Robust multiscale algorithms for gradient‐based motion estimation

Gradient‐based techniques represent a very popular class of approaches to estimate motions. A robust multiscale algorithm of hierarchical estimation for gradient‐based motion estimation is proposed in this article using a combination of robust statistical method and multiscale technique. In such a multiscale approach of hierarchical estimation, motion at each level of the pyramid is estimated using different gradient filters. The iterative multiscale estimation begins by using five‐tap central filter, and it is switched to nine‐tap Timoner filter after a few iterations. In addition, robust M‐estimators are applied at each level of the pyramid to overcome the problem of the outliers caused by illumination variations and motion discontinuities in motion estimation. Experimental simulations show that the new algorithm not only provides an improvement in estimator accuracy, but also achieves computational speedups. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 17, 333–340, 2007     

2-D high-frame-rate dynamic elastography using delay compensated and angularly compounded motion vectors: preliminary results

This paper describes a new ultrasound-based system for high-frame-rate measurement of periodic motion in 2-D for tissue elasticity imaging. Similarly to conventional 2-D flow vector imaging, the system acquires the RF signals from the region of interest at multiple steering angles. A custom sector subdivision technique is used to increase the temporal resolution while keeping the total acquisition time within the range suitable for real-time applications. Within each sector, 1-D motion is estimated along the beam direction. The intra- and inter-sector delays are compensated using our recently introduced delay compensation algorithm. In-plane 2-D motion vectors are then reconstructed from these delay-compensated 1-D motions. We show that Young's modulus images can be reconstructed from these 2-D motion vectors using local inversion algorithms. The performance of the system is validated quantitatively using a commercial flow phantom and a commercial elasticity phantom. At the frame rate of 1667 Hz, the estimated flow velocities with the system are in agreement with the velocity measured with a pulsed-wave Doppler imaging mode of a commercial ultrasound machine with manual angle correction. At the frame rate of 1250 Hz, phantom Young's moduli of 29, 6, and 54 kPa for the background, the soft inclusion, and the hard inclusion, are estimated to be 30, 11, and 53 kPa, respectively.     

Content‐aware full search scheme for motion estimation

Taking into consideration computational complexity and design regularity, this article proposes a content‐aware full search (CAFS) block matching scheme for motion estimation. Full search (FS) is widely employed in hardware design of block matching because of its regular data flow. But the huge computational complexity of FS makes it infeasible especially in low‐power environments. To reduce the required computational complexity, CAFS using a content‐aware computation allocation mechanism dynamically distributes computation to blocks with distinct motion content based on center‐biased distribution characteristics of motion vectors. Because all operations of CAFS can be performed by a series of ±2 FSs, the hardware of CAFS can be easily extended by the design of FS. Experimental results indicates that CAFS can achieve about 0.5–1.4 dB quality improvement over original FS in football and table tennis sequences under the same computation. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 14, 246–252, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20028     

A technique of object‐adaptive vertex‐based shape coding for MPEG‐4 videos

The MPEG‐4 visual standard is the first international standard that allows the transmission of arbitrarily shaped video objects and provides technologies to view, access, and manipulate objects rather than pixels. It addresses the encoding of video objects by shape coding, motion estimation, and texture coding for interactivity, high compression, and scalability. Current binary shape‐coding techniques can be classified into two categories: bitmap based and contour based. O'Connell (1997) proposed an object‐adaptive vertex‐based shape‐coding method to improve the efficiency of shape coding. This method encodes the relative locations of a video object's vertices by adapting the representation to the dynamic range of the relative locations and by exploiting an octant‐based representation for each relative location. We propose an extension of O'Connell's method. Two relative locations of a video object's vertices are grouped and the x pairs and y pairs of the locations are encoded, respectively. Simulation results demonstrate that our method outperforms O'Connell's method. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 11, 277–282, 2000     

An improved continued‐fraction‐based high‐order transmitting boundary for time‐domain analyses in unbounded domains

