基于解析张量投票的散乱点云特征提取

针对传统张量投票算法在散乱点云特征提取过程中计算复杂、算法效率低等问题,提出了基于解析张量投票的散乱点云特征提取。首先,深入分析张量投票理论的基本思想,分析传统张量投票算法的不足及其根源。其次,设计了一种新的解析棒张量投票机制,实现了解析棒张量投票的直接求取,在此基础上,利用解析棒张量投票不依赖参考坐标系的特性,设计并求解了解析板张量投票和解析球张量投票表达式,而传统张量投票理论仅能通过迭代数值进行估算,过程复杂、效率低、精度与效率存在矛盾。然后,对解析张量投票后的散乱点云张量矩阵进行特征分解,根据特征显著性值实现特征提取。最后,通过仿真分析和对比实验验证了该算法在精度和计算效率方面的性能均优于传统张量投票算法,能够实现散乱点云的鲁棒特征提取。     

利用张量投票的机载LiDAR点云道路骨架线提取

针对机载LiDAR数据中道路骨架线检测存在的噪声干扰问题,结合道路多层特征显著性,提出了一种基于道路最大宽度快速确定最小尺度因子的张量投票道路骨架线提取方法。将预处理后三维道路点云转化成二维强度图像,最小尺度因子参与图像球张量投票,利用极性特征分割道路边缘点;为了进一步增强道路线状特征,利用新的最小尺度因子再次进行球张量投票和棒张量投票,填补道路空洞,顺滑道路边界;细化处理获取道路骨架线。与数学形态学方法相比,该方法在噪声背景的道路数据中提取的道路线精度更高。     

应用分形维数的自适应张量投票算法

张量投票算法是感知聚类方法中一种比较常用的计算方法,可以应用到图像处理等各个方面,具有较强的鲁棒性,非迭代等特性。张量投票算法中尺度参数的自适应选取对于投票域的建立起着至关重要的作用。通过分形维数来选取尺度参数,建立了尺度参数与分形维数的关系,提出了基于分形维数的自适应张量投票算法,并将该方法应用于图像的线特征提取和边缘修复。与传统的张量投票算法进行比较,该方法在图像线特征提取和边缘修复方面获得了较好的实验结果。     

基于张量投票的摄像机自标定方法研究

针对传统的基于Kruppa方程摄像机自标定算法的欠鲁棒性,首次提出将鲁棒的张量投票算法用于摄像机自标定方法中。利用基于尺度不变的SIFT算法查找并匹配出每对图像的特征点,其中待匹配图像由摄像机对同一场景从三个不同角度位置拍摄,对图像张量投票后按棒张量特征值降序排序,由此筛选得到具有鲁棒性边缘特征的前八对特征点,利用八点算法求解相应的基础矩阵和极点,根据Kruppa方程和三维重建（SFM）算法求得摄像机参数矩阵。实验结果证明,该方法具有较高标定精度,并通过加入高斯噪声的仿真实验证明该算法是一种鲁棒的摄像机自标定方法。     

基于用户近邻的N维张量分解推荐算法

基于张量分解的推荐算法存在推荐精度较低和数据稀疏的问题。为此,在传统的张量分解模型基础上,引入用户近邻信息,提出一种新的N维张量分解算法。利用上下文感知信息,把隐式反馈信息作为张量的第3维度,以建立N维张量分解模型,为进一步提高推荐质量,加入用户近邻信息来优化N维张量分解模型,以提高张量分解推荐算法的准确率。实验结果表明,融合用户近邻的张量分解推荐算法比传统的张量分解算法具有更好的准确性,能有效解决稀疏性和准确性问题。     

广义逆张量Padé逼近的连分式递推算法

张量指数函数已经广泛应用于控制论、图像处理和各个工程领域.鉴于此,在矩阵广义逆的基础上,首次在张量内积空间上定义一种有效的张量广义逆,从而构造张量Padé逼近的一种连分式算法.利用张量t-积成功计算张量的幂,由此递推地给出张量指数函数的幂级数展开式.在前面两个工作的基础上,利用设计的连分式算法逼近张量指数函数,其特点在于,该算法可以编程实现递推计算,而且在计算过程中不必计算张量的乘积,也不必计算张量的逆.给出的两个张量指数函数的数值实验表明,将连分式算法与目前通常使用的截断法进行比较,在不降低逼近阶的条件下,所提出算法是有效的.如果张量的维数较大,基于张量广义逆的连分式算法仍然具有一定优势.     

