Pose Estimation in Conformal Geometric Algebra Part II: Real-Time Pose Estimation Using Extended Feature Concepts

Part II uses the foundations of Part I [35] to define constraint equations for 2D-3D pose estimation of different corresponding entities. Most articles on pose estimation concentrate on specific types of correspondences, mostly between points, and only rarely use line correspondences. The first aim of this part is to extend pose estimation scenarios to correspondences of an extended set of geometric entities. In this context we are interested to relate the following (2D) image and (3D) model types: 2D point/3D point, 2D line/3D point, 2D line/3D line, 2D conic/3D circle, 2D conic/3D sphere. Furthermore, to handle articulated objects, we describe kinematic chains in this context in a similar manner. We ensure that all constraint equations end up in a distance measure in the Euclidean space, which is well posed in the context of noisy data. We also discuss the numerical estimation of the pose. We propose to use linearized twist transformations which result in well conditioned and fast solvable systems of equations. The key idea is not to search for the representation of the Lie group, describing the rigid body motion, but for the representation of their generating Lie algebra. This leads to real-time capable algorithms.Bodo Rosenhahn gained his diploma degree in Computer Science in 1999. Since then he has been pursuing his Ph.D. at the Cognitive Systems Group, Institute of Computer Science, Christian-Albrechts University Kiel, Germany. He is working on geometric applications of Clifford algebras in computer vision.Prof. Dr. Gerald Sommer received a diploma degree in physics from the Friedrich-Schiller-Universität Jena, Germany, in 1969, a Ph.D. degree in physics from the same university in 1975, and a habilitation degree in engineering from the Technical University Ilmenau, Germany, in 1988. Since 1993 he is leading the research group Cognitive Systems at the Christian-Albrechts-Universität Kiel, Germany. Currently he is also the scientific coordinator of the VISATEC project.     

Conformal Geometric Algebra for Robotic Vision

In this paper the authors introduce the conformal geometric algebra in the field of visually guided robotics. This mathematical system keeps our intuitions and insight of the geometry of the problem at hand and it helps us to reduce considerably the computational burden of the problems. As opposite to the standard projective geometry, in conformal geometric algebra we can deal simultaneously with incidence algebra operations (meet and join) and conformal transformations represented effectively using spinors. In this regard, this framework appears promising for dealing with kinematics, dynamics and projective geometry problems without the need to resort to different mathematical systems (as most current approaches do). This paper presents real tasks of perception and action, treated in a very elegant and efficient way: body–eye calibration, 3D reconstruction and robot navigation, the computation of 3D kinematics of a robot arm in terms of spheres, visually guided 3D object grasping making use of the directed distance and intersections of lines, planes and spheres both involving conformal transformations. We strongly believe that the framework of conformal geometric algebra can be, in general, of great advantage for applications using stereo vision, range data, laser, omnidirectional and odometry based systems. Eduardo Jose Bayro-Corrochano gained his Ph.D. in Cognitive Computer Science in 1993 from the University of Wales at Cardiff. From 1995 to 1999 he has been Researcher and Lecturer at the Institute for Computer Science, Christian Albrechts University, Kiel, Germany, working on applications of geometric Clifford algebra to cognitive systems.  His current research interest focuses on geometric methods for artificial perception and action systems. It includes geometric neural networks, visually guidevsd robotics, color image processing, Lie bivector algebras for early vision and robot maneuvering. He is editor and author of the following books: Geometric Computing for Perception Action Systems, E. Bayro-Corrochano, Springer Verlag, 2001; Geometric Algebra with Applications in Science and Engineering, E. Bayro-Corrochano and G. Sobczyk (Eds.), Birkahauser 2001; Handbook of Computational Geometry for Pattern Recognition, Computer Vision, Neurocomputing and Robotics, E. Bayro-Corrochano, Springer Verlag, 2005. He authored more than 90 strictly reviewed papers. Leo Hendrick Reyes-Lozano received his degree in Computer Engineering from the University of Guadalajara in 1999. He earned his MSc. and Ph.D. from the Center of Research and Advanced Studies (CINVESTAV) Guadalajara in 2001 and 2004, respectively. His research interests include Computer Vision, Geometric Algebra and Computer Graphics. Julio Zamora-Esquivel received his degree in Electronic Engineering at the Guzman City Institute of Tecnology in 2000. He earned his MSc. at the Center of Research and Advanced Studies (CINVESTAV) in Guadalajara in 2003. He is currently a Ph.D Candidate at CINVESTAV. His research interests include Computer Vision, Geometric Algebra and Robotics.     