A high‐order local transmitting boundary to model the propagation of acoustic or elastic, scalar or vector‐valued waves in unbounded domains of arbitrary geometry is proposed. It is based on an improved continued‐fraction solution of the dynamic stiffness matrix of an unbounded medium. The coefficient matrices of the continued‐fraction expansion are determined recursively from the scaled boundary finite element equation in dynamic stiffness. They are normalised using a matrix‐valued scaling factor, which is chosen such that the robustness of the numerical procedure is improved. The resulting continued‐fraction solution is suitable for systems with many DOFs. It converges over the whole frequency range with increasing order of expansion and leads to numerically more robust formulations in the frequency domain and time domain for arbitrarily high orders of approximation and large‐scale systems. Introducing auxiliary variables, the continued‐fraction solution is expressed as a system of linear equations in iω in the frequency domain. In the time domain, this corresponds to an equation of motion with symmetric, banded and frequency‐independent coefficient matrices. It can be coupled seamlessly with finite elements. Standard procedures in structural dynamics are directly applicable in the frequency and time domains. Analytical and numerical examples demonstrate the superiority of the proposed method to an existing approach and its suitability for time‐domain simulations of large‐scale systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Mean‐strain eight‐node hexahedron with optimized energy‐sampling stabilization for large‐strain deformation

A method for stabilizing the mean‐strain hexahedron for applications to anisotropic elasticity was described by Krysl (2015). The technique relied on a sampling of the stabilization energy using the mean‐strain quadrature and the full Gaussian integration rule. This combination was shown to guarantee consistency and stability. The stabilization energy was expressed in terms of input parameters of the real material, and the value of the stabilization parameter was fixed in a quasi‐optimal manner by linking the stabilization to the bending behavior of the hexahedral element (Krysl, submitted). Here, the formulation is extended to large‐strain hyperelasticity (as an example, the formulation allows for inelastic behavior to be modeled). The stabilization energy is expressed through a stored‐energy function, and contact with input parameters in the small‐strain regime is made. As for small‐strain elasticity, the stabilization parameter is determined to optimize bending performance. The accuracy and convergence characteristics of the present formulations for both solid and thin‐walled structures (shells) compare favorably with the capabilities of mean‐strain and other high‐performance hexahedral elements described in the open literature and also with a number of successful shell elements. Copyright © 2015 John Wiley & Sons, Ltd.     

Hybrid state‐space time integration in a rotating frame of reference

A time integration algorithm is developed for the equations of motion of a flexible body in a rotating frame of reference. The equations are formulated in a hybrid state‐space, formed by the local displacement components and the global velocity components. In the spatial discretization the local displacements and the global velocities are represented by the same shape functions. This leads to a simple generalization of the corresponding equations of motion in a stationary frame in which all inertial effects are represented via the classic global mass matrix. The formulation introduces two gyroscopic terms, while the centrifugal forces are represented implicitly via the hybrid state‐space format. An angular momentum and energy conserving algorithm is developed, in which the angular velocity of the frame is represented by its mean value. A consistent algorithmic damping scheme is identified by applying the conservative algorithm to a decaying response, which is rendered stationary by an increasing exponential factor that compensates the decay. The algorithmic damping is implemented by introducing forward weighting of the mean values appearing in the algorithm. Numerical examples illustrate the simplicity and accuracy of the algorithm. Copyright © 2011 John Wiley & Sons, Ltd.     

Motion compensation by phase correction for synthetic‐aperture side‐scan sonar imaging

This article presents a robust motion estimation and correction technique for the realization of synthetic‐aperture side‐scan sonar imaging. It utilizes the redundancy provided by the multiple‐element receiver array configuration. Physical‐array subimages are used for the estimation of the motion errors between adjacent receiver positions. Subsequently, the motion errors are formulated in the form of phase perturbations and are corrected accordingly by making adjustments to the wave‐field data samples prior to the formation of synthetic‐aperture images. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 14, 259–261, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20029     

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.     