张量补全算法及其在人脸识别中的应用

数据丢失问题通常可以归结为矩阵补全问题,而矩阵补全是继压缩感知理论之后的又一种重要的信号获取方法。在实际应用中,数据样例往往具有多线性性,即数据集可以表示成高阶张量。本文研究了张量补全问题及其在人脸识别中的应用。基于张量的低维Tucker分解,提出张量补全的迭代算法,并且证明在算法的迭代过程中,估计张量与其Tucker逼近张量的距离是单调递减的。实验结果表明张量补全算法在补全张量和人脸识别上的可行性与有效性。     

各向异性扩散滤波的三维散乱点云平滑去噪算法

针对传统点云去噪算法在去除噪声时易造成模型特征失真的问题,提出一种各向异性扩散滤波的三维散乱点云平滑去噪算法.首先采用张量投票算法计算采样点的张量矩阵,并求解其特征值和特征向量;然后根据采样点的几何特征设计扩散张量的特征值,保证在不同特征方向的扩散速率能自适应调整;最后将重构的扩散张量与三维各向异性扩散滤波方程相结合,构造了点云滤波模型用于点云去噪.对不同含噪点云模型进行去噪的实验结果表明,该算法在点云去除噪声的同时,可以有效地保持原始模型的特征信息,避免了模型的过光顺.     

边界特征保持的网格模型分级二次误差简化算法

在参考张量投票理论的基础上,结合二次误差简化算法,提出一种边界特征保持的几何网格模型分级二次误差简化算法.首先根据张量投票理论对三角网格顶点进行面点、边点、角点类型分类;然后对各边对按照二次误差简化算法进行边折叠代价计算;再将分类顶点按照设定的等级权重加入边对折叠代价中,从而保证渐进式简化过程中能够对顶点进行分级简化.实验结果表明,该算法不但能实现渐进简化,而且能按需保留模型的整体特征和细节特征.     

基于耦合随机投影的张量填充方法

现代信号处理中,越来越多的领域都需要存储和分析规模大、维度高、结构复杂的数据.张量作为向量和矩阵的高阶推广,在保证原始数据内在关系的前提下,可以更为直观地表示大规模数据的结构性.张量填充作为张量分析的一个重要分支,目前已被广泛应用于协同过滤、图像恢复、数据挖掘等领域.张量填充指从被噪声污染或存在数据缺失的张量中恢复出原始张量的手段,文中着眼于当前张量填充技术中时间复杂度较高的缺点,提出了基于耦合随机投影的张量填充方法.该方法的核心包括两个部分:耦合张量分解以及随机投影矩阵.通过随机投影矩阵,文中将原始高维张量投影到低维空间内生成替代张量,同时在低维空间内实现张量填充,进而提高算法的执行效率.同时,所提算法还利用耦合张量分解将填充后的低维张量映射到高维空间,从而实现原始张量的重构.最后,通过实验分析了所提算法的有效性和高效性.     

On improving the efficiency of tensor voting

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.     

