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     

On the use of shadows in stance recovery

The image of an object and of the shadow it casts on a planar surface provides important cues for three‐dimensional (3D) stance recovery. We assume that the position of the plane on which the shadow lies with respect to a pinhole camera is known and that the position of the light source is unknown. If the light source is sufficiently far away that parallel projection may be assumed, then knowledge of two point correspondences between images of feature points and images of their shadows is enough to determine the position of the object and the direction of the light source. If the light source is close enough that the shadow points are obtained via perspective projection, then there is a one‐parameter infinite family of solutions for the position of the object and the light source. Determining the stance of an object is highly sensitive to noise, so we provide algorithms for stance recovery that take into account known information about the object. In our experiments, the errors for the location of the 3D feature points obtained by these algorithms are generally less than 0.2% times the error in pixels in the image points and the errors for the 3D directions of the links is roughly 0.04° times the error in pixels, normalized by the distance to the object from the camera and the length of the link. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 11, 315–330, 2000     

Optimum rigid motion with one perspective view

One of the central problems in dynamic computer vision is the determination of motion from correspondence of points on the visible surface of a moving object obtained at two different times. In the problem we consider, the initial position of several feature points on some object is assumed to be known. Then at some later time instant the corresponding perspective projection of those points is given. The moving body may be nonrigid or the measurements may be corrupted with noise. In either case, we determine the multiplicity of possible solution for the best-fitting rigid motion. We show that whenever at least three point correspondences are given, there are at most two possible solutions for the best-fitting rigid motion if the object space is two-dimensional, while there are at most forty possible solutions if the object space is three-dimensional. In the latter case the number of possible solutions drops to four if three point correspondence are known, the body is rigid, and the measurements are noise-free. Several examples are worked out to illustrate our results.©1994 John Wiley & Sons Inc     

Inverse scattering for optical coherence tomography

Inverse scattering theory for optical coherence tomography (OCT) is developed. The results are used to produce algorithms to resolve three-dimensional object structure, taking into account the finite beam width, diffraction, and defocusing effects. The resolution normally achieved only in the focal plane of the OCT system is shown to be available for all illuminated depths in the object without moving the focal plane. Spatially invariant resolution is verified with numerical simulations and indicates an improvement of the high-resolution cross-sectional imaging capabilities of OCT.     

Fully plastic analyses of plane strain single-edge-cracked specimens subject to combined tension and bending

Accurate yield surfaces of plane strain single-edge-cracked specimens having shallow as well as deep cracks are developed using finite element limit analyses and monotonic interpolation functions. Fully plastic shallow crack configurations are classified based on certain aspects of the yield surfaces. Relationships between incremental plastic crack tip and crack mouth opening displacements and incremental load point displacement/rotation are obtained for a wide range of relative crack depths and loading ratios. Fully plastic crack-tip fields for a sufficiently deep crack in a single-edge cracked specimen are examined to provide the stress triaxiality and the angular orientation of flow line at the crack tip in terms of the remotely applied tension-to-bending ratio. Evidence for fully plastic crack-tip stress fields consisting of an incomplete Prandtl fan and a crack plane constant state region is discussed.     

射影线束形成的二阶曲线及其退化形式

论文用图示法首次系统表达了在二射影平面场中,存在3种形式的射影对应线束。这些对应线束形成二阶曲线时有一定的变化规律。其中底都为非固有点的二线束形成双曲线;底为固有点和非固有点的二线束形成抛物线;底都为固有点的二线束,只要旋转其中之一就可以分别形成双曲线、抛物线和椭圆。这些结论为我们实现二阶曲线之间的转换奠定了理论基础。     

A 2.5D finite/infinite element approach for modelling visco‐elastic bodies subjected to moving loads

The objective of this study is to propose a 2.5D finite/infinite element procedure for dealing with the ground vibrations induced by moving loads. Besides the two in‐plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out‐of‐plane wave transmission. The profile of the half‐space is divided into a near field and a semi‐infinite far field. The near field containing loads and irregular structures is simulated by the finite elements, while the far field covering the soils extending to infinity by the infinite elements with due account taken of the radiation effects for moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, the accuracy of the proposed method is verified through comparison with a number of analytical solutions. Copyright © 2001 John Wiley & Sons, Ltd.     

