Solutions and Ambiguities of the Structure and Motion Problem for 1D Retinal Vision

In this paper we investigate the geometry and algebra of multiple one-dimensional projections of a two-dimensional environment. This is relevant for one-dimensional cameras, e.g. as used in certain autonomous guided vehicles. It is also relevant for understanding the projection of lines in ordinary vision. A third application is on ordinary vision of vehicles undergoing so called planar motion. The structure and motion problem for such cameras is studied and the two possible minimal cases is solved. The technique of solving these questions reveal interesting ambiguities. It is shown that for each solution with three images there is an ambiguous solution. It is also shown that for each solution for four points there is an ambiguous solution. The connection between these two different types of ambiguities is also given. Although the paper deals with calibrated cameras, it is shown that similar results exist for uncalibrated cameras.     

Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA

We consider the problem of segmenting multiple rigid-body motions from point correspondences in multiple affine views. We cast this problem as a subspace clustering problem in which point trajectories associated with each motion live in a linear subspace of dimension two, three or four. Our algorithm involves projecting all point trajectories onto a 5-dimensional subspace using the SVD, the PowerFactorization method, or RANSAC, and fitting multiple linear subspaces representing different rigid-body motions to the points in ℝ⁵ using GPCA. Unlike previous work, our approach does not restrict the motion subspaces to be four-dimensional and independent. Instead, it deals gracefully with all the spectrum of possible affine motions: from two-dimensional and partially dependent to four-dimensional and fully independent. Our algorithm can handle the case of missing data, meaning that point tracks do not have to be visible in all images, by using the PowerFactorization method to project the data. In addition, our method can handle outlying trajectories by using RANSAC to perform the projection. We compare our approach to other methods on a database of 167 motion sequences with full motions, independent motions, degenerate motions, partially dependent motions, missing data, outliers, etc. On motion sequences with complete data our method achieves a misclassification error of less that 5% for two motions and 29% for three motions.     

Ambiguous Configurations for the 1D Structure and Motion Problem

In this paper we investigate, determine and classify the critical configurations for solving structure and motion problems for 1D retina vision. We give a complete categorization of all ambiguous configurations for a 1D (calibrated or uncalibrated) perspective camera irrespective of the number of points and views. It is well-known that the calibrated and uncalibrated case are linked through the circular points. This link enables us to solve for both cases simultaneously. Another important tool is the duality in exchanging points and cameras and its corresponding Cremona transformation. These concepts are generalized to the 1D case and used for the investigation of ambiguous configurations. Several examples and illustrations are also provided to explain the results and to provide geometrical insight.     

具有丢失数据的可分解马尔可夫网络结构学习

具有丢失数据的可分解马尔可夫网络结构学习是一个重要而困难的研究课题,数据的丢失使变量之间的依赖关系变得混乱,无法直接进行可靠的结构学习．文章结合最大似然树和Gibbs抽样,通过对随机初始化的丢失数据和最大似然树进行迭代修正一调整,得到修复后的完整数据集;在此基础上基于变量之间的基本依赖关系和依赖分析思想进行可分解马尔可夫网络结构学习,能够避免现有的丢失数据处理方法和可分解马尔可夫网络结构学习方法存在的效率和可靠性低等问题．试验结果显示,该方法能够有效地进行具有丢失数据的可分解马尔可夫网络结构学习．     

具有丢失数据的贝叶斯网络结构学习研究

目前主要基于EM算法和打分-搜索方法进行具有丢失数据的贝叶斯网络结构学习,算法效率较低,而且易于陷入局部最优结构.针对这些问题,建立了一种新的具有丢失数据的贝叶斯网络结构学习方法.首先随机初始化未观察到的数据,得到完整的数据集,并利用完整数据集建立最大似然树作为初始贝叶斯网络结构,然后进行迭代学习.在每一次迭代中,结合贝叶斯网络结构和Gibbs sampling修正未观察到的数据,在新的完整数据集的基础上,基于变量之间的基本依赖关系和依赖分析思想调整贝叶斯网络结构,直到结构趋于稳定.该方法既解决了标准Gi     

Anisotropic Curvature Motion for Structure Enhancing Smoothing of 3D MR Angiography Data

