多参数加权的无缝纹理映射算法

目的 针对基于图像3维重建中纹理映射存在缝隙的问题,提出一种多参数加权的无缝纹理映射算法。方法 算法根据图像的标定信息对三角格网进行聚类分割,将重建模型聚类成不同参考图像的网格贴片,并对贴片排序生成纹理图像,加权融合重建顶点的法线角度、图像视点、模型深度等信息生成纹理贴片像素,最后采用多分辨率分解融合技术消除纹理贴片缝隙,实现无缝的纹理映射。结果 对不同的测试数据进行了验证,本文算法在保持一定清晰度的前提下消除了纹理的缝隙,即使对于构网误差较大的区域也能得到较为满意的结果,同时本文算法支持大数据的3维纹理映射。结论 提出了一种无缝的纹理映射算法,算法通过构造一个平滑的加权方程融合多源信息消除纹理的接缝,实验结果表明了本文算法的有效性及实用性,得到了高保真的无缝纹理映射效果,可应用到城市级别的大场景3维重建领域。     

体参数化模型离散调和映射生成

目的 体参数化模型具有诸多优良特性和广泛的应用前景,如何生成有效的体参数化模型是迫切需要解决的问题.方法 首先定义了样条体参数化模型表达式,提出控制点设定是体参数化的核心问题.给定6个表面样条曲面的控制点,从计算域到参数域的调和映射方程的差分形式出发,给出了生成体参数化模型控制点的方法.提出雅克比矩阵和等参网两种方法用以检测体参数化模型的网格质量.结果 基于点云模型,构建了体参数化模型,且将该方法与离散孔斯插值法、凸组合插值法两种方法生成的体参数化模型网格质量进行了对比.结果表明,离散调和函数法生成的体参数化模型相对更为稳定与优化.结论 离散调和映射能初步生成体参数化模型,但需要进一步优化并提供了良好初始化条件.     

从表面重构的体数据实现3维网格剖分

目的 针对有限元分析中网格最优化问题,提出一种改进的生成四面体网格的自组织算法。方法 该算法首先应用几何方法将三角形表面模型重新构造成规定大小的分类体数据,同时由该表面模型建立平衡八叉树,计算用以控制网格尺寸的3维数组;然后将体数据转换成邻域内不同等值面的形态一致的边界指示数组;结合改进的自组织算法和相关3维数据的插值函数,达到生成四面体网格的目的。结果 实验结果对比表明,该方法能够生成更高比例的优质四面体,增强了对扁平面体的抑制能力,同时很好地保证了边界的一致。结论 在对封闭的3维表面网格进行有限元建模时,本文算法为其提供了一种有效、可靠的途径。     

基于Arnold映射的分块双层自适应扩散图像加密算法

目的 针对图像安全保障问题,提出一种基于Arnold映射的分块双层自适应扩散数字图像加密(BDAM)算法,提高图像加密效率及安全性.方法 首先利用Logistic映射、Tent映射和Sine映射,进行两两组合构建3种新1维混沌映射,提取初始混沌序列;然后定义一个与明文图像矩阵大小相同的初始加密图像矩阵,对其进行分块,预处理Arnold映射参数,正反向联合映射将明文图像矩阵中随机位置像素值,存入初始加密矩阵随机块中的随机位置,并同时进行块内像素、块间自适应扩散,直至填满初始加密矩阵,完成加密.结果 针对多种类型灰度图像,通过仿真实验与性能对比分析表明: BDAM算法在信息熵、密钥空间、相关性、敏感性等方面均优于其他加密算法,置乱效果好,对密钥及明文的敏感性高,可取得较好加密效果.结论 结合随机置乱的分块双层非线性自适应扩散BDAM算法可有效抵御多种攻击,安全性较高,适用于各种类型灰度图像加密,具有潜在应用价值.     