On exact solutions of the unsteady navierstokes equations—the vortex with instantaneous curvilinear axis

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve Γ, the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether ω is greater than, equal to or less than σ, where ω is angular velocity of the basic rotation and σ is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve Γ is illustrated graphically by considering an example of the flow between coaxial rotating disks.     

基于时空坐标图像的运动点目标检测方法

针对复杂背景下运动点目标检测方法存在的局限性,提出从时间空间角度检测运动目标的方法.在时间空间域里,背景的复杂纹理表现为无限长直线,运动目标则表现为有限长线段.针对该特点,运用逐点灰度均值将背景与运动点目标分离,并根据投影关系将目标投影到二维空间,获得直观的目标运动轨迹.试验结果表明,该方法能较好地从复杂背景中分离出速度不大于1像素/帧的点目标,且可同时进行多目标的检测,抗噪声能力强.     

Stokes flow due to infinite arrays of stokeslets in three dimensions

Infinite periodic arrays of stokeslets in three dimensions are summed up by obtaining various rapidly converging infinite series. The three cases treated here are: 1. Identical stokeslets distributed at constant intervals on a line parallel to a plate, 2. An array of identical stokeslets distributed on a two-dimensional periodic lattice on a plane parallel to a plate, 3. The same array, but parallel to and in between two plates. Computational results are shown and comparisons with previously averaged expressions are made.     

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.     

Analytical solutions of fully plastic crack-tip higher order fields under antiplane shear

Analytical solutions of higher order fields in a fully plastic power-law hardening material are presented. By the use of hodograph transformation and asymptotic analysis the stress and strain exponents, angular distributions of shear stresses and strains are analytically determined. Special cases, such as linearly elastic, perfectly plastic materials are discussed. Similar characteristics between mode III and mode I plane strain, and mode II plane stress are examined. Comparison of four-term asymptotic solutions with exact and leading term solutions in an infinite strip with a semi-infinite crack under constant displacements along its edges is provided.     

Reconstruction of three-dimensional chemiluminescence images with a maximum entropy deconvolution algorithm

Three-dimensional (3D) images of flame emission are reported using a single direction of optical access. A Cassegrain system was designed with narrow depth of field. Images from this system are dominated by emission from the focused object plane with defocused contributions from out-of-plane structures. Translation of one mirror in the system allows for scanning the object plane through the flame. Images were taken at various depths to create a family of images. Reconstruction of the 3D flame structure was accomplished using a maximum entropy algorithm adapted for use with 3D imaging. Spatial resolution in the direction of imaging is examined using laminar flames with variable offset.     

Method of determining an abutting line or plane from measurement data

Conclusions The determination of abutting neighborhoods, straight lines, and planes causes difficulties for measuring laboratory workers. If for computing the abutting neighborhood method [1] is adopted, then for determination of non-rectilinearity and nonplanarity only partial solutions are worked out.The proposed method of determining an abutting straight line or plane completely satisfies the requirements of GOST 10356-63, and has an accuracy sufficient for practical use (for suitable scaling of the graphs). It eliminates the need for time-consuming alignment of a part during measurements (Appendix 2 of GOST 10356-63), which does not ensure accuracy in the results. The advantages of the method proposed in this article are especially evident in these cases: 1) accurate measurements, 2) large surfaces, and 3) irregular change of the ordinates of the points of the actual surface.Translated from Izmeritel'naya Tekhnika, No. 9, pp. 88–92, September, 1968.     

Shape and motion reconstruction of non rigid objects from their 2D projections under uniform expansion conditions

This paper deals with the 3D-motion and structure reconstruction of a particular class of nonrigid objects based on a sequence of their 2D orthographic projections (images). The investigation focuses on the case where it is known a-pri-ori that the object deforms continuously in a uniform manner performing either expansion or contraction at a constant but, at the same time, unknown rate. Epipolar equations are properly extended to meet the requirements of this particular problem. It is shown that four point correspondences over four views yield a unique solution to motion and structure reconstruction. The theory is supported by a numerical result.     

