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.     

Efficient 3D shape matching and retrieval using a concrete radialized spherical projection representation

We present a 3D shape retrieval methodology based on the theory of spherical harmonics. Using properties of spherical harmonics, scaling and axial flipping invariance is achieved. Rotation normalization is performed by employing the continuous principal component analysis along with a novel approach which applies PCA on the face normals of the model. The 3D model is decomposed into a set of spherical functions which represents not only the intersections of the corresponding surface with rays emanating from the origin but also points in the direction of each ray which are closer to the origin than the furthest intersection point. The superior performance of the proposed methodology is demonstrated through a comparison against state-of-the-art approaches on standard databases.     

一种基于球面调和描述子的3维模型相似性比较算法

提出了一种基于球面调和描述子的3维模型相似性比较算法。首先,对3维模型进行一分为二的递归分解,然后对每次递归分解得到的3维模型顶点集合进行球面映射得到其球面图像,最后计算所有球面图像的球面调和描述子得到3维模型的特征二叉树。通过对3维模型特征二叉树进行相似性比较可以得到3维模型的相似性。实验结果表明,该算法不仅能较好地比较3维模型相似性,而且对坐标系旋转变换、模型噪声、网格简化和细分具有较好的鲁棒性。     

A survey of content based 3D shape retrieval methods

Recent developments in techniques for modeling, digitizing and visualizing 3D shapes has led to an explosion in the number of available 3D models on the Internet and in domain-specific databases. This has led to the development of 3D shape retrieval systems that, given a query object, retrieve similar 3D objects. For visualization, 3D shapes are often represented as a surface, in particular polygonal meshes, for example in VRML format. Often these models contain holes, intersecting polygons, are not manifold, and do not enclose a volume unambiguously. On the contrary, 3D volume models, such as solid models produced by CAD systems, or voxels models, enclose a volume properly. This paper surveys the literature on methods for content based 3D retrieval, taking into account the applicability to surface models as well as to volume models. The methods are evaluated with respect to several requirements of content based 3D shape retrieval, such as: (1) shape representation requirements, (2) properties of dissimilarity measures, (3) efficiency, (4) discrimination abilities, (5) ability to perform partial matching, (6) robustness, and (7) necessity of pose normalization. Finally, the advantages and limitations of the several approaches in content based 3D shape retrieval are discussed.

Benchmarking shape signatures against human perceptions of geometric similarity

Manual indexing of large databases of geometric information is both costly and difficult. Because of this, research into automated retrieval and indexing schemes has focused on the development of methods for characterising 3D shapes with a relatively small number of parameters (e.g. histograms) that allow ill-defined properties such as “geometric similarity” to be computed. However although many methods of generating these so called shape signatures have been proposed, little work on assessing how closely these measures match human perceptions of geometric similarity has been reported. This paper details the results of a trial that compared the part families identified by both human subjects and three published shape signatures.To do this a similarity matrix for the Drexel benchmark datasets was created by averaging the results of twelve manual inspections. Three different shape signatures (D2 shape distribution, spherical harmonics and surface portioning spectrum) were computed for each component in the dataset, and then used as input to a competitive neural network that sorted the objects into numbers of “similar” clusters. Comparison of human and machine generated clusters (i.e. families) of similar components allows the effectiveness of the signatures at duplicating human perceptions of shapes to be quantified.The work reported makes two contributions. Firstly the results of the human perception test suggest that the Drexel dataset contains objects whose perceived similarity levels ranged across the recorded spectrum (i.e. 0.1 to 0.9); Secondly the results obtained from benchmarking the three shape signatures against human perception demonstrate a low rate of false positives for all three signatures and a false negative rate that varied almost linearly with the amount of perceived similarity. In other words the shape signatures studied were reasonably effective at matching human perception in that they returned few wrong results and excluded parts in direct proportion to the level of similarity demanded by the user.     

A fast algorithm for ICP-based 3D shape biometrics

In a biometrics scenario, gallery images are enrolled into the database ahead of the matching step, which gives us the opportunity to build related data structures before the probe shape is examined. In this paper, we present a novel approach, called “Pre-computed Voxel Nearest Neighbor”, to reduce the computational time for shape matching in a biometrics context. The approach shifts the heavy computation burden to the enrollment stage, which is done offline. Experiments in 3D ear biometrics with 369 subjects and 3D face biometrics with 219 subjects demonstrate the effectiveness of our approach.     