视景建模中树木纹理图像的随机变形网格方法

目的 视景建模中,采用“公告板”贴图法对同树种不同个体树建模时,需生成各种形态各异的树木纹理图像,为此提出一种新的生成树木纹理图像的随机变形网格方法。方法 首先将树木的原始纹理图像进行网格划分,再对网格顶点进行随机变形,最后将生成的不规则网格中的图像映射到新图像中相应的规则网格上,得到变形后的纹理图像。结果 应用随机参数控制树木图像的变形,模拟出成长环境因素对树木形态的影响。本文方法比采集多幅个体树图像贴图方法更简便,容易实现;比用同一幅图像进行多个个体贴图的视觉效果更真实。结论 本文方法生成的树木纹理图像应用于“公告板”贴图时,在视景模型中能较好地模拟出同一树种的多个个体树情景。该方法基于图像的局部变形,仍然保持原始图像内容的整体基本形态和内部结构的连续性,因此,同样适用于其他不规则形状的自然景物(如山峦、河流、海浪等)的图像处理。     

可变形网格引导的群体队形仿真

目的 许多群体运动仿真算法侧重于模拟由大量自由移动个体所组成的群体行为,而针对具有特定队形的群体运动仿真算法较少。为解决这一问题,采用改进的网格引导方法,利用可变形网格对群体运动进行控制。方法 首先,对群体队形进行三角划分,建立一个连接所有智能体的队形网格。然后,利用障碍势场法在群体运动的过程中对队形网格进行变形,使智能体在避免与障碍物发生穿透的同时尽可能保持整体队形稳定。最后,针对障碍物穿过队形网格时可能造成的局部智能体 “错位现象”,提出了基于吸引点的网格引导方法,使群体绕过障碍物后能迅速恢复原来队形。结果 使用Unity软件对军队行进、动态车流、群体表演等场景中的智能体编队移动进行仿真,并设置了不同规模的群组交换实验进行对比。本文算法的实时计算花销主要集中在网格变形阶段：在队形网格顶点总数为1 000时,单位仿真步内网格变形阶段的平均运行时间为20.15 ms。队形网格划分阶段是一个预先进行的过程,不影响算法实时性。基于吸引点的网格引导方法提高了智能体的全局移动效率,使队形变化更加自然流畅。结论 实验结果表明,可变形网格引导的群体队形仿真算法在群体运动过程中能有效维持队形稳定,无论障碍环境是静态的还是动态的都能实现良好的群体避障,说明算法的有效性。     

具有直线结构保护的网格化图像拼接

目的 基于网格变形的图像配准方式,针对待拼接图片重叠区域的视差具有一定的容忍性,并且能够适应更复杂的图像拼接场景。在NISwGSP （natural image stitching with the global similarity prior）算法基础上提出了一种具有直线结构保护的图像拼接算法（MISwLP）,该算法通过提取图片中的直线结构并施加约束,可以得到视觉效果自然、畸变较小的图像拼接结果。方法 首先对图片进行网格划分,建立网格优化模型,针对网格顶点坐标集定义能量函数,在保证图片重叠区域高度对齐的同时,对网格进行相似性连续约束,并辅以直线结构约束,最后使用共轭梯度最小二乘法求解得到最优网格顶点集,指导网格变形。结果 针对不同场景下的图片进行拼接实验,同时和几种比较流行的图像拼接软件和算法进行比较。结果表明,同经典拼接算法,比如Autostitch相比,基于网格优化的图像拼接算法能够适应更加复杂的多平面场景,在减小投影失真和对齐误差方面表现更好;同现在比较好的几种网格拼接算法,比如SPHP （shape-preserving half-projective warps for image stitching）、APAP （as-projective-as-possible image stitching with moving DLT）、NISwGSP等的比较,MISwLP算法不仅能够很好地对齐图像和避免投影失真,并且能够保持图像重叠区域到非重叠区域的一致性,即保护原图中的直线结构。结论 提出了一种基于网格优化的直线约束方法,对于具有显著几何结构的图像拼接场景,能够较好地保护拼接后图像中原有的直线结构,具有较好的应用价值。     

