Localization and comparison of two free-form surfaces

Comparison of two free-form surfaces based on discrete data points is of paramount importance for reverse engineering. It can be used to assess the accuracy of the reconstructed surfaces and to quantify the difference between two such surfaces. The entire process involves three main steps: data acquisition, 3D feature localization and quantitative comparison. This paper presents models and algorithms for 3D feature localization and quantitative comparison. Complex free-form surfaces are represented by bicubic parametric spline surfaces using discrete points. A simple yet effective pseudoinverse algorithm was developed and implemented for localization. It consists of two iterative operations, namely, constructing a pseudo transformation matrix and point matching. A computing algorithm was developed to compare two such surfaces using optimization techniques. Since this approach does not involve solving non-linear equations for the parameters of positions and orientations, it is fast and robust. The algorithm was implemented and tested with several examples. It is effective and can be used in industry for sculptured surface comparison.     

Poisson Manifold Reconstruction — Beyond Co-dimension One

Screened Poisson Surface Reconstruction creates 2D surfaces from sets of oriented points in 3D (and can be extended to co-dimension one surfaces in arbitrary dimensions). In this work we generalize the technique to manifolds of co-dimension larger than one. The reconstruction problem consists of finding a vector-valued function whose zero set approximates the input points. We argue that the right extension of screened Poisson Surface Reconstruction is based on exterior products: the orientation of the point samples is encoded as the exterior product of the local normal frame. The goal is to find a set of scalar functions such that the exterior product of their gradients matches the exterior products prescribed by the input points. We show that this setup reduces to the standard formulation for co-dimension 1, and leads to more challenging multi-quadratic optimization problems in higher co-dimension. We explicitly treat the case of co-dimension 2, i.e., curves in 3D and 2D surfaces in 4D. We show that the resulting bi-quadratic problem can be relaxed to a set of quadratic problems in two variables and that the solution can be made effective and efficient by leveraging a hierarchical approach.     

Integrating adaptive mutations and family competition into genetic algorithms as function optimizer

 In this paper, we propose a robust evolutionary algorithm, called adaptive mutations genetic algorithm, for function optimization problems. Our main contribution is robustly optimizing problems whose number of variables from 2 to 200. In order to have a fair comparison, we propose the criteria for constructing a testing bed and for classifying these problems into different complexity degrees. The proposed approach, based on the family competition and multiple adaptive rules, successfully integrates the decreasing-based Gaussian mutation and self-adaptive Cauchy mutation to balance the exploitation and exploration. It is implemented and applied to widely used test functions and several nonseparable multimodal functions. Experimental results indicate that our approach is more robust than ten evolutionary algorithms.     

Shape differentiation of freeform surfaces using a similarity measure based on an integral of Gaussian curvature

Freeform surfaces are popularly used to design and model complex 3D objects. These 3D models are stored as computerized models in databases. To facilitate data retrieval and shape matching, a major challenge lies in defining and computing the level of similarity between two or more freeform surfaces. In order to explore the useful 3D information associated with the surfaces, an integrated approach based on the integral of Gaussian curvature is proposed to develop the measures of similarity of freeform surfaces. Specifically, the integral of Gaussian curvature is mapped into the 2D space, and a shape-based measure is developed using statistical methods to compute the level of similarity. For smooth surfaces, a fast approximation algorithm is developed to calculate the curvature of individual subregions. In cases where the target surface has a complex topological structure or a smooth surface is not available, the integral of Gaussian curvature for the discrete surface is first calculated at each vertex, followed by mapping onto a 2D spherical coordinate. The distance measure focuses on the local geometry, which is critical to investigate models with a certain level of resemblance such as products in a family. This proposed approach can be applied to surfaces under various transformations, as well as 3D data from various sources.     