Efficient shape parameterization method for multidisciplinary global optimization and application to integrated ship hull shape optimization workflow

Multidisciplinary global shape optimization requires a geometric parameterization method that keeps the shape generality while lowering the number of free variables. This paper presents a reduced parameter set parameterization method based on integral B-spline surface capable of both shape and topology variations and suitable for global multidisciplinary optimization. The objective of the paper is to illustrate the advantages of the proposed method in comparison to standard parameterization and to prove that the proposed method can be used in an integrated multidisciplinary workflow. Non-linear fitting is used to test the proposed parameterization performance before the actual optimization. The parameterization method can in this way be tested and pre-selected based on previously existing geometries. Fitting tests were conducted on three shapes with dissimilar geometrical features, and great improvement in shape generality while reducing the number of shape parameters was achieved. The best results are obtained for a small number (up to 50) of optimization variables, where a classical applying of parameterization method requires about two times as many optimization variables to obtain the same fitting capacity.The proposed shape parameterization method was tested in a multidisciplinary ship hull optimization workflow to confirm that it can actually be used in multiobjective optimization problems. The workflow integrates shape parameterization with hydrodynamic, structural and geometry analysis tools. In comparison to classical local and global optimization methods, the evolutionary algorithm allows for fully autonomous design with an ability to generate a wide Pareto front without a need for an initial solution.     

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.     

使用形状变化描述三维模型

针对三维模型检索中的形状特征提取问题,提出利用三维模型自身形状变化信息构造形状特征描述符的方法.首先选择一组等间距互相平行的平面切割三维模型,得到三维模型的切片集合;然后定义相邻切片的 差来描述切片间的形状变化,并通过所有相邻切片间的差值来反映三维模型自身的形状变化,以此作为三维模型的形状特征描述符.该方法与三维模型的旋转、平移无关,同时不依赖于模型的点云分布,并且精简模型三角面片对算法的影响较小.实验结果验证了该方法的有效性.     

改进的三维模型形状分布检索算法

针对传统D1距离形状分布函数获取采样点计算复杂、模型内容描述不充分和检索速率低下等问题提出了一种改进方法。该方法的关键点是：首先采用平移和缩放对模型进行标准化处理,用于减少面片之间的差异,使得采样点均匀地落在模型的表面;其次采用三角面片的索引号进行随机数的生成,并且利用三角面片的重心和质心进行有效的计算,以便用于缩短模型的处理时间和提高检索速率。利用普林斯顿大学三维模型数据库中的部分模型作为实验数据,实现结果表明：改进的方法不会降低模型的检索性能,并有效地减少了模型查询和处理时间。     

用于3D模型检索的扩展距离球面调和表达

使用光线投射方法对3D模型定义了一个对应的球函数--扩展距离球函数,然后引入了球面调和分析方法,构造了一种对于平移、缩放和旋转变换具有不变性的特征向量,并用于基于形状的3D模型检索中.与基于向径方法结合,提高了检索的效果,扩大了应用范围.     

基于IsoRank的三维耳廓形状匹配

基于IsoRank算法实现了耳廓剖分图的匹配,进而实现了基于耳廓三维形状的身份鉴别.基于主成分分析提取待匹配三维耳廓上的关键点,构造耳廓关键点的三维网格图;基于IsoRank算法求2个关键点三维网格图结点之间的对应关系,实现耳廓关键点的图匹配.由于采用了IsoRank算法,耳廓关键点网格图得到了全局对齐,两耳廓之间的整体匹配得到最大化.实验结果表明,基于IsoRank算法的耳廓匹配方法具有较低的时间复杂度以及较高的匹配精度和匹配效率.     