整合ChaCha20哈希运算的分块扩散自适应图像加密算法

目的 针对数字图像网络传输安全性和混沌加密算法自适应差的问题,提出一种基于ChaCha20哈希运算的分块扩散自适应图像加密算法(BDCH)。方法 BDCH算法首先通过分段线性混沌映射(PWLCM)产生的混沌序列填充明文图像,使其成为方形图像;其次,利用初始输入密钥及明文图像总和,通过ChaCha20哈希运算生成8×8的初始哈希矩阵,并与PWLCM混沌映射生成的伪随机序列作用,联合产生哈希密钥矩阵,PWLCM的迭代初值选取为初始密钥矩阵均值、初始密钥及明文图像归一化均值;然后,利用Arnold和PWLCM映射同步置乱扩散整幅图像,并分成互不重叠的8×8大小图像块;最后,采用哈希密钥矩阵对图像块进行两轮扩散,完成图像加密。结果 灰度及彩色图像的计算机仿真与性能分析表明,BDCH算法的信息熵、峰值性噪比、密钥敏感性指标优于其他加密算法,并且解决了直接使用初始哈希矩阵会产生的弱密钥问题,密钥空间大。结论 结合同步置乱扩散和哈希密钥矩阵非线性分块扩散的BDCH算法可有效抵抗各种攻击,安全性高、自适应性强,适合各种类型的灰度及彩色图像加密,潜在应用价值大。     

带法向约束的隐式T样条曲线重构

目的 隐式曲线能够描述复杂的几何形状和拓扑结构,而传统的隐式B样条曲线的控制网格需要大量多余的控制点满足拓扑约束。有些情况下,获取的数据点不仅包含坐标信息,还包含相应的法向约束条件。针对这个问题,提出了一种带法向约束的隐式T样条曲线重建算法。方法 结合曲率自适应地调整采样点的疏密,利用二叉树及其细分过程从散乱数据点集构造2维T网格;基于隐式T样条函数提出了一种有效的曲线拟合模型。通过加入偏移数据点和光滑项消除额外零水平集,同时加入法向项减小曲线的法向误差,并依据最优化原理将问题转化为线性方程组求解得到控制系数,从而实现隐式曲线的重构。在误差较大的区域进行T网格局部细分,提高重建隐式曲线的精度。结果 实验在3个数据集上与两种方法进行比较,实验结果表明,本文算法的法向误差显著减小,法向平均误差由10^-3数量级缩小为10^-4数量级,法向最大误差由10^-2数量级缩小为10^-3数量级。在重构曲线质量上,消除了额外零水平集。与隐式B样条控制网格相比,3个数据集的T网格的控制点数量只有B样条网格的55.88%、39.80%和47.06%。结论 本文算法能在保证数据点精度的前提下,有效降低法向误差,消除了额外的零水平集。与隐式B样条曲线相比,本文方法减少了控制系数的数量,提高了运算速度。     

边界简化与多目标优化相结合的高质量四边形网格生成

目的 高质量四边形网格生成是计算机辅助设计、等几何分析与图形学领域中一个富有挑战性的重要问题。针对这一问题,提出一种基于边界简化与多目标优化的高质量四边形网格生成新框架。方法 首先针对亏格非零的平面区域,提出一种将多连通区域转化为单连通区域的方法,可生成高质量的插入边界;其次,提出"可简化角度"和"可简化面积比率"两个阈值概念,从顶点夹角和顶点三角形面积入手,将给定的多边形边界简化为粗糙多边形;然后对边界简化得到的粗糙多边形进行子域分解,并确定每个子域内的网格顶点连接信息;最后提出四边形网格的均匀性和正交性度量目标函数,并通过多目标非线性优化技术确定网格内部顶点的几何位置。结果 在同样的离散边界下,本文方法与现有方法所生成的四边网格相比,所生成的四边网格顶点和单元总数目较少,网格单元质量基本类似,计算时间成本大致相同,但奇异点数目可减少70% 80%,衡量网格单元质量的比例雅克比值等相关指标均有所提高。结论 本文所提出的四边形网格生成方法能够有效减少网格中的奇异点数目,并可生成具有良好光滑性、均匀性和正交性的高质量四边形网格,非常适用于工程分析和动画仿真。     

Texture mapping with hard constraints using warping scheme

Texture mapping with positional constraints is an important and challenging problem in computer graphics. In this paper, we first present a theoretically robust, foldover-free 2D mesh warping algorithm. Then we apply this warping algorithm to handle mapping texture onto 3D meshes with hard constraints. The proposed algorithm is experimentally evaluated and compared with the state-of-the-art method for examples with more challenging constraints. These challenging constraints may lead to large distortions and foldovers. Experimental results show that the proposed scheme can generate more pleasing results and add fewer Steiner vertices on the 3D mesh embedding.     

