Motion and structure from line correspondences: Some further results

A great deal of dynamic computer vision literature deals with the determination of motion and structure of rigid objects by observing points on objects at two or more time instants. In some situations point correspondences may not be available but line correspondences may be, such as when edges on the objects are visible. In this article we investigate the multiplicity of solutions when various numbers of line correspondences among several snapshots of an object are known. The case given the most consideration is that in which the object is moving with constant motion, that is, with constant rotation about an unknown center which itself is moving with constant translation. In this case we show that there is a unique solution given three line correspondences over three frames, two line correspondences over four frames, and one line correspondence over five or more frames. With fewer line correspondences there are infinitely many solutions. In the more general case where the motion is allowed to vary between successive frames, we show that there can be no more than 600 solutions to motion and structure with six line correspondences over three views, and that there is a unique solution with seven line correspondences. Several examples are given to illustrate our results.©1994 John Wiley & Sons Inc     

Spectrum analysis of motion parallax in a 3D cluttered scene and application to egomotion

Previous methods for estimating observer motion in a rigid 3D scene assume that image velocities can be measured at isolated points. When the observer is moving through a cluttered 3D scene such as a forest, however, pointwise measurements of image velocity are more challenging to obtain because multiple depths, and hence multiple velocities, are present in most local image regions. We introduce a method for estimating egomotion that avoids pointwise image velocity estimation as a first step. In its place, the direction of motion parallax in local image regions is estimated, using a spectrum-based method, and these directions are then combined to directly estimate 3D observer motion. There are two advantages to this approach. First, the method can be applied to a wide range of 3D cluttered scenes, including those for which pointwise image velocities cannot be measured because only normal velocity information is available. Second, the egomotion estimates can be used as a posterior constraint on estimating pointwise image velocities, since known egomotion parameters constrain the candidate image velocities at each point to a one-dimensional rather than a two-dimensional space.     

Pose estimation for autonomous grasping with a robotic arm system

A robust and accurate method for estimating the 3-D pose of a planar rigid object is presented. This article demonstrates that 3-D pose estimation becomes feasible by using the 2-D tracking points on an object of scale-invariant feature transform (SIFT) and 3-D point cloud detected by stereo vision on an object, assuming that a 3-D geometric model of an object is known a priori. The roll and pitch angles of an object are estimated by the normal vector of approximate plane of 3-D point cloud on an object and the yaw angle is estimated by 2-D tracking point on an object of SIFT. Accurate object detection and localization in the camera coordinate system is crucial for grasping. In the motion planning, the bidirectional rapidly exploring random tree algorithm is used to search for a valid path for efficient grasping. Our robot arm can robustly and autonomously grasp a randomly rotative rigid object detected by SIFT in 3-D space. We have realized a grasping scenario with a dexterous arm (ADAM) such that an object in front of ADAM can be grasped. This demonstration shows how the proposed components build a dexterous and robust system integrating object detection, pose estimation, and motion planning.     

Motion and structure from line correspondences under orthographic projection

In this article we determine the multiplicity of solutions in several cases where line correspondences from orthographic projections over three views are known. We show that in the general case where the motion may vary between frames, seven line correspondences over three views are sufficient to guarantee that in general there is a unique solution for the rotation and directions of the lines, up to a reflection about a plane parallel to the camera plane. There is a three-parameter infinite family of solutions for the translations and depths of each line in this case. If the object is experiencing constant rotation, then four lines are sufficient to obtain solutions up to the same ambiguities. If the object is moving with constant rotation about a center of rotation which itself is moving in a straight line at constant velocity, then three lines are sufficient, and there is just a one-parameter infinite family of solutions for the translation and depths of the lines. Several examples are given to illustrate our results. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 301–312, 1997     

Algebraic methods in 3-d motion estimation from two-view point correspondences

We consider the problem of determining motion (3-D rotation and translation) of rigid objects from their images taken at two time instants. We assume that the locations of the perspective projection on the image plane of n points from the surface of the rigid body are known at two time instants. For n = 5, we show that there are at most ten possible motion values (in rotation and translation) and give many examples. For n ≥ 6, we show that the solution is generally unique. We derive a variety of necessary and sufficient conditions a solution must satisfy, show their equivalence, and use algebraic geometry to derive the bound on the number of solutions. A homotopy method is then used to compute all the solutions. Several examples are worked out and our computational experience is summarized.     