Non-rigid 3D shape tracking from multiview video

We present a fast and efficient non-rigid shape tracking method for modeling dynamic 3D objects from multiview video. Starting from an initial mesh representation, the shape of a dynamic object is tracked over time, both in geometry and topology, based on multiview silhouette and 3D scene flow information. The mesh representation of each frame is obtained by deforming the mesh representation of the previous frame towards the optimal surface defined by the time-varying multiview silhouette information with the aid of 3D scene flow vectors. The whole time-varying shape is then represented as a mesh sequence which can efficiently be encoded in terms of restructuring and topological operations, and small-scale vertex displacements along with the initial model. The proposed method has the ability to deal with dynamic objects that may undergo non-rigid transformations and topological changes. The time-varying mesh representations of such non-rigid shapes, which are not necessarily of fixed connectivity, can successfully be tracked thanks to restructuring and topological operations employed in our deformation scheme. We demonstrate the performance of the proposed method both on real and synthetic sequences.     

基于分层策略的三维非刚性模型配准算法

在三维非刚性模型分析中,通常需要对不同姿态下的模型进行配准。针对传统配准算法存在复杂度高、计算量大、精确度低等问题,提出一种新的基于分层策略的三维非刚性模型配准算法。首先,定义热核签名函数为模型的标量域,使用同源聚类算法提取模型的特征点和特征区域,进而提出三维几何模型的树形表示方法:它的根节点为三维几何模型,内部节点为模型的特征区域,叶节点为包含在相应区域的特征点。然后,根据三维几何模型的树形表示提出模型的分层配准算法。在SHREC 2010模型配准数据集上对比分析了分层配准算法、推广的多维尺度变换算法（GMDS）和博弈论方法在等距变换、孔洞、小孔洞、尺度变换、局部尺度变换、重采样、噪声、散粒噪声以及拓扑变换等情况下的性能。实验结果表明,在以上三维几何模型数据受干扰的情况下,分层配准算法的准确性明显优于GMDS方法和博弈论方法,同时具有较低的计算复杂度。     

A mathematical morphology approach to image based 3D particle shape analysis

Angularity is a critically important property in terms of the performance of natural particulate materials. It is also one of the most difficult to measure objectively using traditional methods. Here we present an innovative and efficient approach to the determination of particle angularity using image analysis. The direct use of three-dimensional data offers a more robust solution than the two-dimensional methods proposed previously. The algorithm is based on the application of mathematical morphological techniques to range imagery, and effectively simulates the natural wear processes by which rock particles become rounded. The analysis of simulated volume loss is used to provide a valuable measure of angularity that is geometrically commensurate with the traditional definitions. Experimental data obtained using real particle samples are presented and results correlated with existing methods in order to demonstrate the validity of the new approach. The implementation of technologies such as these has the potential to offer significant process optimisation and environmental benefits to the producers of aggregates and their composites. The technique is theoretically extendable to the quantification of surface texture.     

Progressive 3D shape segmentation using online learning

In this article, we propose a progressive 3D shape segmentation method, which allows users to guide the segmentation with their interactions, and does segmentation gradually driven by their intents. More precisely, we establish an online framework for interactive 3D shape segmentation, without any boring collection preparation or training stages. That is, users can collect the 3D shapes while segment them, and the segmentation will become more and more precise as the accumulation of the shapes.Our framework uses Online Multi-Class LPBoost (OMCLP) to train/update a segmentation model progressively, which includes several Online Random forests (ORFs) as the weak learners. Then, it performs graph cuts optimization to segment the 3D shape by using the trained/updated segmentation model as the optimal data term. There exist three features of our framework. Firstly, the segmentation model can be trained gradually during the collection of the shapes. Secondly, the segmentation results can be refined progressively until users’ requirements are met. Thirdly, the segmentation model can be updated incrementally without retraining all shapes when users add new shapes. Experimental results demonstrate the effectiveness of our approach.     

基于内容和语义的三维模型检索综述

多媒体信息的检索是信息复用的重要途径。三维模型检索作为三维建模过程中的关键技术之一,近年来随着三维建模的广泛运用而被深入研究。针对目前三维模型检索技术的进展,首先介绍了基于内容的检索技术,按照提取的特征将其分为四类：基于统计数据、基于几何外形、基于拓扑结构和基于视觉特征,分别介绍各类技术的主要成果和优缺点;然后介绍考虑语义信息,解决“语义鸿沟”现象的基于语义的检索方法,根据切入角度将其分为三类：相关性反馈、主动学习和本体技术,随后介绍了各类技术的相互关系与特点;最后总结和提出了三维模型检索的未来研究的发展方向。