Watermarking 3D mesh by spherical parameterization

In this paper, a robust 3D trianglular mesh watermarking algorithm is presented by applying spherical parameterization. First, we transform the coordinate signals of the 3D triangular mesh into spherical signals using a global spherical parameterization and an even sampling scheme. Then, spherical harmonic transformation is used to generate some data for embedding watermarks. As a result, the watermarks can be embedded in the Fourier-frequency domain of the original mesh. Experimental results show that our watermarking algorithm is robust since watermarks can be extracted without mesh alignment or re-meshing under a variety of attacks, including noise addition, crop, filtering, enhancement, rotation, translation, scale and re-sampling.     

Mesh parameterization based on one-step inverse forming

A novel planar mesh parameterization algorithm via flattening or unfolding is proposed by introducing a so-called one-step inverse approach (IA) based on physical plastic deformation of metal materials. As opposed to methods based on geometric idea, the algorithm is more suitable for CAD models, e.g. rapid prediction of blank shape in sheet metal forming for auto-body panels. Benefiting from proper pre-processing steps, rapid simulation of sheet metal forming and optimal initial solution guess, the proposed algorithm flattens meshes onto a plane with lower area distortion and minimizes the angular distortion. Some numerical examples of results generated by the new parameterization method are provided, and the corresponding analyses are given as well, such as distributions of strain, stress, thickness distribution and formability, etc.     

3D surface filtering using spherical harmonics

This paper presents a novel approach for 3D surface filtering over two-manifold meshes. A robust spherical parameterization algorithm is proposed to transform the input surface into a spherical vector function/signal. This signal is then decomposed into frequency domain using spherical harmonic transforms. Finally, traditional filtering techniques are generalized to process such spherical signals in either the frequency or spatial domain. Our major contribution is the two-phase spherical parameterization algorithm, which can handle meshes with complex shapes by incorporating local parameterization into the progressive mesh. A number of experimental examples demonstrate the potential of our algorithm.     

Feature-based 3D non-manifold freeform object construction

This paper presents a novel technique for modeling a 3D non-manifold freeform model around a 3D reference model. To represent both the design abstractions and the incomplete topological information, a new non-manifold data structure is first defined. Our data structure embodies the functional vitalities of both the boundary representation data structure and the complex-based data structure. Along with our data structure, a set of topological operators is defined to manipulate the entities in the data structure. Based on the non-manifold data structure and the topological operators, we develop a technique to construct 3D freeform objects around a reference model. Intuitive 2D sketches are adopted to specify the detailed profile of the object constructed. The construction method is feature-based – every reference model has pre-defined features, and the feature template of the constructed object is related to the features of the reference model by feature node encoding. Therefore, the surfaces derived from one reference model can be regenerated automatically on another reference model with the same features. The geometry coverage of our geometric modeling approach includes both manifold and non-manifold 3D freeform objects.     

A novel 3D morphing approach for tooth occlusal surface reconstruction

Reconstruction of the tooth occlusal surface is an important aspect of dental CAD systems. The design surface should fit to the existing tooth articulation and keep the morphological features of the generic teeth. This paper presents the use of a 3D morphing technique to reconstruct the missing inlay or crown occlusal surface. This method involves three necessary steps of tooth cavity contour extraction, feature points identification and tooth surface deformation. Because the missing occlusal surface is often determined by the outline of the cavity inside the remaining tooth, the cavity contour is tracked firstly by a 3D optimal path searching algorithm. Then through identifying a number of corresponding feature points on the standard tooth and the remaining tooth by a Snake model algorithm, the method uses a mapping function called Radial Basis Function (RBF) to define the spatial relations of all points in both teeth, and interpolate the intermediate feature positions, such that the standard tooth surface is deformed into alignment, and the missing surface is determined. This presents a direct and simple method to automatically reconstruct the occlusal surface. The corresponding features are fully considered in the morphing algorithm, consequently the morphological features of the tooth are well retained.     

Mesh resolution augmentation using 3D skin bank

We present a 3D skin containing the 3D detail information of a high resolution facial mesh. Our 3D skin bank is derived from several scanned faces with resolutions up to several million triangles where even the pores are clearly visible. We present a method to raise the resolution of any given low quality face’s geometry by making use of the 3D skin, where the resultant model’s final resolution is high enough to be used in computer-generated films. Our method can be deployed to produce numerous high resolution versions of a single low quality face, each bearing different skin characteristics.     

Stabilizing 3D modeling with geometric constraints propagation

This paper proposes a technique for estimating piecewise planar models of objects from their images and geometric constraints. First, assuming a bounded noise in the localization of 2D points, the position of the 3D point is estimated as a polyhedron containing all the possible solutions of the triangulation. Then, given the topological structure of the 3D points cloud, geometric relationships among facets, such as coplanarity, parallelism, orthogonality, and angle equality, are automatically detected. A subset of them that is sufficient to stabilize the 3D model estimation is selected with a flow-network based algorithm. Finally, a feasible instance of the 3D model, i.e. one that satisfies the geometric constraints and whose 3D vertices lie within the associated polyhedral bounds, is computed by solving a Constraint Satisfaction Problem. The process accommodates uncertainty in a non-probabilistic fashion and thus provides rigorous results. Synthetic and real experiments illustrate the approach.     