Integration of Hough Transform of lines and planes in the framework of conformal geometric algebra for 2D and 3D robot vision

This paper presents the application of 2D and 3D Hough Transforms together with conformal geometric algebra to build 3D geometric maps using the geometric entities of lines and planes. Among several existing techniques for robot self-localization, a new approach is proposed for map matching in the Hough domain. The geometric Hough representation is formulated in such a way that one can easily relate it to the conformal geometric algebra framework; thus, the detected lines and planes can be used for algebra-of-incidence computations to find geometric constraints, useful when perceiving special configurations in 3D visual space for exploration, navigation, relocation and obstacle avoidance. We believe that this work is very useful for 2D and 3D geometric pattern recognition in robot vision tasks.     

Omnidirectional Robot Vision Using Conformal Geometric Computing

In this paper, we show how to use the conformal geometric algebra (CGA) as a framework to model the different catadioptric systems using the unified model (UM). This framework is well suited since it can not only represent points, lines and planes, but also point pairs, circles and spheres (geometric objects needed in the UM). We define our model using the great expressive capabilities of the CGA in a more general and simpler way, which allows an easier implementation in more complex applications. On the other hand, we also show how to recover the projective invariants from a catadioptric image using the inverse projection of the UM. Finally, we present applications in navigation and object recognition. Carlos Alberto López-Franco is a doctoral student at CINVESTAV, GEOVIS Laboratory, Unidad Guadalajara, México. He received in 2003 the M.S. degree in Computer Science from CINVESTAV, Unidad Guadalajara. His scientific interests are in the fields of computer vision, robotics and the applications of geometric algebra for mobile robots. Eduardo Jose Bayro-Corrochano gained his Ph.D. in Cognitive Computer Science in 1993 from the University of Wales at Cardiff. From 1995 to 1999 he has been Researcher and Lecturer at the Institute for Computer Science, Christian Albrechts University, Kiel, Germany, working on applications of geometric Clifford algebra to cognitive systems. At present is a full professor at CINVESTAV Unidad Guadalajara, México, Department of Electrical Engineering and Computer Science. His current research interest focuses on geometric methods for artificial perception and action systems. It includes geometric neural networks, visually guided robotics, color image processing, Lie bivector algebras for early vision and robot maneuvering. He developed the quaternion wavelet transform for quaternion multi-resolution analysis using the phase concept. He is associate editor of Robotics and Journal of Advanced Robotic Systems and member of the editorial board of Journal of Pattern Recognition, Journal of Mathematical Imaging and Vision, Iberoamerican Journal of Computer and Systems and Journal Of Theoretical And Numerical Approximation. He is editor and author of the following books: Geometric Computing for Perception Action Systems, E. Bayro-Corrochano, Springer Verlag, 2001; Geometric Algebra with Applications in Science and Engineering, E. Bayro-Corrochano and G. Sobczyk (Eds.), Birkahauser 2001; Handbook of Geometric Computing for Pattern Recognition, Computer Vision, Neurocomputing and Robotics, E. Bayro-Corrochano, Springer Verlag, 2005. He has published over 120 refereed journal, book chapters and conference papers.     

