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.     

一种新的全向立体视觉系统的设计

本文介绍了用一个普通相机实现的全向立体视觉系统的设计，系统的配置使得其具有结构和几何计算简单、对应点匹配容易、系统成像无遮挡的优点。误差分析表明其具有较高的精度。本系统可用于机器人探测障碍物、环境深度信息的自动获取以及其它要求实时性计算的机器视觉。     

共形几何代数与几何不变量的代数运算

几何不变量的使用是计算机视觉和图形学的一个重要手段.发现一个不变量后,如何找到它与其他不变量的关系,是实际应用中的一个重要问题,这种关系的探讨主要依靠在不变量层次上的代数运算.文中介绍了共形几何代数中的基本、高级和有理不变量如何在几何问题中自然出现,它们之间如何进行代数运算,以及如何通过不变量的化简,自然地得到几何条件的充分必要化和几何定理的完全化.几何定理的机器证明作为几何定理完全化的副产品,被发展成几何定理的关系定量化,这种量化的几何还原就是几何定理的自然推广.几何不变量之间的几何关系的计算是这些技术的一个具体应用.     

共形几何代数--几何代数的新理论和计算框架

共形几何代数是一个新的几何表示和计算工具.作为几何的高级不变量和协变量系统的结合,它为经典几何提供了统一和简洁的齐性代数框架,以及高效的展开、消元和化简算法,从而可以进行极其复杂的符号几何计算,在几何建模与计算方面表现出很大的优势.主要讲述共形几何代数的产生背景和意义,共形几何代数的数学理论和它最有特色的几个部分,包括Grassmann结构、统一几何表示和旋量作用、基本不变量系统和高级不变量系统、新的计算思想、展开和化简技术等.     

基于主动式全景视觉的移动机器人障碍物检测

针对现有的移动机器人视觉系统计算资源消耗大、实时性能欠佳、检测范围受限等问题,提出一种基于主动式全景视觉传感器(AODVS)的移动机器人障碍物检测方法。首先,将单视点的全方位视觉传感器(ODVS)和由配置在1个平面上的4个红色线激光组合而成的面激光发生器进行集成,通过主动全景视觉对移动机器人周边障碍物进行检测;其次,移动机器人中的全景智能感知模块根据面激光发生器投射到周边障碍物上的激光信息,通过视觉处理方法解析出移动机器人周边障碍物的距离和方位等信息;最后,基于上述信息采用一种全方位避障策略,实现移动机器人的快速避障。实验结果表明,基于AODVS的障碍物检测方法能在实现快速高效避障的同时,降低对移动机器人的计算资源的要求。     

共形几何代数与运动和形状的刻画

共形几何代数在基于运动和形状刻画的视觉和图形学若干问题中的应用,反映了它能够提供统一和有效的表示和算法,这些应用主要集中在采纳几何体的Grassmann分级表示以及刚体运动的旋量和扭量表示.着重介绍了Grassmann分级表示如何被应用于单眼视觉问题并带来解决方法的简化;通过对刚体运动不同表示的分析,介绍旋量和扭量表示如何克服刚体运动蹬矩阵表示中参数空间具有过多非线性约束的缺点,从而为姿态估计、形状逼近和曲线拼接等问题的解决提供简化方案.     

A Geometric Approach for the Theory and Applications of 3D Projective Invariants

A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing position. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes in the observation parameters. The study of such geometric invariance is a field of active research. This paper presents the theory and computation of projective invariants formed from points and lines using the geometric algebra framework. This work shows that geometric algebra is a very elegant language for expressing projective invariants using n views. The paper compares projective invariants involving two and three cameras using simulated and real images. Illustrations of the application of such projective invariants in visual guided grasping, camera self-localization and reconstruction of shape and motion complement the experimental part.     

Pose Estimation in Conformal Geometric Algebra Part I: The Stratification of Mathematical Spaces

2D-3D pose estimation means to estimate the relative position and orientation of a 3D object with respect to a reference camera system. This work has its main focus on the theoretical foundations of the 2D-3D pose estimation problem: We discuss the involved mathematical spaces and their interaction within higher order entities. To cope with the pose problem (how to compare 2D projective image features with 3D Euclidean object features), the principle we propose is to reconstruct image features (e.g. points or lines) to one dimensional higher entities (e.g. 3D projection rays or 3D reconstructed planes) and express constraints in the 3D space. It turns out that the stratification hierarchy [11] introduced by Faugeras is involved in the scenario. But since the stratification hierarchy is based on pure point concepts a new algebraic embedding is required when dealing with higher order entities. The conformal geometric algebra (CGA) [24] is well suited to solve this problem, since it subsumes the involved mathematical spaces. Operators are defined to switch entities between the algebras of the conformal space and its Euclidean and projective subspaces. This leads to another interpretation of the stratification hierarchy, which is not restricted to be based solely on point concepts. This work summarizes the theoretical foundations needed to deal with the pose problem. Therefore it contains mainly basics of Euclidean, projective and conformal geometry. Since especially conformal geometry is not well known in computer science, we recapitulate the mathematical concepts in some detail. We believe that this geometric model is useful also for many other computer vision tasks and has been ignored so far. Applications of these foundations are presented in Part II [36].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.     

