Bending polyhedral objects

A geometric algorithm for performing bending operations on polyhedral objects is described. The hypotheses, conditions and model of the bending process are defined, and then the mathematical model of bending is developed for each element of the boundary representation of a polyhedron. The algorithm has applications as a new means of generating geometric models and, in the CAD/CAM field, for simulating bending processes used to manufacture parts. The algorithm has been implemented and examples are given of objects transformed by the bending operation.     

Wavelet‐based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis

In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well‐established methodology of diffusion wavelets. This novel construction allows us to rapidly compute a multi‐scale family of Mexican hat wavelet functions, by approximating the derivative of the heat kernel. We demonstrate that this leads to a family of functions that inherit many attractive properties of the heat kernel (e.g. local support, ability to recover isometries from a single point, efficient computation). Due to its natural ability to encode high‐frequency details on a shape, the proposed method reconstructs and transfers ‐functions more accurately than the Laplace‐Beltrami eigenfunction basis and other related bases. Finally, we apply our method to the challenging problems of partial and large‐scale shape matching. An extensive comparison to the state‐of‐the‐art shows that it is comparable in performance, while both simpler and much faster than competing approaches.     

Robust detection of moving objects in video sequences through rough set theory framework

Detection of moving objects in the presence of challenging background situations like swaying vegetation, rippling water, camera jitter etc., is known to be a difficult task. Background subtraction is considered to be better than the other approaches in terms of robustness. Its success primarily depends on the proper choice of background model(s) associated with every pixel for its foreground/background labeling. In this work, we have adopted rough-set theoretic measures to embed the spatial similarity around a neighborhood as a model for the pixel. Basic histon and its associated measure Basic Histon Roughness Index (BHRI) have been reported in the literature. It was applied to still image segmentation with impressive performance. Its adoption in video sequences for foreground/background labeling is proposed herein. We extended the histon concept to a 3D histon, which considers the intensities across the color planes in a combined manner, instead of considering independent color planes. Further, we also incorporated fuzziness into the 3D HRI measure. The labeling decision is based on Bhattacharyya distance between the model HRI and the corresponding measure in the current frame. Adoption of rough set theoretic concept into moving object segmentation is nontrivial, as the model updating requires careful consideration so that the pixels associated with gradually changing background or dynamic background are labeled as background and at the same time, slow moving objects are never adopted into the background model. A novel background model update strategy proposed herein takes these into consideration and also eliminates the need of having exclusive ideal background frame initially.     

Boolean set operations on non-manifold boundary representation objects

For Boolean operations on geometric models, we have developed an intersection algorithm for non-manifold boundary models with vertices, linear edges, planar faces, and volumetric regions. The algorithm operates by intersecting entities in an ordered manner, from vertex to edge, then to face elements. Singular intersections are systematically handled by determining if an entity in one object is within a tolerance region of the entity in the other object. The algorithm performs Boolean operations between objects of different dimensionality as well as solids. An implementation of the proposed algorithm and the experimental results are briefly discussed.     

利用代数样条磨光凸多面体的集合运算

提出了一种方法来磨光凸多面体之间的交、并、差等运算。提出的方法是以空间剖分和代数样条为基础的。提出了一些例子来演示磨光的效果。与已有的方法相比,提出的方法直观、易行,能得到低次的磨光曲面,且有自由参数控制磨光的范围。     

3D sketching for aesthetic design using fully free-form deformation features

This paper addresses the designers’ activity and in particular the way designers express an object shape in 2D sketches through character lines and how these lines form a basis for sketching shapes in 3D. The tools currently available in commercial CAS/CAD systems to manipulate the digital models are still not sufficiently suited to support design. In this paper, the so-called fully free-form deformation features (δ-F⁴) are introduced as a modelling method to take into account the curve-oriented stylists’ way of working. Both the advantages of a free-form surface deformation method and a feature-based approach are merged to define these high-level modelling entities allowing for a direct manipulation of surfaces through a limited number of intuitive parameters. Such features incorporate several characteristics designed to handle the uncertainties and/or inconsistencies of the designer's input during a sketching activity. In addition, a δ-F⁴ classification is proposed to enable a fast access to the desired shape according to its semantics and characteristics.     

RASP—A language with operations on fuzzy set

At the Center for Multidisciplinary Studies, University of Belgrade, Yugoslavia, a high level language for easily manipulating fuzzy set operations was developed. In this paper, after a brief introduction to the theory of fuzzy sets, some features and possibilities are described from the user point of view, and an application in picture enhancement is shown. The language presented was written in BASIC, thus any microcomputer, for personal/home use, should be able to execute RASP.     

粗糙集概念与运算的知识粒度表示

探讨了知识粒度的一些重要性质和定理。在此基础上,从知识粒度的角度对粗糙集进行研究,给出了粗糙集中主要概念与运算的知识粒度表示,最后证明了属性约简在知识粒度与代数两种不同表示下是等价的。     

Entropy of capacities on lattices and set systems

We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where the family of subsets is not necessarily the Boolean lattice of all subsets. Our definition encompasses the classical definition of Shannon for probability measures, as well as the entropy of Marichal defined for classical capacities. Some properties and examples are given.     