Stereophotogrammetric 3D real-time machine vision

Signal processing algorithms often have to be modified significantly for implementation in hardware. Continuous real-time image processing at high speed is a particularly challenging task. In this paper a hardware-software codesign is applied to a stereophotogrammetric system. To calculate the depth map, an optimized algorithm is implemented as a hierarchical-parallel hardware solution. By subdividing distances to objects and selecting them sequentially, we can apply 3D scanning and ranging over large distances. We designed processor-based object clustering and tracking functions. We can detect objects utilizing density distributions of disparities in the depth map (disparity histogram). Motion parameters of detected objects are stabilized by Kalman filters. The text was submitted by the authors in English. Michael Tornow was born in Magdeburg, Germany, in 1977. He received his diploma engineer degree (Dipl.-Ing.) in electrical engineering at the University of Magdeburg, Germany, in 2002. He is currently working on a PhD thesis focusing on hardware adapted image processing and vision based driver assistance. Robert W. Kuhn received his diploma engineer degree (Dipl.-Ing.) in geodesy at the Technical University of Berlin, Germany, in 2000. His current work on a PhD thesis focuses on calibration and image processing. Jens Kaszubiak was born in Blankenburg, Germany, in 1977. He received his diploma engineer degree (Dipl.-Ing.) in electrical engineering at the University of Magdeburg, Germany, in 2002. His current research work focuses on vision-based driver assistance and hardware-software codesign. Bernd Michaelis was born in Magdeburg, Germany, in 1947. He received a Masters Degree in Electronic Engineering from the Technische Hochschule, Magdeburg, in 1971 and his first PhD in 1974. Between 1974 and 1980 he worked at the Technische Hochschule, Magdeburg, and was granted a second doctoral degree in 1980. In 1993 he became Professor of Technical Computer Science at the Otto-von-Guericke University, Magdeburg. His research work concentrates on the field of image processing, artificial neural networks, pattern recognition, processor architectures, and microcomputers. Professor Michaelis is the author of more than 150 papers. Gerald Krell was born in Magdeburg, Germany, in 1964. He earned his diploma in electrical engineering in 1990 and his doctorate in 1995 at Otto-von-Guericke University of Magdeburg. Since then he has been a research assistant. His primary research interest is focused on digital image processing and compression, electronic hardware development, and artificial neural networks.     

Accurate reconstruction of 3D model of a human face using structured light

An automated system for the reconstruction of textured 3D models of human faces has been developed. 3D information is read using the structured lighting used in calibrated projector-camera system. The accuracy of 3D reconstruction is studied experimentally. De Wansa Wickramarante Viktor Klementovich. Born 1983. Graduated from the Moscow State Institute of Radioengineering, Electronics, and Automation (Technical University). Post graduate student of MSIREA. Scientific interests: pattern recognition, biometry, 3D scanners. Author of 5 papers. Awarded the 3 degree diploma at the All-Russian Conference MMRO-13; the incentive diploma at the International Conference ROAI-8-2007. Vladimir Vasilievich Ryazanov. Vladimir V. Ryazanov gratuated from the Moscow Institute of Physical Technology in 1973 and the post-graduate courses at the Computer Center, Academy of Sciences, USSR, in 1976. Received Ph.D. in 1977 (“Computer Science”) and Professor degree in 1994 (“Applications of Mathematical Methods, Mathematical Modeling and Computers in Scientific Investigations”). At the Dorodnicin Computer Center of the Russian Academy of Sciences since 1976. Head of the Situations Recognition Sector in the Department of Recognition Problems and Combinatorial Analysis. Author of approximately 150 papers. Scientific interests: data mining, mathematical models of pattern recognition, classification and forecasting, optimization of recognition and classification models, learning, synthesis of optimal collective solutions in the classification problem, creation of intelligent program systems for data analysis and recognition, and practical applications in technology, medicine, industry. Alexander Vinogradov. Born in 1951. Graduate from Moscow Institute of Physics and Technology in 1974. Kandidat degree in mathematical cybernetics, 1978. Spere of main interests—geometric and algebraic methods in data analysis and image processing. Author of about 50 scientific publications.     

Pose analysis using spectral geometry

We propose a novel method to analyze a set of poses of 3D models that are represented with triangle meshes and unregistered. Different shapes of poses are transformed from the 3D spatial domain to a geometry spectrum domain that is defined by Laplace–Beltrami operator. During this space-spectrum transform, all near-isometric deformations, mesh triangulations and Euclidean transformations are filtered away. The different spatial poses from a 3D model are represented with near-isometric deformations; therefore, they have similar behaviors in the spectral domain. Semantic parts of that model are then determined based on the computed geometric properties of all the mapped vertices in the geometry spectrum domain. Semantic skeleton can be automatically built with joints detected as well. The Laplace–Beltrami operator is proved to be invariant to isometric deformations and Euclidean transformations such as translation and rotation. It also can be invariant to scaling with normalization. The discrete implementation also makes the Laplace–Beltrami operator straightforward to be applied on triangle meshes despite triangulations. Our method turns a rather difficult spatial problem into a spectral problem that is much easier to solve. The applications show that our 3D pose analysis method leads to a registration-free pose analysis and a high-level semantic part understanding of 3D shapes.     