Registration of 3D Points Using Geometric Algebra and Tensor Voting

We address the problem of finding the correspondences of two point sets in 3D undergoing a rigid transformation. Using these correspondences the motion between the two sets can be computed to perform registration. Our approach is based on the analysis of the rigid motion equations as expressed in the Geometric Algebra framework. Through this analysis it was apparent that this problem could be cast into a problem of finding a certain 3D plane in a different space that satisfies certain geometric constraints. In order to find this plane in a robust way, the Tensor Voting methodology was used. Unlike other common algorithms for point registration (like the Iterated Closest Points algorithm), ours does not require an initialization, works equally well with small and large transformations, it cannot be trapped in “local minima” and works even in the presence of large amounts of outliers. We also show that this algorithm is easily extended to account for multiple motions and certain non-rigid or elastic transformations.     

基于几何－拓扑广域三维地图和全向视觉的移动机器人自定位

面向大规模室内环境, 研究了基于全向视觉的移动机器人自定位. 提出用分层的几何－拓扑三维地图管理广域环境特征, 定义了不同层次的三维局部环境特征及全局拓扑属性, 给出了分层地图的应用方法. 构建了全向视觉传感器成像模型及其不确定性传播方法, 使得地图中的概率元素能够在系统中有效应用. 采用随机点预估搜索的方法提取环境元素对应的曲线边缘特征. 用带反馈的分层估计方法在融合中心对多观测特征产生的相应估计状态进行总体融合. 以分层逻辑架构设计实现了移动机器人交互式自定位系统. 实验分析了真实环境中不同初始位姿和观测信息情况下定位系统的收敛性和定位精度, 在考虑动态障碍物的遮挡情况下完成了机器人的在线环境感知和运动自定位任务. 实验结果表明本文方法的可靠性和实用性.     

Active Appearance-Based Robot Localization Using Stereo Vision

A vision-based robot localization system must be robust: able to keep track of the position of the robot at any time even if illumination conditions change and, in the extreme case of a failure, able to efficiently recover the correct position of the robot. With this objective in mind, we enhance the existing appearance-based robot localization framework in two directions by exploiting the use of a stereo camera mounted on a pan-and-tilt device. First, we move from the classical passive appearance-based localization framework to an active one where the robot sometimes executes actions with the only purpose of gaining information about its location in the environment. Along this line, we introduce an entropy-based criterion for action selection that can be efficiently evaluated in our probabilistic localization system. The execution of the actions selected using this criterion allows the robot to quickly find out its position in case it gets lost. Secondly, we introduce the use of depth maps obtained with the stereo cameras. The information provided by depth maps is less sensitive to changes of illumination than that provided by plain images. The main drawback of depth maps is that they include missing values: points for which it is not possible to reliably determine depth information. The presence of missing values makes Principal Component Analysis (the standard method used to compress images in the appearance-based framework) unfeasible. We describe a novel Expectation-Maximization algorithm to determine the principal components of a data set including missing values and we apply it to depth maps. The experiments we present show that the combination of the active localization with the use of depth maps gives an efficient and robust appearance-based robot localization system.     

Using Real-Time Stereo Vision for Mobile Robot Navigation

This paper describes a working vision-based mobile robot that navigates and autonomously explores its environment while building occupancy grid maps of the environment. We present a method for reducing stereo vision disparity images to two-dimensional map information. Stereo vision has several attributes that set it apart from other sensors more commonly used for occupancy grid mapping. We discuss these attributes, the errors that some of them create, and how to overcome them. We reduce errors by segmenting disparity images based on continuous disparity surfaces to reject spikes caused by stereo mismatches. Stereo vision processing and map updates are done at 5 Hz and the robot moves at speeds of 300 cm/s.     

Catadioptric Projective Geometry

Catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera. Central catadioptric sensors are the class of these devices having a single effective viewpoint. In this paper, we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications. We show that a central catadioptric projection is equivalent to a two-step mapping via the sphere. The second step is equivalent to a stereographic projection in the case of parabolic mirrors. Conventional lens-based perspective cameras are also central catadioptric devices with a virtual planar mirror and are, thus, covered by the unifying model. We prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images (conics). It turns out that planar and parabolic mirrors build a dual catadioptric projection pair. As a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system.     