Geometric deformations based on 3D volume morphing

This paper presents a new geometric deformation method based on 3D volume morphing by using a new cocept called directinal polar coordinate.The user specifies the source control object and the destination control object which act as the embedded spaces.The source and the destination control objects deterine a 3D volume morphing which maps the space enclosed in the source control object to that of the destination cotrol object.By embedding the object to be deformed into the source control boject,the 3D volume morphing determines the deformed object automatically without the tiring moving of control points.Experiments show that this deformation model is efficient and intuitive ,and it can achieve some deformation effects which are difficult to achieve for traditional methods.     

一种基于球面调和分析的三维模型检索算法

提取关于坐标旋转不变的特征描述符以及提高特征描述符对噪声的鲁棒性是基于内容三维模型检索技术中有待进一步研究解决的问题之一。将三维模型表面离散成三维点数据,然后使用球面调和方法对得到的点数据进行调和分析得到三维模型旋转不变的特征向量,并且能够增加算法对模型表面噪声的鲁棒性提高检索准确度。实验证明该算法在检索准确度和对噪声的鲁棒性上都有所提高。     

3D shape metamorphosis based on T-spline level sets

We propose a new method for 3D shape metamorphosis, where the in-between objects are constructed by using T-spline scalar functions. The use of T-spline level sets offers several advantages: First, it is convenient to handle complex topology changes without the need of model parameterization. Second, the constructed objects are smooth (C² in our case). Third, high quality meshes can be easily obtained by using the marching triangulation method. Fourth, the distribution of the degrees of freedom can be adapted to the geometry of the object. Given one source object and one target object, we firstly find a global coordinate transformation to approximately align the two objects. The T-spline control grid is adaptively generated according to the geometry of the aligned objects, and the initial T-spline level set is found by approximating the signed distance function of the source object. Then we use an evolution process, which is governed by a combination of the signed distance function of the target object and a curvature-dependent speed function, to deform the T-spline level set until it converges to the target shape. Additional intermediate objects are inserted at the beginning/end of the sequence of generated T-spline level sets, by gradually projecting the source/target object to the initial/final T-spline level set. A fully automatic algorithm is developed for the above procedures. Experimental results are presented to demonstrate the effectiveness of our method.     

临近特征点类型匹配的多边形渐变表达模型

提出一种基于Morphing技术的多边形连续尺度地图表达模型。依据多边形的凸壳多叉树建立了多边形特征点的层次结构;基于临近性原则及特征点前后弧段形状的对照关系实现两个关键尺度的同一多边形要素各层次特征点的匹配;在多边形的对应特征点间利用Morphing内插技术得到两个关键尺度间任意尺度的多边形表达。实验表明,对于两个关键尺度下的同一多边形,使用该模型能获取任意中间尺度下的多边形表达,在尺度变化时,多边形图形的过渡自然平稳。     

A Survey on Data‐driven Dictionary‐based Methods for 3D Modeling

Dictionaries are very useful objects for data analysis, as they enable a compact representation of large sets of objects through the combination of atoms. Dictionary‐based techniques have also particularly benefited from the recent advances in machine learning, which has allowed for data‐driven algorithms to take advantage of the redundancy in the input dataset and discover relations between objects without human supervision or hard‐coded rules. Despite the success of dictionary‐based techniques on a wide range of tasks in geometric modeling and geometry processing, the literature is missing a principled state‐of‐the‐art of the current knowledge in this field. To fill this gap, we provide in this survey an overview of data‐driven dictionary‐based methods in geometric modeling. We structure our discussion by application domain: surface reconstruction, compression, and synthesis. Contrary to previous surveys, we place special emphasis on dictionary‐based methods suitable for 3D data synthesis, with applications in geometric modeling and design. Our ultimate goal is to enlight the fact that these techniques can be used to combine the data‐driven paradigm with design intent to synthesize new plausible objects with minimal human intervention. This is the main motivation to restrict the scope of the present survey to techniques handling point clouds and meshes, making use of dictionaries whose definition depends on the input data, and enabling shape reconstruction or synthesis through the combination of atoms.     

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.     

Interactive design of 3D models with geometric constraints

In this paper, an interactive graphical approach for the design of parameterized part-hierarchies is presented. Primitive solids can be grouped into compound objects, and multiple instances of a compound object can be used in further designs. Geometric relations between primitives and instances are specified by geometric constraints between their local coordinate systems. The user can specify and edit a model by direct manipulation on a perspective or parallel projection with a mouse, whereas a procedural model representations is automatically generated via visual programming. The obtained twoview approach offers two concurrent interface styles to the end-user and enables the combination of an intuitive direct manipulation interface with the expressiveness of a procedural modeling language.     