Lie Algebra and System Identification Techniques for 3D Rigid Motion Estimation and Monocular Tracking

This paper addresses the parameters’ estimation of 2D and 3D transformations. For the estimation we present a method based on system identification theory, we named it the “A-method”. The transformations are considered as elements of the Lie group GL(n) or one of its subgroups. We represent the transformations in terms of their Lie Algebra elements. The Lie algebra approach assures to follow the shortest path or geodesic in the involved Lie group. To prove the potencial of our method, two experiments are presented. The first one is a monocular estimation of 3D rigid motion of an object in the visual space. With this aim, the six parameters of the rigid motion are estimated based on measurements of the six parameters of the affine transformation in the image. Secondly, we present the estimation of the affine or projective transformations involved in monocular region tracking. Jaime Ortegón-Aguilar received his degree in computer sciences at the Universidad Autonoma de Yucatan in Merida, Mexico in 2000. He earned his M.Sc. degree at the Cinvestav in Guadalajara, Mexico in 2002. He received his PhD degree from Cinvestav in 2006. His research interests include image processing, computer vision, robotics and applications of geometric algebra. Eduardo Jose Bayro-Corrochano gained his Ph.D. in Cognitive Computer Science in 1993 from the University of Wales at Cardiff. From 1995 to 1999 he has been Researcher and Lecturer at the Institute for Computer Science, Christian Albrechts University, Kiel, Germany, working on applications of geometric Clifford algebra to cognitive systems. At present is a full professor at CINVESTAV Unidad Guadalajara, México, Department of Electrical Engineering and Computer Science. His current research interest focuses on geometric methods for artificial perception and action systems. It includes geometric neural networks, visually guided robotics, humanoids, color image processing, Lie bivector algebras for early vision and robot maneuvering. He developed the quaternion wavelet transform for quaternion multi-resolution analysis using the phase concept. He is associate editor of Robotics and Journal of Advanced Robotic Systems and member of the editorial board of Journal of Pattern Recognition, Journal of Mathematical Imaging and Vision, Iberoamerican Journal of Computer and Systems and Journal of Theoretical and Numerical Approximation. He is editor and author of the following books: Geometric Computing for Perception Action Systems, E. Bayro-Corrochano, Springer Verlag, 2001; Geometric Algebra with Applications in Science and Engineering, E. Bayro-Corrochano and G. Sobczyk (Eds.), Birkhauser 2001; Handbook of Geometric Computing for Pattern Recognition, Computer Vision, Neurocomputing and Robotics, E. Bayro-Corrochano, Springer Verlag, 2005. He has published over 120 refereed journal, book chapters and conference papers. He is fellow of the IAPR society.     

On-line modeling for real-time 3D target tracking

Model-based object tracking can provide autonomous mobile robotic systems with real-time 6-dof pose information, for example, enabling them to rendezvous with targets from a particular desired direction. Most existing model-based trackers, however, require the geometric model of the target to be known a priori, which may pose a practical problem in real-world environments. This paper presents a novel 3D modeler capable of building an approximate model of a target object on-line. The proposed technique rapidly constructs a 3D tessellated enveloping mesh and uses projective texture mapping to further model the target object’s surface features. Separation of the target object from background clutter is achieved via customizable interest filters. The resulting real-time object-tracking system was tested extensively via simulations and experiments.     