Necking in coating flow over periodic substrates

The free-boundary problem determining the shape of a layer of viscous fluid coating a substrate while draining steadily under gravity is solved analytically for substrates taking the form of a periodic array of long plates of arbitrary width and spacing. The mathematical problem involves solving Poisson’s equation with constant forcing term in the fluid layer subject to vanishing Neumann and Dirichlet conditions on the free boundary. By considering the problem in a potential plane and using conformal mapping, a two-parameter family of solutions is obtained in the form of an infinite series. Explicit, closed-form solutions are derived in the limiting cases of a single gap perforating an infinitely wide plate, and for an array of evenly spaced point plates. In these cases explicit expressions are obtained for the thinning, or necking, of the fluid layer in the gap regions between plates.     

运动背景中结合特征位移矢量场模糊分割与 OTSU法的运动检测

运动背景中的运动检测难度较大,背景运动补偿后差分以及分割光流场可实现动目标和背景的分离,差分前需进行鲁棒的背景估计,且差分后易出现空洞,而光流估计在噪声以及目标运动速度较大时并不准确,尤其在光照变化时,两种方法均易失效。本文提出一种特征点位移矢量场模糊分割与图像自适应阈值化相结合的运动检测方法,实现在无任何关于运动目标或者运动背景先验信息条件下的动目标检测。通过改进的 SIFT匹配方法生成鲁棒的特征位移矢量场,采用模糊 C均值聚类算法对 SIFT位移矢量场进行无监督分类,实现动目标与背景特征的自适应分离。 OTSU法和形态学操作实现图像的自适应分割,用以修正特征点凸包,最终分割出动目标区域。与鲁棒的背景运动补偿后差分以及光流估计的对比实验表明,在目标运动速度较大、光照变化以及噪声情况下,本文方法均能够检测出运动目标,且在光照变化下的优势明显。     

Waves Past Porous Structures in a Two-layer Fluid

Havelock’s type of expansion theorems, for an integrable function having a single discontinuity point in the domain where it is defined, are utilized to derive analytical solutions for the radiation or scattering of oblique water waves by a fully extended porous barrier in both the cases of finite and infinite depths of water in two-layer fluid with constant densities. Also, complete analytical solutions are obtained for the boundary-value problems dealing with the generation or scattering of axi-symmetric water waves by a system of permeable and impermeable co-axial cylinders. Various results concerning the generation and reflection of the axisymmetric surface or interfacial waves are derived in terms of Bessel functions. The resonance conditions within the trapped region are obtained in various cases. Further, expansions for multipole-line-source oblique-wave potentials are derived for both the cases of finite and infinite depth depending on the existence of the source point in a two-layered fluid.     

Self-similar cylindrical magnetogasdynamic and ionizing shock waves

Self-similar flows behind a cylindrical blast wave in magnetogasdynamics are studied. The shock is assumed to be propagating in a medium at rest with non-uniform density permeated by an azimuthal magnetic field generated by a constant line current passing along the line source of the blast wave. The shock is a magnetogasdynamic or ionizing type according as the electrical conductivity of the gas is infinite everywhere or infinite behind the shock and zero ahead of it. For both these cases adiabatic flows as well as flows with zero temperature gradient (Isothermal) are considered. Numerical solutions for the same are obtained and a comparative study is made. It is found that, for Isothermal flows, self similar solutions do not exist, when the ambient density varies as the inverse square of the distance from the axis of symmetry along which flows the line current. A particular analytical solution has been obtained for the adiabatic flow.     

A new kernel in BIE and the exterior boundary value problem in plane elasticity

A new kernel with formulation of the relevant BIE (boundary integral equation) in plane elasticity is introduced. The new kernel is derived from a fundamental solution expressed in a pure deformable form. If the kernel is used, the regularity condition is satisfied for any loadings on the contour of the hole. The exterior boundary value problem is studied. The applied loadings on the contour in the exterior boundary value problem may not be in equilibrium. From the solutions of the exterior von Neumann problem and the exterior Dirichlet problem, numerical examinations and comparison based on the usage of the new kernel and the usual kernel are presented. It is proved that the usual kernel cannot be used for the case in which the loadings on the contour are not in equilibrium. A particular exterior Dirichlet problem for an infinite plate with an elliptic inclusion is considered. Resultant forces and moment are applied on the inclusion. In the problem, one must assume some additional translation and rotation for the inclusion that are determined by the applied loading condition.