板材排样问题中不规则多边形优化组合策略研究

板材排样问题是从一组给定的矩形（或非矩形）板材上切割出一批规则的和不规则形状的零件，且使板材的耗费最低。本文研究不规则多边形优化组合策略，提出一种相同零件受限递归组合算法。     

移动机器人视觉抖动的Kalman滤波补偿

消除视觉抖动是机器人移动中对接作业的关键。基于仿射变换,建立了图像的递推运动模型;设计了基于梯度的分区域的KLT特征提取算法,分析了梯度与灰度变化的关系;利用绝对误差和最优进行特征点的匹配,并利用菱形搜索算法来提高匹配速度,设计自适应模板算法来解决匹配结果不惟一的问题;利用最小二乘法求解超定运动方程组,得到运动参数。推导得到有意运动参数的观测模型;利用Kalman滤波去除无意运动;利用滤波后的运动参数重构图像,对含抖动的视频进行稳像补偿。在非平整路面内移动机器人上开展实验。结果表明,相对参数滤波比绝对参数滤波更平滑,且算法对x和y方向的抖动补偿无相互干扰,经过该算法处理后的视频序列与原序列相比结果得到较大改善,满足准确性要求。     

基于嵌入式机器视觉的流水线分拣机器人设计

针对传统流水线上人工错误率高、速度慢和人工成本高的问题,设计了一种深度学习的流水线智能分拣机器人来缓解流水线的压力。该机器人采用分层结构设计,上位机采用Jetson Nano来完成机器人的图像采集、识别和处理,下位机由STM32G0作为主控,通过舵机和电机实现机器人的功能控制。同时上位机与下位机之间进行有效的数据交互,实现了机器人的抓取和分拣协调工作。在实验测试中,该机器人能够通过学习样本实现自动分拣不同类型的对象,并且能够精确识别。该流水线分拣机器人融入了计算机视觉与嵌入式系统,不仅使分拣机器人结构更紧凑,而且有利于提高社会生产力水平,具有良好的应用前景。     

Acquisition of Weld Seam Dimensional Position Information for Arc Welding Robot Based on Vision Computing

Recognition and identification of weld environment and seam dimensional position by computer vision is a key technology for developing advanced autonomous welding robot. Aiming at requirements for recognition of weld seam image characteristics, this paper first presents an improved algorithm of subpixel edge detection based on Zernike moments. Comparing with the Ghosal’s original algorithm, the improved algorithm deals with mask effect and first derivative model on edge gradient direction so that it has the strong robust to noise, self-thinning ability and higher locating precision. An algorithm based on ZMs to extract line is also proposed, the comparative results with SHT and RHT show the method has the highest calculation speed and accuracy. The stereovision technology is developed to identify dimensional position of weld seam by computing dimensional coordinates of the weld seam. According to characteristics of weld seam, view field scope model and stereovision model based on baseline are studied and a stereo matching method is presented. In order to evaluate the algorithms and models presented in this paper, a welding robot systems with single camera fixed on the weld torch end-effector has been established for the robot to identify the dimensional position of typical weld seam by one-item and two-position method. The experiment results on S-shape and saddle-shape weld seams show that the vision computing method developed in this paper can be used for acquiring weld seam dimensional position information in welding robot system. Thus the welding path is mapped before the welding operation is executed.     

An Experiment with Reactive Data-flow Tasking in Active Robot Vision

This paper presents an experiment with the synchronous approach to reactive systems programming, and particularly the Signal language, applied to a significant problem in robot vision: active visual reconstruction. This application consists of the specification of a system dealing with various domains such as robot control, computer vision and transitions between different modes of control. It illustrates the adequacy in such domains of Signal, a data flow programming language and environment. The programming environment features tools for formal specification, analysis, consistency checking and code generation. Signal and its language-level extension for task preemption SignalGTi are used at the different levels of the application: data-flow function for the camera motion control (visual servoing), reconstruction method (in parallel to visual servoing, involving the dynamical processes), and reconstruction of complex scenes (with transitions between several robotics tasks). The combination of these levels constitutes a hybrid behavior with (sampled) continuous control and discrete transitions. These techniques are validated experimentally by an implementation on a robotic cell. © 1997 by John Wiley & Sons, Ltd.     

Real-Time Active SLAM and Obstacle Avoidance for an Autonomous Robot Based on Stereo Vision

Abstract

In this article, the problem of real-time robot exploration and map building (active SLAM) is considered. A single stereo vision camera is exploited by a fully autonomous robot to navigate, localize itself, define its surroundings, and avoid any possible obstacle in the aim of maximizing the mapped region following the optimal route. A modified version of the so-called cognitive-based adaptive optimization algorithm is introduced for the robot to successfully complete its tasks in real time and avoid any local minima entrapment. The method’s effectiveness and performance were tested under various simulation environments as well as real unknown areas with the use of properly equipped robots.