Classification of 3D shape deviation using feature recognition operating on parameterization control points

A numerically efficient expert system for evaluation of 3D shape based on features extracted from the parameterization control points data-set is developed. Reference shapes are stored and periodically compared with current shapes at the level of windowed control-point data grids for the purpose of detection of 3D shape deviation. Classification heuristics for the respective types of deviations which operate on the control point sets rather than the original raw point clouds are developed based on operations of windowing, coordinate transformation, filtering and singular value decomposition (SVD)/principal component analysis (PCA). The methodology is demonstrated with the cases of detecting and computationally recognizing local impact damage and cavities, narrow gaps or fatigue cracks and wear-based surface deterioration on a wind turbine blade.     

Real-time 3D face tracking based on active appearance model constrained by depth data

Active Appearance Model (AAM) is an algorithm for fitting a generative model of object shape and appearance to an input image. AAM allows accurate, real-time tracking of human faces in 2D and can be extended to track faces in 3D by constraining its fitting with a linear 3D morphable model. Unfortunately, this AAM-based 3D tracking does not provide adequate accuracy and robustness, as we show in this paper. We introduce a new constraint into AAM fitting that uses depth data from a commodity RGBD camera (Kinect). This addition significantly reduces 3D tracking errors. We also describe how to initialize the 3D morphable face model used in our tracking algorithm by computing its face shape parameters of the user from a batch of tracked frames. The described face tracking algorithm is used in Microsoft's Kinect system.     

限制失真的网格参数化方法

针对当前网格参数化效率较低、映射失真较严重的问题，提出一种限制失真的网格参数化方法。首先，预处理原始网格模型。输入原3D网格模型，采用Half-Edge数据结构来重新组织网格并切割网格模型产生相应的切缝；构建Tutte映射把3D网格映射到一个2D凸多边形域，即构建2D网格模型。然后，进行限制失真的网格参数化计算。将Tutte映射后的2D网格模型作为限制失真计算的初始数据，建立相对于原3D模型网格的失真度量函数；求得该度量函数的最小值点，即为映射后的网格坐标集合；将映射后的网格作为限制失真映射的输入网格，设定迭代终止条件，循环迭代直至迭代结束，得到收敛的最优网格坐标；在计算映射失真度时，针对等距映射失真采用Dirichlet能量函数度量，针对共形映射失真采用尽可能等距（MIPS）能量函数度量；在求解映射失真度量函数的最小值点时采用代理函数法结合组合牛顿法的最优解方法。最终，实现了该方法并开发了一个原型系统。在原型系统中，分别设计了限制等距失真和限制共形失真的网格参数化实验，对程序执行时间和失真能量下降情况进行了统计和对比，提供了相应的纹理映射效果展示。实验数据表明，所提出的方法执行效率高、映射失真能量下降快，最优值收敛质量稳定；纹理映射时纹理着色均匀、布局紧致、线条均匀，符合实际应用的标准。     

Recognition of 3-D objects by forward checking constrained search

An attempt to recognize 3-D objects from range images is described. Objects are represented by surface patches obtained by segmenting image at depth or orientation discontinuity. To find the best matching pairs between model surface patches (MSPs) and scene surface patches (SSPs), we use forward checking constrained tree search that is a sequential constrained tree search with a forward checking mechanism. It checks geometric constraints between current partial matching pairs and unexplored possible pairs and drastically reduces the number of candidate MSPs matchable to unexplored SSPs. Futhermore, it yields powerful search termination criteria. As an alternative to the sequential search method, we also applied the optimal search algorithm (A^*). To verify advantages of the forward checking, we evaluated the perfomance of the matching algorithms using real range images. The experimental results demonstrated significant gains in computation. Comparing with other methods, our approach is particularly advantageous for the difficult problems in that model objects are very much similar to each other. Our method detects part in difference in advance and so reduces time to discriminate the similar objects. It is confirmed by an evaluation.     

3D shape acquisition and integral compact representation using optical scanning and enhanced shape parameterization

An efficient computational methodology for shape acquisition, processing and representation is developed. It includes 3D computer vision by applying triangulation and stereo-photogrammetry for high-accuracy 3D shape acquisition. Resulting huge 3D point clouds are successively parameterized into mathematical surfaces to provide for compact data-set representation, yet capturing local details sufficiently. B-spline surfaces are employed as parametric entities in fitting to point clouds resulting from optical 3D scanning. Beyond the linear best-fitting algorithm with control points as fitting variables, an enhanced non-linear procedure is developed. The set of best fitting variables in minimizing the approximation error norm between the parametric surface and the 3D cloud includes the control points coordinates. However, they are augmented by the set of position parameter values which identify the respectively closest matching points on the surface for the points in the cloud. The developed algorithm is demonstrated to be efficient on demanding test cases which encompass sharp edges and slope discontinuities originating from physical damage of the 3D objects or shape complexity.     

基于隐式参数化的车身多学科轻量化设计

为实现整车综合性能的快速方案验证和优化设计,在新车型设计阶段构建车身隐式参数化模型,并对其进行模态、刚度和安全等综合性能计算,验证参数化模型的有效性。基于灵敏度分析、试验设计（design of experiments, DOE）方法和近似模型优化等策略,对某白车身进行多学科轻量化设计。优化设计结果表明,白车身的模态、刚度和安全性能均满足设计要求。