Quasi-static consideration of high-frequency modes for more efficient flexible multibody simulations

A number of sets of modes, for example eigenmodes, constraint modes, inertia-relief attachment modes, may be used to describe the linear elastic deformation of a flexible body in multibody dynamics. It is always possible to transform modes so that the conditions of the Buckens-frame are fulfilled. The latter frame leads to serious simplifications in the equations of motion, but cannot avoid a coupling between the body’s rotational rigid body motion and its elastic deformation. In the present paper the deformation modes will be subdivided into low- and high-frequency modes. It will be shown that the latter-mentioned coupling effect of the second ones can be safely neglected in comparison with the first ones. Consequently, the high-frequency components can be removed from time integration at all, which leads to significant savings of computational effort while the accuracy regarding the body’s deformation remains almost the same. In the case of a known frequency content of external excitation, an algorithm is given so that the available modes can be automatically separated into such low- and high-frequency modes. While the number of low-frequency modes remains more or less constant, there is a significant trend to use an increased number of high-frequency modes. Examples are moving loads (e.g., guidance) or distributed loads as they occur in contact problems or when fluid pressure is acting on surfaces. A final numerical example is given in order to demonstrate the potential of the proposed method.     

一种特征点跟踪的运动目标检测

提出一种基于特征点跟踪的运动目标分割算法。在角点跟踪过程中,8等分匹配点邻域,构造方向子邻域提高匹配精度;提出一种新的聚类准则抽取最优特征子集估计运动参数;结合统计方法消除残差噪声;采用时域滤波滤除孤立区域检测出运动目标。对200帧可见光视频序列和100帧红外图像序列中运动汽车进行检测分割实验,检出率分别达到96%和94%。     

The motion of the free-surface separation point during the initial stage of horizontal impulsive displacement of a floating circular cylinder

The initial stage of unsteady two-dimensional flow caused by the impulsive horizontal motion of a floating circular cylinder is investigated by using methods of asymptotic analysis. Initially the cylinder is half-submerged and the liquid free surface is flat and horizontal. The liquid is of infinite depth. Then the cylinder suddenly starts to move horizontally with a speed given as a function of time. The liquid is assumed ideal and incompressible and its flow potential. The initial flow is provided by pressure-impulse theory, with an account of a possible separation of the liquid free surface from the trailing face of the rigid surface of the cylinder. The initial position of the separation point on the surface of the moving body is determined by using the condition that the fluid velocity is finite at the separation point (Kutta condition). The motion of the separation point along the surface of the cylinder is numerically determined with the help of the second-order outer solution of the problem and the Kutta condition at the moving separation point. It is shown that the length of the wetted part of the cylinder surface increases at a rate proportional to the speed of the cylinder. The speed of the separation point depends on the Froude number. The pressure on the wetted part of the cylinder can be below the atmospheric pressure for relatively high speed.     

Importance and use of rigid body mode in boundary element method

The superposition of a rigid body mode on a body should result in a corresponding change in displacement values but should not affect the stresses. However, in the numerical solution by the boundary element method (BEM) large errors may be obtained for displacements and stresses if a rigid body mode is present in the input data. To eliminate the effects of the rigid body mode on the numerical accuracy of the solution, the fundamental solutions for displacements must be correctly interpreted and used. The rigid body mode may be unknowingly present in the boundary condition data. It may be present because the boundary data are not known accurately. Or it may be present if the displacement values at the support have been computed from a separate analysis. A rigid body mode may arise due to the collocation nature of satisfying the boundary conditions. The point values of the applied load at the collocation point may not satisfy equilibrium. Or the point values of the specified displacements may not satisfy the condition of zero translation and rotation. For bodies under pure traction, we know that the analytical solution can contain an arbitrary amount of rigid body mode. Numerically, however, some unknown value is assigned to this rigid body mode. It might be desirable (for example in limit analysis) to eliminate the rigid body mode from the displacements to obtain deformation of a point with respect to a point on the body. In addition, knowledge and elimination of the rigid body mode is necessary for the implementation of a scheme described by this author in an earlier work. The importance of the earlier work is that it reduced the sensitivity of the BEM to changes and errors in the input data. In this paper the causes, and the effects of the rigid body mode on the BEM, the correct interpretation of the fundamental solution for displacements and an algorithm for determining and accounting for the rigid body mode are discussed. A numerical example validates the ideas in this paper for the indirect version. The algorithm for the direct version is presented without a numerical example in the Appendices.     