We propose a novel concept of shape prior for the processing of tubular structures in 3D images. It is based on the notion of an anisotropic area energy and the corresponding geometric gradient flow. The anisotropic area functional incorporates a locally adapted template as a shape prior for tubular vessel structures consisting of elongated, ellipsoidal shape models. The gradient flow for this functional leads to an anisotropic curvature motion model, where the evolution is driven locally in direction of the considered template. The problem is formulated in a level set framework, and a stable and robust method for the identification of the local prior is presented. The resulting algorithm is able to smooth the vessels, pushing solution toward elongated cylinders with round cross sections, while bridging gaps in the underlying raw data. The implementation includes a finite-element scheme for numerical accuracy and a narrow band strategy for computational efficiency. Oliver Nemitz received his Diploma in mathematics from the university of Duisburg, Germany in 2003. Then he started to work on his Ph.D. thesis in Duisburg. Since 2005 he is continuing the work on his Ph.D. project at the Institute for Numerical Simulation at Bonn University. His Ph.D. subject is fast algorithms for image manipulation in 3d, using PDE’s, variational methods, and level set methods. Martin Rumpf received his Ph.D. in mathematics from Bonn University in 1992. He held a postdoctoral research position at Freiburg University. Between 1996 and 2001, he was an associate professor at Bonn University and from 2001 until 2004 full professor at Duisburg University. Since 2004 he is now full professor for numerical mathematics and scientific computing at Bonn University. His research interests are in numerical methods for nonlinear partial differential equations, geometric evolution problems, calculus of variations, adaptive finite element methods, image and surface processing. Tolga Tasdizen received his B.S. degree in Electrical Engineering from Bogazici University, Istanbul in 1995. He received the M.S. and Ph.D. degrees in Engineering from Brown University in 1997 and 2001. From 2001 to 2004 he was a postdoctoral research associate with the Scientific Computing and Imaging Institute at the University of Utah. Since 2004 he has been with the School of Computing at the University of Utah as a research assistant professor. He also holds an adjunct assistant professor position with the Department of Neurology and the Center for Alzheimer’s Care, Imaging and Research, and a research scientist position with the Scientific Computing and Imaging Institute at the University of Utah. Ross Whitaker received his B.S. degree in Electrical Engineering and Computer Science from Princeton University in 1986, earning Summa Cum Laude. From 1986 to 1988 he worked for the Boston Consulting Group, entering the University of North Carolina at Chapel Hill in 1989. At UNC he received the Alumni Scholarship Award, and completed his Ph.D. in Computer Science in 1994. From 1994–1996 he worked at the European Computer-Industry Research Centre in Munich Germany as a research scientist in the User Interaction and Visualization Group. From 1996–2000 he was an Assistant Professor in the Department of Electrical Engineering at the University of Tennessee. He is now an Associate Professor at the University of Utah in the College of Computing and the Scientific Computing and Imaging Institute.     

仿生眼运动视觉与立体视觉3维感知

为使机器人同时具备双目立体视觉和单目运动视觉的仿人化环境感知能力,克服双目视场狭窄、单目深度感知精度低的缺陷,本文基于人眼结构特点,设计了一个具有4个旋转自由度的双目仿生眼平台,并分别基于视觉对准策略和手眼标定技术实现了该平台的初始定位和参数标定.给出了基于外部参数动态变化的双目立体感知方法和单目运动立体感知方法,前者通过两架摄像机实时获取的图像信息以及摄像机相对位姿信息进行3维感知,后者综合利用单个摄像机在多个相邻时刻获取的多个图像及其对应姿态进行3维感知.实验结果中的双目视觉相对感知精度为0.38%,单目运动视觉相对感知精度为0.82%.本文方法不但能够有效拓宽传统双目视觉的感知视野,而且能够保证双目感知和单目运动感知的准确性.     

融合运动信息的三维视觉显著性算法研究

计算机视觉领域中的视觉显著性研究大多局限于二维图像层面,而忽略人的视觉注意力决策是在三维动态场景下发生的。为此,在融合多种特征的显著性计算框架基础上,提出一种三维视觉显著性算法。通过场景的颜色信息、运动信息和深度信息分别计算各个特征通道下的显著性结果,再经过动态的融合得到最终的显著性结果。同时针对三维场景下显著性数据集的稀缺问题,给出一个用于评价三维动态场景下显著性算法的数据集。与HC算法、RC算法、GMR算法的对比结果验证了该算法具有明显的优势,并且更符合人眼的视觉注意力机制。     

Practical, Unified, Motion and Missing Data Treatment in Degraded Video

Recently, the problem of automated restoration of archived sequences has caught the attention of the Video Broadcast industry. One of the main problems is deadling with Blotches caused by film abrasion or dirt adhesion. This paper presents a new framework for the simultaneous treatment of missing data and motion in degraded video sequences. Using simple, translational models of motion, a joint solution for the detection, and reconstruction of missing data is proposed. The framework also incorporates the unique notion of dealing with occlusion and uncovering as it pertains to picture building. The idea is to use MCMC to solve the resulting problem articulated under a Bayesian framework, but to deploy purely deterministic mechanisms for dealing with the solution. This results in a relatively fast implementation that unifies many of the pixel-by-pixel schemes previously described in the literature.     