The 3L algorithm for fitting implicit polynomial curves andsurfaces to data

We introduce a completely new approach to fitting implicit polynomial geometric shape models to data and to studying these polynomials. The power of these models is in their ability to represent nonstar complex shapes in two(2D) and three-dimensional (3D) data to permit fast, repeatable fitting to unorganized data which may not be uniformly sampled and which may contain gaps, to permit position-invariant shape recognition based on new complete sets of Euclidean and affine invariants and to permit fast, stable single-computation pose estimation. The algorithm represents a significant advancement of implicit polynomial technology for four important reasons. First, it is orders of magnitude taster than existing fitting methods for implicit polynomial 2D curves and 3D surfaces, and the algorithms for 2D and 3D are essentially the same. Second, it has significantly better repeatability, numerical stability, and robustness than current methods in dealing with noisy, deformed, or missing data. Third, it can easily fit polynomials of high, such as 14th or 16th, degree. Fourth, additional linear constraints can be easily incorporated into the fitting process, and general linear vector space concepts apply     

Computing general geometric structures on surfaces using Ricci flow

Systematically generalizing planar geometric algorithms to manifold domains is of fundamental importance in computer aided design field. This paper proposes a novel theoretic framework, geometric structure, to conquer this problem. In order to discover the intrinsic geometric structures of general surfaces, we developed a theoretic rigorous and practical efficient method, Discrete Variational Ricci flow.Different geometries study the invariants under the corresponding transformation groups. The same geometry can be defined on various manifolds, whereas the same manifold allows different geometries. Geometric structures allow different geometries to be defined on various manifolds, therefore algorithms based on the corresponding geometric invariants can be applied on the manifold domains directly.Surfaces have natural geometric structures, such as spherical structure, affine structure, projective structure, hyperbolic structure and conformal structure. Therefore planar algorithms based on these geometries can be defined on surfaces straightforwardly.Computing the general geometric structures on surfaces has been a long lasting open problem. We solve the problem by introducing a novel method based on discrete variational Ricci flow.We thoroughly explain both theoretical and practical aspects of the computational methodology for geometric structures based on Ricci flow, and demonstrate several important applications of geometric structures: generalizing Voronoi diagram algorithms to surfaces via Euclidean structure, cross global parametrization between high genus surfaces via hyperbolic structure, generalizing planar splines to manifolds via affine structure. The experimental results show that our method is rigorous and efficient and the framework of geometric structures is general and powerful.     

Simultaneous and Sequential Reconstruction of Visual Primitives with Bundle Adjustment

In this paper, we compare the various methods for the simultaneous and sequential reconstruction of points, lines, planes, quadrics, plane conics and degenerate quadrics using Bundle Adjustment, both in projective and metric space. In contrast, most existing work on projective reconstruction focuses mainly on one type of primitive. We also compare the simultaneous refinement of all primitives through Bundle Adjustment with various sequential methods were only certain primitives are refined together. We found that even though the sequential methods may seem somewhat arbitrary on the choice of which primitives are refined together, a higher precision and speed is achieved in most cases. Leo Reyes graduated in Computer Engineering at the University of Guadalajara in 1999 and gained his Master’s and Doctoral degrees in Computer Science from the Center of Research and Advanced Studies Guadalajara (Centro de Investigación y Estudios Avanzados del IPN, CINVESTAV Unidad Guadalajara) in 2001 and 2004, respectively. He is currently working on a private company doing automatic inspection research. Eduardo Jose Bayro-Corrochano gained his Ph.D. in Cognitive Computer Science in 1993 from the University of Wales at Cardiff. From 1995 to 1999 he has been Researcher and Lecturer at the Institute for Computer Science, Christian Albrechts University, Kiel, Germany, working on applications of geometric Clifford algebra to cognitive systems. At present he is a full professor at CINVESTAV, Unidad Guadalajara, Computer Science Group and he is responsible for the GEOVIS laboratory. His current research interest focuses on geometric methods for artificial perception and action systems. It includes geometric neural networks, visually guided robotics, color image processing, Lie bivector algebras for early vision and robot maneuvering. He developed the quaternion wavelet transform for quaternion multi-resolution analysis using the phase concept. He is editor and author of the following books: Geometric Computing for Perception Action Systems, E. Bayro-Corrochano, Springer Verlag, 2001; Geometric Algebra with Applications in Science and Engineering, E. Bayro-Corrochano and G. Sobczyk (Eds.), Birkahauser 2001; Handbook of Computational Geometry for Pattern Recognition, Computer Vision, Neurocomputing and Robotics, E. Bayro-Corrochano, Springer Verlag, 2005. He has published over 100 refereed journal and conference papers.     