The fast spinning motion of a rigid body in the presence of a gyrostatic momentum ?3

Summary In this paper, the rotational motion of a rigid body about a fixed point in the Newtonian force field [1] with a gyrostatic momentum ₃ about thez-axis is considered. The equations of motion and their first integrals are obtained and reduced to a quasi-linear autonomous system with two degrees of freedom with one first integral. Poincaré's small parameter method [2] is applied to investigate the analytical periodic solutions of the equations of motion of the body with one point fixed, rapidly spinning about one of the principal axes of the ellipsoid of inertia. A geometric interpretation of motion is given by using Euler's angles [3] to describe the orientation of the body at any instant of time.     

Magnetic compatibility of magnetic induction transducers with a moving object

Different technical solutions are proposed to solve the problem of magnetic compatibility of magnetic induction transducers with a moving object. The solutions are based on measuring the difference between magnetic induction vectors due to the object and the external magnetic field at selected points in space and by finding the Poisson parameters of the object at the transducer location. Translated from Izmeritel'naya Tekhnika, No. 9, pp. 44–46, September, 1997.     

Flexible body dynamics in a local frame with explicitly predicted motion

This paper deals with formulation of dynamics of a moving flexible body in a local frame of reference. In a conventional approach the local frame is normally fixed to the corresponding body and always represents the positions and angles of the body: the positions and angles are represented by Cartesian coordinates and Euler angles or Euler parameters, respectively. The elastic degrees of freedom are expressed by, e.g. nodal coordinates in a finite element analysis, modal coordinates, etc. However, the choice of these variables as the generalized coordinates makes the resulting equations of motion extremely complicated. This is because the representation of the rotation of a body is highly non‐linear and this non‐linearity makes the coefficient matrices dependent on the coordinates themselves. In this paper, we propose an alternative way of treating the issue by explicitly predicting the body motions and regularly updating the local frame. First, the motion of the local frame is assumed to explicitly follow the associated moving body. Then, the equations of motion are derived in a set of generalized coordinates that express both rigid‐body and elastic degrees of freedom in the local frame. These equations are solved by a time integration with a given time interval. The motion of the local frame in the interval is estimated from a prediction of the rigid‐body motions. Then, the gap between the predicted and the actual motions is evaluated. Finally, the predictions are iteratively corrected by the obtained responses in the rigid‐body motions so that the gap should remain within an imposed tolerance. Copyright © 2009 John Wiley & Sons, Ltd.     

从正投影光流场计算刚体运动参数和结构

从光流场恢复刚体三维运动和结构是计算机视觉中一个基本问题。本文研究从正投影光流场恢复刚体三维运动和结构问题,建立了光流运动方程,提出一种判别多个光流点是否共面或是否属于同一刚体的有效方法。证明了平移运动刚体有两个自由度,旋转运动刚体有一个自由度,一般运动刚体有三个自由度,至少需要四个光流点才能获得一般运动刚体的流参数(含一比例因子)。     

Research and Application for the Regularity of Distribution about Curvature Radius and Curvature Center of the Linkage Point Track in a Link Mechanism

It is illustrated that there exists an inflection circle on the linkage rigid body by the principle of relative motion. Confirmed methods of the inflection circle, curvature radius and curvature center of the point track on the linkage rigid body are given in the case of the different contact type of move instantaneous center line and static instantaneous center line. The regularity of distribution of curvature radius and curvature center of the point track is researched. The identification methods called determination parameters and auxiliary vertical line of the diameter and direction of the inflection circle in the four bar mechanism are pointed out. A design method of the crane hoisting mechanism is discussed in the end of this paper.     