An RBF-based reparameterization method for constrained texture mapping

Texture mapping has long been used in computer graphics to enhance the realism of virtual scenes. However, to match the 3D model feature points with the corresponding pixels in a texture image, surface parameterization must satisfy specific positional constraints. However, despite numerous research efforts, the construction of a mathematically robust, foldover-free parameterization that is subject to positional constraints continues to be a challenge. In the present paper, this foldover problem is addressed by developing radial basis function (RBF)-based reparameterization. Given initial 2D embedding of a 3D surface, the proposed method can reparameterize 2D embedding into a foldover-free 2D mesh, satisfying a set of user-specified constraint points. In addition, this approach is mesh free. Therefore, generating smooth texture mapping results is possible without extra smoothing optimization.     

Practical Foldover‐Free Volumetric Mapping Construction

In this paper, we present a practically robust method for computing foldover‐free volumetric mappings with hard linear constraints. Central to this approach is a projection algorithm that monotonically and efficiently decreases the distance from the mapping to the bounded conformal distortion mapping space. After projection, the conformal distortion of the updated mapping tends to be below the given bound, thereby significantly reducing foldovers. Since it is non‐trivial to define an optimal bound, we introduce a practical conformal distortion bound generation scheme to facilitate subsequent projections. By iteratively generating conformal distortion bounds and trying to project mappings into bounded conformal distortion spaces monotonically, our algorithm achieves high‐quality foldover‐free volumetric mappings with strong practical robustness and high efficiency. Compared with existing methods, our method computes mesh‐based and meshless volumetric mappings with no prescribed conformal distortion bounds. We demonstrate the efficacy and efficiency of our method through a variety of geometric processing tasks.     

Constrained Texture Mapping using Image Warping

We introduce in this paper a new method for smooth foldover-free warping of images. It allows users to specify the constraints in two different ways: positional constraints to constrain the position of points in the image and gradient constraints to constrain the orientation and scaling of some parts of the image. We then show how our method is used for texture mapping with hard constraints. We start with an unconstrained planar embedding of the target mesh calculated with conventional methods. In order to obtain a mapping that satisfies the user-defined constraints, we use our warping method to align the features of the texture image with those of the unconstrained embedding. Compared to previous work, our method generates a smoother texture mapping and offers higher level of control for defining the constraints.     

Rigidity Constraints for Large Mesh Deformation

It is a challenging problem of surface-based deformation to avoid apparent volumetric distortions around largely deformed areas. In this paper, we propose a new rigidity constraint for gradient domain mesh deformation to address this problem. Intuitively the proposed constraint can be regarded as several small cubes defined by the mesh vertices through mean value coordinates. The user interactively specifies the cubes in the regions which are prone to volumetric distortions, and the rigidity constraints ...     

Gradient field based inhomogeneous volumetric mesh deformation for maxillofacial surgery simulation

This paper presents a novel inhomogeneous volumetric mesh deformation approach by gradient field manipulation, and uses it for maxillofacial surgery simulation. The study is inspired by the state-of-the-art surface deformation techniques based on differential representations. Working in the volumetric domain instead of on only the surface can preserve the volumetric details much better, avoid local self-intersections, and achieve better deformation propagation because of the internal mesh connections. By integrating the mesh cell material stiffness parameter into our new discrete volumetric Laplacian operator, it is very convenient to incorporate inhomogeneous materials into the deformation framework. In addition, the system matrix for solving the volumetric harmonic field to handle the local transformation problem is the same used for Poisson reconstruction equation, thus it requires solving essentially only one global linear system. The system is easy to use, and can accept explicit rotational constraints, or only translational constraints to drive the deformation. One typical maxillofacial surgery case was simulated by the new methodology with inhomogeneous material estimated directly from CT data, and compared to the commonly used finite element method (FEM) approach. The results demonstrated that the deformation methodology achieved good accuracy, as well as interactive performance. Therefore, the usage of our volumetric mesh deformation approach is relevant and suitable for daily clinical practice.     