Random set framework for multiple instance learning

Multiple instance learning (MIL) is a technique used for learning a target concept in the presence of noise or in a condition of uncertainty. While standard learning techniques present the learner with individual samples, MIL alternatively presents the learner with sets of samples. Although sets are the primary elements used for analysis in MIL, research in this area has focused on using standard analysis techniques. In the following, a random set framework for multiple instance learning (RSF-MIL) is proposed that can directly perform analysis on sets. The proposed method uses random sets and fuzzy measures to model the MIL problem, thus providing a more natural mathematical framework, a more general MIL solution, and a more versatile learning tool. Comparative experimental results using RSF-MIL are presented for benchmark data sets. RSF-MIL is further compared to the state-of-the-art in landmine detection using ground penetrating radar data.     

基于深度八叉树的三维数据场LOD可视化

提出了广度八叉树、深度八叉树概念,分析了它们逻辑结构和存储结构,探讨了这两种数据结构在三维数据场可视化中的应用,把深度八叉树应用于三维数据场LOD体绘制算法中。算法在某三维震波数据场进行了体绘制实验,并与传统方法进行了比较分析。结果表明,该方法通过逐层简化细节来减少场景的复杂性,提高了渲染效率,将全局和局部体绘制相结合,既提高了绘制速度,又实现了精细观察。     

FARM: Functional Automatic Registration Method for 3D Human Bodies

We introduce a new method for non-rigid registration of 3D human shapes. Our proposed pipeline builds upon a given parametric model of the human, and makes use of the functional map representation for encoding and inferring shape maps throughout the registration process. This combination endows our method with robustness to a large variety of nuisances observed in practical settings, including non-isometric transformations, downsampling, topological noise and occlusions; further, the pipeline can be applied invariably across different shape representations (e.g. meshes and point clouds), and in the presence of (even dramatic) missing parts such as those arising in real-world depth sensing applications. We showcase our method on a selection of challenging tasks, demonstrating results in line with, or even surpassing, state-of-the-art methods in the respective areas.     

New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications

The aim of this paper is to develop some new logarithm operational laws (LOL) with real number base for the Pythagorean fuzzy sets. Some properties of LOL have been studied and based on these, various weighted averaging and geometric operators have been developed. Then, we utilized it to solve the decision-making problems. The validity of the proposed method is demonstrated with a numerical example and compared the results with the several existing approaches result. Finally, the influences of logarithmic operation and the selection of the logarithmic base in practice are discussed.     

在点模型上实现三维纹理合成的算法

为了避免网格重建过程而直接在三维点采样表面上进行纹理合成,研究了在点模型上的三维纹理合成的算法。利用KDtree这种数据结构在离散采样点上构建点与点的邻域关系,通过投影和建立匹配窗得到每一个待合成纹理的点与样图的映射关系,根据映射关系在样图中找出与待定点纹理值最佳匹配的点。最后将该匹配点的纹理值赋给待定点,同时结合邻域关系实现多点同时赋值。实验结果表明,该算法能有效地保持了生成的纹理结构和视觉效果的连续性和平滑性,具有耗时短、灵活可控、较好的鲁棒性等特点。     

水平集活动轮廓模型的3维牙齿重建

目的 建立患者口腔每颗牙齿独立的3维模型对于计算机口腔修复的精确定位和量化评估具有十分重要的意义。针对口腔CT图像序列的牙齿形态变化和排列特点,提出一种新颖的基于水平集活动轮廓模型的3维牙齿重建方法。方法 基于层间映射机制,对不同部位牙层切片采用不同的分割模型：利用先验形状约束能量、基于Flux模型的边缘梯度能量、基于先验灰度的局部区域能量相结合构造的单相混合水平集模型分割牙根层切片轮廓;利用结合区域竞争约束的双相混合水平集模型分割牙冠层切片轮廓;最后利用这些层间轮廓重建出牙齿3维模型。结果 对不同位置的牙齿CT图像进行分割实验,结果表明,与现有的方法相比,本文方法具有较好的分割效果和较高的准确率,平均分割相似系数达到96%。结论 本文的混合水平集模型能有效克服牙髓腔和牙槽骨的干扰以及图像灰度不均匀等问题,较准确地重建出每颗牙齿独立的3维模型,从而为制定口腔修复规划、生物力学分析等奠定坚实的基础。     

Introducing blending operations in feature models

We describe the implementation of a blending facility in the context of a feature modelling system where solid and feature-based modelling operations can be utilized in parallel during the design process of a part. The definition of blends can be done in a graphical user interface by selecting edges to be blended. Feature recognition of blends facilitates the definition process of blends. Alternatively, a special feature editor can be used to add blends to the feature model. The particular implementation style chosen gives rise to aflexible and easy-to-use modelling tool.     

New construction of perfect sequence set and low correlation zone sequence set

For a given binary ideal autocorrelation sequence, we construct a perfect sequence set by changing a few bits of the sequence. The set has a large size with respect to the period of its sequences. Based on the constructed perfect sequence set, a new class of low correlation zone sequence sets whose low correlation zone length can be chosen flexibly is obtained. Moreover, the new constructed low correlation zone sequence sets can attain Tang-Fan-Matsufuji＇s bound with suitably chosen parameters.     

结合模糊集理论的粗糙集属性约简算法*

结合模糊关系的理论,对粗糙集理论的属性约简算法进行研究,提出了一个新的属性约简算法,并给出了一个应用实例.