Optimization of product configuration design using functional requirements and constraints

We consider the general problem of designing mechanical parts moving in contact under the influence of externally applied loads. Geometrically, the problem may be characterized in terms of a conjugate triplet, which is formed by the two shapes moving in contact and their relative motion. We show that every such triplet belongs to one or more classes of functionally equivalent designs that may be represented uniquely by maximal triplets, corresponding respectively to the two largest contact shapes that are guaranteed to contain all other possible solutions to the contact design problem. In practical terms, the proposed characterization of the contact problem enables the systematic exploration of the design space using fully defined representatives of the functionally equivalent class of parts. Furthermore, such exploration may be performed using standard tools from geometric modeling, and without assuming any particular parameterization that necessarily restrict both the design space and possible computational techniques for exploring feasible designs. Because the proposed approach supports the generation of an essentially unlimited space of design solutions for a given contact problem, it is particularly effective at the conceptual design stage. Electronic Publication     

基于转动惯量的刚体9个惯性参数的测量

针对三维空间,提出了一种可以同时测量刚体9个惯性参数的新方法。利用气体静压轴承低速自由转动时其角速度是一个随时间衰减的单指数函数这一运动规律,测量物体绕任意轴的转动惯量,通过9次测量最终求出刚体的9个惯性参数。设计了一套物体惯性参数测量仪,该测量仪可以同时测量三维空间中物体的9个惯性参数。测量过程中无需重新装配,减少了中间测试量及人为干预误差,使测量时间缩短,测量精度提高。     

In-plane dynamic speckle interferometry: comparison between a combined speckle interferometry/speckle correlation and an update of the reference image

A common problem during study of, for instance, tensile tests with interferometers is that the sample moves too much so that the speckles decorrelate and no phase information is obtained. Two ways to overcome this problem are compared: a combination of speckle interferometry and speckle correlation and a method in which the reference image is updated during the experiment. The comparison shows that both techniques can be used to measure the deformation of an object even if it is exposed to rigid body motions. Both techniques are applied to measurements of microscale deformation fields of an adhesive joint in a carbon-fiber epoxy composite.     

A NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF VEHICLES MOVING ON FLEXIBLE STRUCTURES HAVING GAPS

A numerical method is presented for the dynamic analysis of vehicles moving on flexible structures which contain gaps. The Lagrange multipliers associated with the kinematic constraints of the vehicle components and the contact forces between the rigid wheels of the vehicle and the flexible structures are simultaneously computed with the solutions of the equations of motion by using the iterative schemes. On the kinematic joints and on the possible contact points the velocity and acceleration constraints as well as the displacement constraints are satisfied by the monotone reductions of the corresponding error vectors. And a well-developed simple one-step time integration of ordinary differential equation is employed for the solution of the equations of motion. Convergences of the iterative schemes are analysed and numerical simulations are conducted. © 1997 by John Wiley & Sons, Ltd.     

Towards Eliminating the Displacement Bias Due to Out‐Of‐Plane Motion in 2D Inverse Problems: A Case of General Rigid‐Body Motion

This article reports an important development related to the inverse characterization of material constitutive parameters using 2D optical displacement field measurements. The out‐of‐plane motion of the specimen, which has traditionally been considered detrimental to the accuracy of these experiments, is generally of two types: (a) a global out‐of‐plane rigid‐body motion of the specimen relative to the camera and (b) out‐of‐plane deformations resulting from material heterogeneity or out‐of‐plane loads. In an earlier article, we proposed to partially relax the condition of no out‐of‐plane motion by allowing for (b) in 2D inverse procedures, in the context of finite element update method, and introduced a compensation strategy by redefining the cost function on the object plane of the acquisition system. The experimental errors due to (a) were assumed negligible. Here, we propose that the global rigid‐body motion (a) may also be recovered within the inverse procedures, hence completely waiving the condition of strictly in‐plane displacements for inverse problems. The recovery is achieved by identifying and including the possible modes of global rigid‐body motion within the cost function together with careful selection of test configuration. The effects of individual rigid‐body modes on the computed displacement fields are studied in detail and utilized as a guideline for selection of test configuration. The approach is fully demonstrated and validated by simulated as well as real experiments for determining elastic constants of isotropic and orthotropic materials using different experimental setups. Effects of improving the optimization routine, for cost function minimization, and experimental noise are also presented.