PnP Problem Revisited

Perspective-n-Point camera pose determination, or the PnP problem, has attracted much attention in the literature. This paper gives a systematic investigation on the PnP problem from both geometric and algebraic standpoints, and has the following contributions: Firstly, we rigorously prove that the PnP problem under distance-based definition is equivalent to the PnP problem under orthogonal-transformation-based definition when n > 3, and equivalent to the PnP problem under rotation-transformation-based definition when n = 3. Secondly, we obtain the upper bounds of the number of solutions for the PnP problem under different definitions. In particular, we show that for any three non-collinear control points, we can always find out a location of optical center such that the P3P problem formed by these three control points and the optical center can have 4 solutions, its upper bound. Additionally a geometric way is provided to construct these 4 solutions. Thirdly, we introduce a depth-ratio based approach to represent the solutions of the whole PnP problem. This approach is shown to be advantageous over the traditional elimination techniques. Lastly, degenerated cases for coplanar or collinear control points are also discussed. Surprisingly enough, it is shown that if all the control points are collinear, the PnP problem under distance-based definition has a unique solution, but the PnP problem under transformation-based definition is only determined up to one free parameter. Yihong Wu received her Bachelor of Science degree in Mathematics from Shanxi Yanbei Normal College in 1995; a Master of Science degree in Computational Algebra from Shaanxi Normal University in 1998; a Doctor of Science degree in Geometric Invariants and Applications from MMRC, Institute of Systems Science, Chinese Academy of Sciences, in 2001. From June 2001 to July 2003, she did her postdoctoral research in NLPR, Institute of Automation, Chinese Academy of Sciences. After then, she joined NLPR as an associate professor. Her research interests include polynomial elimination and applications, geometric invariant and applications, automated geometric theorem proving, camera calibration, camera pose determination, and 3D reconstruction. She has published more than 15 papers on major international journals and major international conferences. Zhanyi Hu was born in Shanxi province, P. R. China in 1961. He received the B.S. Degree in Automation from the North China University of Technology in 1985, the Ph.D. Degree (Docteur d’Etat) in Computer Science from the University of Liege, Belgium, in Jan. 1993. Since 1993, he has been with the Institute of Automation, Chinese Academy of Sciences. From May 1997 to May 1998, he also acted as a visiting scholar of Chinese University of Hong Kong on invitation. Dr. Hu now is a Research Professor of Computer Vision, a member of the Executive Expert Committee of the Chinese National High Technology R&D Program, a deputy editor-in-chief for Chinese Journal of CAD and CG, and an associate editor for Journal of Computer Science and Technology. His current research interests include Camera Calibration, 3D Reconstruction, Feature Extraction, Vision Guided Robot Navigation etc. Dr. Hu has published more than 70 peer-reviewed papers on major national and international journals.     

Detecting causal relationships in distributed computations: In search of the holy grail

Summary The paper shows that characterizing the causal relationship between significant events is an important but non-trivial aspect for understanding the behavior of distributed programs. An introduction to the notion of causality and its relation to logical time is given; some fundamental results concerning the characterization of causality are presented. Recent work on the detection of causal relationships in distributed computations is surveyed. The issue of observing distributed computations in a causally consistent way and the basic problems of detecting global predicates are discussed. To illustrate the major difficulties, some typical monitoring and debugging approaches are assessed, and it is demonstrated how their feasibility is severely limited by the fundamental problem to master the complexity of causal relationships. Reinhard Schwarz received a diploma in computer science from the University of Kaiserslautern, Germany, in 1990. Since then, he is working as a research assistant at the computer science department. His research interests include debugging and monitoring of distributed systems, runtime support for object-oriented distributed programming, and distributed algorithms. Friedemann Mattern received the diploma in computer science from Bonn University, Germany, and the Ph.D. degree from the University of Kaiserslautern, Germany, in 1983 and 1989, respectively. Since 1991 he is a professor of computer science at the University of Saarland in Saarbrücken, Germany. His current research interests include programming of distributed systems, distributed applications, and distributed algorithms.The work presented in this paper was carried out as part of the PARAWAN project supported by the Bundesministerium für Forschung und Technologie (BMFT)     