缺失数据数据集的组增量式特征选择

实际应用中获取到的数据集通常是动态增加的,且随着数据获取工具的迅速发展,新数据通常会一组一组地增加。为此,针对含有缺失数据的动态数据集,基于粗糙集理论,提出了一种组增量式的粗糙特征选择算法。首先分析、证明了信息熵的组增量计算公式,并以信息熵作为特征重要度的度量,在此基础上设计了基于信息熵的可有效处理含有缺失数据的动态数据集的组增量式特征选择算法。实验结果进一步证明了新算法的可行性和高效性。     

Multilinear Factorizations for Multi-Camera Rigid Structure from Motion Problems

Camera networks have gained increased importance in recent years. Existing approaches mostly use point correspondences between different camera views to calibrate such systems. However, it is often difficult or even impossible to establish such correspondences. But even without feature point correspondences between different camera views, if the cameras are temporally synchronized then the data from the cameras are strongly linked together by the motion correspondence: all the cameras observe the same motion. The present article therefore develops the necessary theory to use this motion correspondence for general rigid as well as planar rigid motions. Given multiple static affine cameras which observe a rigidly moving object and track feature points located on this object, what can be said about the resulting point trajectories? Are there any useful algebraic constraints hidden in the data? Is a 3D reconstruction of the scene possible even if there are no point correspondences between the different cameras? And if so, how many points are sufficient? Is there an algorithm which warrants finding the correct solution to this highly non-convex problem? This article addresses these questions and thereby introduces the concept of low-dimensional motion subspaces. The constraints provided by these motion subspaces enable an algorithm which ensures finding the correct solution to this non-convex reconstruction problem. The algorithm is based on multilinear analysis, matrix and tensor factorizations. Our new approach can handle extreme configurations, e.g. a camera in a camera network tracking only one single point. Results on synthetic as well as on real data sequences act as a proof of concept for the presented insights.     

An Analytically Stable Structure and Motion Observer Based on Monocular Vision

This paper presents a novel nonlinear sliding-mode differentiator-based complete-order observer for structure and motion identification with a calibrated monocular camera. In comparison with earlier work that requires prior knowledge of either the Euclidean geometry of the observed object or the linear acceleration of the camera and is restricted to establishing stability and convergence from image-plane measurements of a single tracked feature, the proposed scheme assumes partial velocity state feedback to asymptotically identify the true-scale Euclidean coordinates of numerous observed object features and the unknown motion parameters. The dynamics of the motion parameters are assumed to be described by a model with unknown parameters that incorporates a bounded uncertainty, and a Lyapunov analysis is provided to prove that the observer yields exponentially convergent estimates that converge to a uniform ultimate bound under a generic persistency of excitation condition. Numerical and experimental results are obtained that demonstrate the robust performance of the current scheme in the presence of model error and measurement noise.     

Distributed Filtering for Multi-sensor Systems with Missing Data

This paper studies distributed estimation problems for multi-sensor systems with missing data. Missing data may occur during sensor measuring or data exchanging among sensor nodes due to unreliability of communication links or external disturbances. Missing data include random missing measurements of sensor itself and random missing estimates of neighbor nodes. Three distributed Kalman filter (DKF) algorithms with the Kalman-like form are designed for each sensor node. When it is available whether a datum is missing or not at each time, an optimal DKF (ODKF) dependent on the knowledge of missing data is presented, where filter gains and covariance matrices require online computing. To reduce online computational cost, a suboptimal DKF (SDKF) is presented, where filter gains and covariance matrices dependent on missing probabilities can be computed offline. When it is unavailable whether a datum is missing or not, a probability-based DKF (PDKF) dependent on missing probabilities is presented. For each DKF algorithm, an optimal Kalman filter gain for measurements of sensor itself and different optimal consensus filter gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense, respectively. Mean boundedness of covariance matrix of the proposed ODKF is analyzed. Stability and steady-state properties of the proposed SDKF and PDKF are analyzed. Also, the performance of three DKF algorithms is compared. Simulation examples demonstrate effectiveness of the proposed algorithms.     