一种基于投票机制的代表点选择算法

代表点选择是面向数据挖掘与模式识别的数据预处理的重要内容之一，是提高分类器分类正确率和执行效率的重要途径。提出了一种基于投票机制的代表点选择算法，该算法能使所得到的代表点尽可能分布在类别边界上，且投票选择机制易于排除异常点，减少数据量，从而有利于提高最近邻分类器的分类精度和效率。通过与多个经典的代表点选择算法的实验比较分析，表明所提出的基于投票机制的代表点选择算法在提高最近邻分类器分类精度和数据降低率上都具有一定的优势。     

Inference of segmented color and texture description by tensor voting

A robust synthesis method is proposed to automatically infer missing color and texture information from a damaged 2D image by (N)D tensor voting (N > 3). The same approach is generalized to range and 3D data in the presence of occlusion, missing data and noise. Our method translates texture information into an adaptive (N)D tensor, followed by a voting process that infers noniteratively the optimal color values in the (N)D texture space. A two-step method is proposed. First, we perform segmentation based on insufficient geometry, color, and texture information in the input, and extrapolate partitioning boundaries by either 2D or 3D tensor voting to generate a complete segmentation for the input. Missing colors are synthesized using (N)D tensor voting in each segment. Different feature scales in the input are automatically adapted by our tensor scale analysis. Results on a variety of difficult inputs demonstrate the effectiveness of our tensor voting approach.     

Development of the Kansa method for solving seepage problems using a new algorithm for the shape parameter optimization

In this research, the Kansa or Multiquadric method (MQ) has been developed for solving the seepage problems in 2D and 3D arbitrary domains. This research is the first application of this method for seepage analysis in both confined and unconfined porous media. The domain decomposition approach has been employed for applying MQ method easily in inhomogeneous and irregular complex geometries and decreasing the computational costs. For determining the optimum shape parameter that affects strongly the accuracy of MQ and other RFB methods, a new scheme that decreases drastically the computational time is introduced. The efficiency of the proposed algorithm has been examined under various radial basis functions, variations of number of interpolating points and points distribution, through a numerical example with analytical solution. Eventually, three examples including different boundary conditions are presented. Comparing results of the examples with other numerical methods indicates that the present approach has high capability and accuracy in solving seepage problems.     

Tensor voting for image correction by global and local intensity alignment

This work presents a voting method to perform image correction by global and local intensity alignment. The key to our modeless approach is the estimation of global and local replacement functions by reducing the complex estimation problem to the robust 2D tensor voting in the corresponding voting spaces. No complicated model for replacement function (curve) is assumed. Subject to the monotonic constraint only, we vote for an optimal replacement function by propagating the curve smoothness constraint using a dense tensor field. Our method effectively infers missing curve segments and rejects image outliers. Applications using our tensor voting approach are proposed and described. The first application consists of image mosaicking of static scenes, where the voted replacement functions are used in our iterative registration algorithm for computing the best warping matrix. In the presence of occlusion, our replacement function can be employed to construct a visually acceptable mosaic by detecting occlusion which has large and piecewise constant color. Furthermore, by the simultaneous consideration of color matches and spatial constraints in the voting space, we perform image intensity compensation and high contrast image correction using our voting framework, when only two defective input images are given.     

A closed-form solution to tensor voting: theory and applications

We prove a closed-form solution to tensor voting (CFTV): Given a point set in any dimensions, our closed-form solution provides an exact, continuous, and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway.     

On the accuracy and efficiency of a finite element tensor product algorithm for fluid dynamics applications

A finite element numerical solution algorithm is derived for application to problems in computational fluid dynamics. Through extension of the basic error extremization constraints offered using the method of weighted residuals, a selective dissipation mechanism is introduced to control phase error and/or non-linearly induced error. Using an implicit integration algorithm, the Jacobian of a Newton iteration procedure is replaced by a tensor matrix product construction for solution economy. Numerical results for multi-dimensional equations, modeling the substantial time derivative within the Navier-Stokes system, are utilized to assess solution accuracy, stability and error control.     

Compact grid-characteristic schemes of higher orders of accuracy for a 3D linear transport equation

A numerical solution of a 3D linear transport equation on parallelepipedic computational grids is considered. By the technique of splitting in coordinates, compact grid-characteristic schemes of higher orders of accuracy are generalized to the 3D case. The influence of particular steps of the computational algorithm on the accuracy of the resulting scheme is investigated. The approach for retaining the order of convergence of a scheme on a smooth solution and minimizing nonphysical oscillations on a discontinuous solution in the 3D case is proposed.