activation and contractile properties on a reconstructed endocardial surface allows for the diagnosis of cardiac arrhythmia and myocardial infarct. However, it is difficult for an interventionalist to acquire heart surface contacts by navigating a catheter to the desired region of interest under minimal visual aid. This paper discusses a new method for the progressive reconstruction of an endocardial surface during a heart mapping procedure. A generic mesh is first aligned with a set of anchor points to obtain a first approximation of the surface. Subsequent deformations are constrained by the preservation of local surface characteristics and the fidelity of new contact points. The mesh is refined by local subdivision and its geometrical shape is further improved by edge swapping. Compared to prior art, the new method can reconstruct a realistic surface from a set of sparse and random data. It can advantageously provide a smooth reconstruction at initial acquisition and ensure a geometrical consistency between consecutive reconstructions. The accurate reconstruction of a heart chamber provides important visual cues for an interventionalist to decide on the next mapping site, thus constructively influencing the final diagnosis.     

一类纯反馈非线性系统的动态面控制

针对一类非仿射输入纯反馈非线性系统,提出了一种动态面控制算法.不同于运用中值定理,该算法通过引入一个辅助系统,将原系统转化为输入仿射系统,结合动态面控制与反推设计法,消除了反推法中"计算膨胀"问题.所设计控制器保证了闭环系统所有信号半全局一致最终有界,且通过选择合适的设计参数可使跟踪误差收敛到原点的一个小邻域内.一个仿真实例进一步验证了所提控制算法的有效性.     

A hybrid nonlinear state observer for concentration profiles reconstruction in nonlinear simulated moving bed

In this paper, a state observer is proposed for the reconstruction of the concentration profiles in a simulated moving bed. The approach is based on a simple Luenberger-like correction term. The observer is used under the assumption that the flow rates are constant during each switching period. The matrix gain of the correction term may then be re-computed at the beginning of each switching period corresponding to flow rates being changed by the controller. Validating simulations are proposed to assess the efficiency of the proposed profile reconstruction and its robustness against uncertainties on modelling parameters. Comparisons are also done with open-loop simulation based-observer in order to strengthen the relevance of the correction term.     

On compatible priors for Bayesian networks

Given a Bayesian network of discrete random variables with a hyper-Dirichlet prior, a method is proposed for assigning Dirichlet priors to the conditional probabilities of structurally different networks. It defines a distance measure between priors which is to be minimized for the assignment process. Intuitively one would expect that if two models priors are to qualify as being `close' in some sense, then their posteriors should also be nearby after an observation. However one does not know in advance what will be observed next. Thus we are led to propose an expectation of Kullback-Leibler distances over all possible next observations to define a measure of distance between priors. In conjunction with the additional assumptions of global and local independence of the parameters, a number of theorems emerge which are usually taken as reasonable assumptions in the Bayesian network literature. A simple example is given to illustrate the technique