New Geometric Methods for Computer Vision: An Application to Structure and Motion Estimation

We discuss a coordinate-free approach to the geometry of computer vision problems. The technique we use to analyse the three-dimensional transformations involved will be that of geometric algebra: a framework based on the algebras of Clifford and Grassmann. This is not a system designed specifically for the task in hand, but rather a framework for all mathematical physics. Central to the power of this approach is the way in which the formalism deals with rotations; for example, if we have two arbitrary sets of vectors, known to be related via a 3D rotation, the rotation is easily recoverable if the vectors are given. Extracting the rotation by conventional means is not as straightforward. The calculus associated with geometric algebra is particularly powerful, enabling one, in a very natural way, to take derivatives with respect to any multivector (general element of the algebra). What this means in practice is that we can minimize with respect to rotors representing rotations, vectors representing translations, or any other relevant geometric quantity. This has important implications for many of the least-squares problems in computer vision where one attempts to find optimal rotations, translations etc., given observed vector quantities. We will illustrate this by analysing the problem of estimating motion from a pair of images, looking particularly at the more difficult case in which we have available only 2D information and no information on range. While this problem has already been much discussed in the literature, we believe the present formulation to be the only one in which least-squares estimates of the motion and structure are derived simultaneously using analytic derivatives.     

结合模糊聚类和投影近似点算法的缺失人体运动捕捉数据重构

针对人体运动捕捉数据缺失问题,提出一种结合模糊聚类和投影近似点算法的缺失数据重构恢复方法.首先对不完整运动序列矩阵的缺失数据位置进行线性插值预处理,粗略补全矩阵以得到较完整的运动序列;然后利用模糊C-均值算法将粗略恢复后的复杂人体运动数据细分为含有多个不同语义运动片段的时序组合;再根据相同运动语义片段数据矩阵存在低秩特性,对细分后相应的各原始运动子片段采取投影近似点算法进行缺失数据恢复,并按照运动片段的时序特性进行组合;最后将原有未缺失数据与其相应位置重构恢复后的数据进行置换,根据人体运动轨迹的局部线性特性进行线性平滑,以保证运动序列的连贯性,从而达到对整体运动捕捉数据重构恢复目的.实验结果表明,该方法能够有效地对缺失运动数据进行恢复,使得重构后的运动序列能够较好地逼近于真实运动轨迹,准确度较高.     

AdaBoost Models for Corporate Bankruptcy Prediction with Missing Data

Very little existing research in corporate bankruptcy prediction discusses modeling where there are missing values. This paper investigates AdaBoost models for corporate bankruptcy prediction with missing data. Three AdaBoost models integrated with different imputation methods are tested on two data sets with very different sample sizes. The experimental results show that the AdaBoost algorithm combined with imputation methods has strong predictive accuracy in both data sets and it is a useful alternative for bankruptcy prediction with missing data.     

An Iterative Multiresolution Scheme for SFM with Missing Data

Several techniques have been proposed for tackling the Structure from Motion problem through factorization in the case of missing data. However, when the percentage of unknown data is high, most of them may not perform as well as expected. Focussing on this problem, an iterative multiresolution scheme, which aims at recovering missing entries in the originally given input matrix, is proposed. Information recovered following a coarse-to-fine strategy is used for filling in the missing entries. The objective is to recover, as much as possible, missing data in the given matrix. Thus, when a factorization technique is applied to the partially or totally filled in matrix, instead of to the originally given input one, better results will be obtained. An evaluation study about the robustness to missing and noisy data is reported. Experimental results obtained with synthetic and real video sequences are presented to show the viability of the proposed approach.

Shape and Motion Reconstruction from 3D-to-1D Orthographically Projected Data via Object-Image Relations

This paper describes an invariant-based shape- and motion reconstruction algorithm for 3D-to-1D orthographically projected range data taken from unknown viewpoints. The algorithm exploits the object-image relation that arises in echo-based range data and represents a simplification and unification of previous work in the literature. Unlike one proposed approach, this method does not require uniqueness constraints, which makes its algorithmic form independent of the translation removal process (centroid removal, range alignment, etc.). The new algorithm, which simultaneously incorporates every projection and does not use an initialization in the optimization process, requires fewer calculations and is more straightforward than the previous approach. Additionally, the new algorithm is shown to be the natural extension of the approach developed by Tomasi and Kanade for 3D-to-2D orthographically projected data and is applied to a realistic inverse synthetic aperture radar imaging scenario, as well as experiments with varying amounts of aperture diversity and noise.