结合稀疏表示和深度学习的视频中3D人体姿态估计

目的 2D姿态估计的误差是导致3D人体姿态估计产生误差的主要原因,如何在2D误差或噪声干扰下从2D姿态映射到最优、最合理的3D姿态,是提高3D人体姿态估计的关键。本文提出了一种稀疏表示与深度模型联合的3D姿态估计方法,以将3D姿态空间几何先验与时间信息相结合,达到提高3D姿态估计精度的目的。方法 利用融合稀疏表示的3D可变形状模型得到单帧图像可靠的3D初始值。构建多通道长短时记忆MLSTM（multi-channel long short term memory）降噪编/解码器,将获得的单帧3D初始值以时间序列形式输入到其中,利用MLSTM降噪编/解码器学习相邻帧之间人物姿态的时间依赖关系,并施加时间平滑约束,得到最终优化的3D姿态。结果 在Human3.6M数据集上进行了对比实验。对于两种输入数据：数据集给出的2D坐标和通过卷积神经网络获得的2D估计坐标,相比于单帧估计,通过MLSTM降噪编/解码器优化后的视频序列平均重构误差分别下降了12.6%,13%;相比于现有的基于视频的稀疏模型方法,本文方法对视频的平均重构误差下降了6.4%,9.1%。对于2D估计坐标数据,相比于现有的深度模型方法,本文方法对视频的平均重构误差下降了12.8%。结论 本文提出的基于时间信息的MLSTM降噪编/解码器与稀疏模型相结合,有效利用了3D姿态先验知识,视频帧间人物姿态连续变化的时间和空间依赖性,一定程度上提高了单目视频3D姿态估计的精度。     

Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration

We investigate the projective properties of the feature consisting of two concentric circles. We demonstrate there exist geometric and algebraic constraints on its projection. We show how these constraints greatly simplify the recoveries of the affine and Euclidean structures of a 3D plane. As an application, we assess the performances of two camera calibration algorithms.     

基于形态和约束结构的几何哈希法

几何哈希法,作为一种有效的模型搜索算法,在物体识别中有着重要的应用。现有的几何哈希法仅适合于仿射变换下的二维景物识别,论文提出了适合透视投影变换下三维物体识别的几何哈希方法。该方法利用物体的三维形态和物体中具有射影不变量的几何约束结构来构造哈希表。一方面,几何约束结构提供了物体模型的索引功能;另一方面,物体的三维形态提供了物体成像位姿的有关信息,使后续的匹配验证得以简化。实验中使用人造物体对该方法进行了验证,实验表明该方法正确有效。     

Projective Fourier analysis for patterns

Identifying as a projective group for patterns in the conformal camera model, the projective harmonic analysis on its double covering group is presented in the noncompact and compact pictures — the pictures used to study different aspects of irreducible unitary representations of semisimple Lie groups. Bypassing technicalities of representation theory, but stressing the motivation and similarities with Euclidean Fourier analysis, each constructed picture of the projective Fourier analysis includes the Fourier transform, Plancherel's theorem and convolution property. Projectively covariant characteristics of the analysis in the noncompact picture allow rendering any of image projective transformations of a pattern (after removing conformal distortions) by using only one projective Fourier transform of the original pattern, what is demonstrated in a computer simulation. The convolution properties in both pictures must by used to develop algorithms for projectively invariant matching of patterns. Work in progress on fast algorithms for computing with projective Fourier transforms and for rendering image projective transformations is discussed. Efficient computations of the convolutions would follow from the both fast projective Fourier transforms and their inverses.     

Algebraic Conditions for Classifying the Positional Relationships Between Two Conics and Their Applications

In many fields of computer science such as computer animation, computer graphics, computer aided geometric design and robotics, it is a common problem to detect the positional relationships of several entities. Based on generalized characteristic polynomials and projective transformations, algebraic conditions are derived for detecting the various positional relationships betweeu two planar conics, namely, outer separation, exterior contact, intersection, interior contact and inclusion. Then the results are applied to detecting the positional relationships between a cylinder (or a cone) and a quadric. The criteria is very effective and easier to use than other known methods.