位移蝶形细分面片的渐进传输

随着三维激光扫描和建模技术的不断进步,三维网格模型的数据量越来越大．与此同时,无处不在的智能计算要求数据必须能够在网络上进行快速的传输,现有的三维网格渐进传输技术无论是基于任意拓扑结构网格的渐进网格技术,还是基于参数化细分面片的渐进传输技术,都存在着传输数据量大、渐进显示效果差的问题,针对这些缺点,提出了首先利用位移蝶形细分面片重建原来的网格模型,然后对于重建后的位移蝶形细分面片设计了一种新的数据简化方法,进而构造了一种渐进传输算法,该算法在减少传输数据总量的同时,提高了渐进传输的视觉效果。     

基于曲面法向量的曲面恢复

从另一个角度研究三维曲面的恢复,即根据曲面法向量,考虑多块曲面的重构.算法输入的数据是估计的曲面法向量,比如输入的数据是根据从阴影恢复形状或从纹理恢复形状等计算机视觉低层次处理中得到.通过球面坐标变换把曲面法向量分解成两个函数;然后再对这两个函数进行滤波处理,通过对这两个分割的叠加将空间曲面分割成几个子曲面;最后利用Green函数分别恢复各个子曲面.虽然只利用了一般的图像处理技术,却能得到比传统的基于曲面法向量的方法更好的结果,特别是边界部分的恢复.这是因为传统的方法只是考虑恢复一个曲面模型,因此在不同曲面的边界上会产生模糊.最后利用模拟数据和由阴影恢复形状算法获取真实数据来评价提出的算法,并都与传统的方法进行了比较.     

Processing of 3D meshed surfaces using spherical wavelets

This paper presents an efficient technique for processing of 3D meshed surfaces via spherical wavelets.More specifically,an input 3D mesh is firstly transformed into a spherical vector signal by a fast low distortion spherical parameterization approach based on symmetry analysis of 3D meshes.This signal is then sampled on the sphere with the help of an adaptive sampling scheme.Finally,the sampled signal is transformed into the wavelet domain according to spherical wavelet transform where many 3D mesh processing operations can be implemented such as smoothing,enhancement,compression,and so on.Our main contribution lies in incorporating a fast low distortion spherical parameterization approach and an adaptive sampling scheme into the frame for processing 3D meshed surfaces by spherical wavelets,which can handle surfaces with complex shapes.A number of experimental examples demonstrate that our algorithm is robust and efficient.     

Registering multiple range images based on distance metric of surface-to-surface

1 Introduction In recent years, there has been growing interest in the range sensing techniques for building 3D computer models of real-world objects and scenes without requiring hu-mans to manually produce these models using laborious and error-prone CAD-based approaches. Using range sensors, users are able to capture 3D range images of objects from different viewpoints that may be combined to form the final model of the object or scene[1]. These models then may be used for a variety of app…     

Enhanced Fuzzy System Models With Improved Fuzzy Clustering Algorithm

Although traditional fuzzy models have proven to have high capacity of approximating the real-world systems, they have some challenges, such as computational complexity, optimization problems, subjectivity, etc. In order to solve some of these problems, this paper proposes a new fuzzy system modeling approach based on improved fuzzy functions to model systems with continuous output variable. The new modeling approach introduces three features: i) an improved fuzzy clustering (IFC) algorithm, ii) a new structure identification algorithm, and iii) a nonparametric inference engine. The IFC algorithm yields simultaneous estimates of parameters of c-regression models, together with fuzzy c-partitioning of the data, to calculate improved membership values with a new membership function. The structure identification of the new approach utilizes IFC, instead of standard fuzzy c-means clustering algorithm, to fuzzy partition the data, and it uses improved membership values as additional input variables along with the original scalar input variables for two different choices of regression methods: least squares estimation or support vector regression, to determine ldquofuzzy functionsrdquo for each cluster. With novel IFC, one could learn the system behavior more accurately compared to other FSM models. The nonparametric inference engine is a new approach, which uses the alike -nearest neighbor method for reasoning. Empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro-fuzzy models based on fuzzy rules bases, as well as other soft computing methods.     

A high-speed integrated renderer for interpreting multiple 3D volume data

This paper proposes an integrated rendering algorithm for visualizing 3D volumetric and geometric data, such as surfaces, lines and points, simultaneously with depth information, and other algorithms for improving the performance of the rendering process of the first. The first algorithm extends a volume rendering algorithm based on ray-tracing so that it can handle both 3D volumetric and geometric data. It processes these data in accordance with their original representation formats to eliminate conversion artefacts such as spurious or missing surfaces, and also gives special treatment to volume segments so as to avoid errors in visibility at the intersections between volume segments and geometric data. The other algorithms employ adaptive termination of ray-tracing, elimination of rays that do not intersect the volume, and adaptive undersampling over an image plane. These improve the performance by three to seven times over the brute-force approach. The cost and versatility of the algorithm are evaluated by using data from the results of 3D computational fluid dynamics.     