Position‐Based Simulation of Elastic Models on the GPU with Energy Aware Gauss‐Seidel Algorithm

In this paper, we provide a smooth extension of the energy aware Gauss‐Seidel iteration to the Position‐Based Dynamics (PBD) method. This extension is inspired by the kinetic and potential energy changes equalization and uses the foundations of the recent extended version of PBD algorithm (XPBD). The proposed method is not meant to conserve the total energy of the system and modifies each position constraint based on the equality of the kinetic and potential energy changes within the Gauss‐Seidel process of the XPBD algorithm. Our extension provides an implicit solution for relatively better stiffness during the simulation of elastic objects. We apply our solution directly within each Gauss‐Seidel iteration and it is independent of both simulation step‐size and integration methods. To demonstrate the benefits of our proposed extension with higher frame rates, we develop an efficient and practical mesh coloring algorithm for the XPBD method which provides parallel processing on a GPU. During the initialization phase, all mesh primitives are grouped according to their connectivity. Afterwards, all these groups are computed simultaneously on a GPU during the simulation phase. We demonstrate the benefits of our method with many spring potential and strain‐based continuous material constraints. Our proposed algorithm is easy to implement and seamlessly fits into the existing position‐based frameworks.     

Consistent Volumetric Discretizations Inside Self‐Intersecting Surfaces

Decades of research have culminated in a robust geometry processing pipeline for surfaces. Most steps in this pipeline, like deformation, smoothing, subdivision and decimation, may create self‐intersections. Volumetric processing of solid shapes then becomes difficult, because obtaining a correct volumetric discretization is impossible: existing tet‐meshing methods require watertight input. We propose an algorithm that produces a tetrahedral mesh that overlaps itself consistently with the self‐intersections in the input surface. This enables volumetric processing on self‐intersecting models. We leverage conformalized mean‐curvature flow, which removes self‐intersections, and define an intrinsically similar reverse flow, which prevents them. We tetrahedralize the resulting surface and map the mesh inside the original surface. We demonstrate the effectiveness of our method with applications to automatic skinning weight computation, physically based simulation and geodesic distance computation.     

Template-based 3D model fitting using dual-domain relaxation

We introduce a template fitting method for 3D surface meshes. A given template mesh is deformed to closely approximate the input 3D geometry. The connectivity of the deformed template model is automatically adjusted to facilitate the geometric fitting and to ascertain high quality of the mesh elements. The template fitting process utilizes a specially tailored Laplacian processing framework, where in the first, coarse fitting stage we approximate the input geometry with a linearized biharmonic surface (a variant of LS-mesh), and then the fine geometric detail is fitted further using iterative Laplacian editing with reliable correspondence constraints and a local surface flattening mechanism to avoid foldovers. The latter step is performed in the dual mesh domain, which is shown to encourage near-equilateral mesh elements and significantly reduces the occurrence of triangle foldovers, a well-known problem in mesh fitting. To experimentally evaluate our approach, we compare our method with relevant state-of-the-art techniques and confirm significant improvements of results. In addition, we demonstrate the usefulness of our approach to the application of consistent surface parameterization (also known as cross-parameterization).     

Topology preserved shape deformation

This paper presents a novel framework for image and shape deformation, and applies the presented method to 2D shape deformation and image/video magnifying. Our proposed framework maintains two distinct advantages. The first is to enforce the topology preservation constraints on a given displacement field. This allows us to develop a foldover-free constrained deformation approach. The second is the ability to easily incorporate the constraint of As-Rigid-As Possible deformation. It guarantees that the resulting distortions are as small as possible. Experiments are carried out on both 2D shape deformations and images/video magnifying.