医学断层图像三维重建的辅助轮廓线法

在原有的轮廓线基础上生成与之相似的辅助轮廓线．然后把各轮廓线三角化形成一层层的三角面片,最后按一定的规则把各层三角面片从外到内直接连接形成四面体,从而完成三维重构．文中算法尤其适合基于断层轮廓线的医学图象三维重构,与已有的三维重构法（如MC．MT,Delaunay四面体化）相比,具有算法简单、思路自然、易于实现的特点．     

An efficient variable partitioning approach for functional decomposition of circuits

Functional decomposition is a process of splitting a complex circuit into smaller sub-circuits. There exist two major strategies in decomposition, namely, serial and parallel decomposition. In serial decomposition the problem the complex function represented as a truth table with support set variables and partitioned into free and bout set variables. The minterms corresponding to the bound set variables are represented as an equivalent function called the predecessor function. Equivalent minterms of the bound set variables are assigned an output code. The assigned output codes and the free set variable minterms are represented as the successor function. Serial decomposition is further categorized into disjoint and non-disjoint decomposition, when the free and bound set variables are disjoint and non-disjoint respectively. This paper deals with the problem of determining the set of best free and bound variables (variable partitioning problem) for disjoint serial decomposition. Variable partitioning is the first step in decomposition process. An efficient variable partition algorithm is one that determines the set of all free and bound set variables that satisfy the decomposition theorem in minimal time and by exploring the search space effectively. This will allow the decomposition algorithm to determine the best variable partition of a function that results in smaller decomposed functions and with maximum number of do not cares in these functions. Classical approaches to determine the best free and bound set use exhaustive search methods. The time and memory requirements for such approaches are exponential or super exponential.A novel heuristic search approach is proposed to determine the set of good variable partitions in minimal time by minimally exploring the search space. There are two heuristics employed in the proposed search approach, (1) r-admissibility based heuristic or pruned breadth first search (PBFS) approach and (2) Information relation based heuristic or improved pruned breadth first search (IPBFS) approach. The r-admissibility based heuristic is based on r-partition characteristics of the free and bound set variables. The information relation and measure based heuristic is based on information relationship of free and bound set variables that are expressed as r-partition heuristics. The proposed variable partition search approach has been successfully implemented and test with MCNC and Espresso benchmarks and the results indicate that the time complexity is comparable to r-admissible heuristic algorithm and the quality of solution is comparable to exact variable partitioning algorithm. A comparison of PBFS and IPBFS heuristics for certain benchmarks are also discussed in this paper.     

一种由二维轮廓线重建物体表面的方法

本文提出一种通过体数据转换实现由轮廓线重建物体表面的方法 .该方法根据“表面投影区”比较两相邻切平面上对应像素点的状态函数值 ,以确定影响等值面生成的像素点 ,从而只进行影响等值面生成的像素点的距离函数的计算 ,并可在根据需要对相邻切平面上的对应点进行插值计算后 ,生成分辨率较高的体数据 .本文采用改进的 MT算法生成等值面 ,完成物体的表面重建 .该方法缩短了体数据的构造时间 ,在保证了重建正确性的前提下提高了整个表面的重建速度     

Offset of curves on tessellated surfaces

Geodesic offset of curves on surfaces is an important and useful tool of computer aided design for applications such as generation of tool paths for NC machining and simulation of fibre path on tool surfaces in composites manufacturing. For many industrial and graphic applications, tessellation representation is used for curves and surfaces because of its simplicity in representation and for simpler and faster geometric operations. The paper presents an algorithm for computing offset of curves on tessellated surfaces. A curve on tessellation (COT) is represented as a sequence of 3D points, with each line segment of every two consecutive points lying exactly on the tessellation. With an incremental approach of the algorithm to compute offset COT, the final offset curve position is obtained through several intermediate offset curve positions. Each offset curve position is obtained by offsetting all the points of COT along the tessellation in such a way that all the line segments gets offset exactly along the faces of tessellation in which the line segments are contained. The algorithm, based entirely on tessellation representation, completely eliminates the formation of local self-intersections. Global self-intersections if any, are detected and corrected explicitly. Offset of both open and closed tessellated curves, either in a plane or on a tessellated surface, can be generated using the proposed approach. The computation of offset COT is very accurate within the tessellation tolerance.     

Decorating surfaces with bidirectional texture functions

We present a system for decorating arbitrary surfaces with bidirectional texture functions (BTF). Our system generates BTFs in two steps. First, we automatically synthesize a BTF over the target surface from a given BTF sample. Then, we let the user interactively paint BTF patches onto the surface such that the painted patches seamlessly integrate with the background patterns. Our system is based on a patch-based texture synthesis approach known as quilting. We present a graphcut algorithm for BTF synthesis on surfaces and the algorithm works well for a wide variety of BTF samples, including those which present problems for existing algorithms. We also describe a graphcut texture painting algorithm for creating new surface imperfections (e.g., dirt, cracks, scratches) from existing imperfections found in input BTF samples. Using these algorithms, we can decorate surfaces with real-world textures that have spatially-variant reflectance, fine-scale geometry details, and surfaces imperfections. A particularly attractive feature of BTF painting is that it allows us to capture imperfections of real materials and paint them onto geometry models. We demonstrate the effectiveness of our system with examples.     

Finding Surface Correspondences Using Symmetry Axis Curves

In this paper, we propose an automatic algorithm for finding a correspondence map between two 3D surfaces. The key insight is that global reflective symmetry axes are stable, recognizable, semantic features of most real‐world surfaces. Thus, it is possible to find a useful map between two surfaces by first extracting symmetry axis curves, aligning the extracted curves, and then extrapolating correspondences found on the curves to both surfaces. The main advantages of this approach are efficiency and robustness: the difficult problem of finding a surface map is reduced to three significantly easier problems: symmetry detection, curve alignment, and correspondence extrapolation, each of which has a robust, polynomial‐time solution (e.g., optimal alignment of 1D curves is possible with dynamic programming). We investigate of this approach on a wide range of examples, including both intrinsically symmetric surfaces and polygon soups, and find that it is superior to previous methods in cases where two surfaces have different overall shapes but similar reflective symmetry axes, a common case in computer graphics.     

Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints

In this work we investigate a generalized interpolation approach using radial basis functions to reconstruct implicit surfaces from polygonal meshes. With this method, the user can define with great flexibility three sets of constraint interpolants: points, normals, and tangents; allowing to balance computational complexity, precision, and feature modeling. Furthermore, this flexibility makes possible to avoid untrustworthy information, such as normals estimated on triangles with bad aspect ratio. We present results of the method for applications related to the problem of modeling 2D curves from polygons and 3D surfaces from polygonal meshes. We also apply the method to problems involving subdivision surfaces and front-tracking of moving boundaries. Finally, as our technique generalizes the recently proposed HRBF Implicits technique, comparisons with this approach are also conducted.     

基于洛仑兹信息度量的三维曲面相似性判别

针对立体赤足迹身份鉴别的需要,提出了一种基于洛伦兹信息度量的三维曲面相似性判别方法。以高斯曲率和法向量为随机变量,将洛伦兹曲线扩展为三维,得到洛伦兹曲面。以两洛伦兹曲面所夹体积来反映两三维曲面高斯曲率和法向量分布的差异,依此构成了三维曲面的相似性判别方法。对立体赤足迹表面的相似性判别实验表明,该判别方法有效。     

Transformation and Normal Vector Calculation of Parametrically Defined Surfaces Based on Dual Vectors and Screw Theory: Application to Phong's Shading Model

This paper presents a new approach for the transformation and normal vector calculation algorithms of parametrically defined surfaces via dual vectors and line transformations. The surface is defined via dual points, the transformation is performed by rotations and translations based on screw theory while normal vector calculation is utilized for shading based on Phong's illumination model. The main benefit of this approach lies into the compactness of the surface's representation since geometrical characteristics, such as tangent vectors, that are necessary for shading algorithms, are included within its definition. An extensive comparison is performed between the proposed approach and the traditional homogeneous model, presenting the merits of our approach. Analytical and experimental determination of the computational cost via computer implementation of 3D surface transformation and shading is presented. Point‐based methods for the representation, transformation and shading of parametrically defined surfaces are compared to the introduced line‐based methods (dual quaternions and dual orthogonal matrices). It is shown that the simplified rendering procedure of 3D objects, is considerably faster using screw theory over the traditional point‐based structures.