Interaction of first- and second-order direction in motion-defined motion

Motion-defined motion can play a special role in the discussion of whether one or two separate systems are required to process first- and second-order information because, in contrast to other second-order stimuli, such as contrast-modulated contours, motion detection cannot be explained by a simple input nonlinearity but requires preprocessing by motion detectors. Furthermore, the perceptual quality that defines an object (motion on the object surface) is identical to that which is attributed to the object as an emergent feature (motion of the object), raising the question of how these two object properties are linked. The interaction of first- and second-order information in such stimuli has been analyzed previously in a direction-discrimination task, revealing some cooperativity. Because any comprehensive integration of these two types of motion information should be reflected in the most fundamental property of a moving object, i.e., the direction in which it moves, we now investigate how motion direction is estimated in motion-defined objects. Observers had to report the direction of moving objects that were defined by luminance contrast or in random-dot kinematograms by differences in the spatiotemporal properties between the object region and the random-noise background. When the dots were moving coherently with the object (Fourier motion), direction sensitivity resembled that for luminance-defined objects, but performance deteriorated when the dots in the object region were static (drift-balanced motion). When the dots on the object surface were moving diagonally relative to the object direction (theta motion), the general level of accuracy declined further, and the perceived direction was intermediate between the veridical object motion direction and the direction of dot motion, indicating that the first- and second-order velocity vectors are somehow pooled. The inability to separate first- and second-order directional information suggests that the two corresponding subsystems of motion processing are not producing independent percepts and provides clues for possible implementations of the two-layer motion-processing network.     

Three‐stage model for robust real‐time face tracking

We propose a novel face tracking framework, the three‐stage model, for robust face tracking against interruptions from face‐like blobs. For robust face tracking in real‐time, we considered two critical factors in the construction of the proposed model. One factor is the exclusion of background information in the initialization of the target model, the extraction of the target candidate region, and the updating of the target model. The other factor is the robust estimation of face movement under various environmental conditions. The proposed three‐stage model consists of a preattentive stage, an assignment stage, and a postattentive stage with a prerecognition phase. The model is constructed by means of effective integration of optimum cues that are selected in consideration of the trade‐off between true positives and false positives of face classification based on a context‐dependant type of categorization. The experimental results demonstrate that the proposed tracking method improves the performance of the real‐time face tracking process in terms of success rates and with robustness against interruptions from face‐like blobs. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 17, 321–327, 2007     

Active stiffness control of wind‐rain‐induced vibration of prototype stay cable

The cables in a cable‐stayed bridge usually possess low inherent damping and are prone to wind‐induced, traffic‐induced, and wind‐rain‐induced vibrations. This paper establishes an active control algorithm using the stiffness control method to suppress wind‐rain‐induced vibration of prototype stay cables. By neglecting the axial inertia force and the modal coupling, the governing equations of motion of wind‐rain‐induced vibration control of prototype stay cables with active stiffness control algorithm are first derived. The fourth‐order Runge–Kutta method is then introduced to find the numerical solutions to the problem. Extensive parameter studies have been carried out for investigating the features of the control method as a design guideline. Copyright © 2007 John Wiley & Sons, Ltd.     

Thermo‐elasto‐plastic finite element analysis of quasi‐state processes in Eulerian reference frames

An Eulerian finite element formulation for quasi‐state one way coupled thermo‐elasto‐plastic systems is presented. The formulation is suitable for modeling material processes such as welding and laser surfacing. In an Eulerian frame, the solution field of a quasi‐state process becomes steady state for the heat transfer problem and static for the stress problem. A mixed small deformation displacement elasto‐plastic formulation is proposed. The formulation accounts for temperature dependent material properties and exhibits a robust convergence. Streamline upwind Petrov–Galerkin (SUPG) is used to remove spurious oscillations. Smoothing functions are introduced to relax the non‐differentiable evolution equations and allow for the use of gradient (stiffness) solution scheme via the Newton–Raphson method. A 3‐dimensional simulation of a laser surfacing process is presented to exemplify the formulation. Results from the Eulerian formulation are in good agreement with results from the conventional Lagrangian formulation. However, the Eulerian formulation is approximately 15 times faster than the Lagrangian. Copyright © 2001 John Wiley & Sons, Ltd.     

A continued‐fraction‐based high‐order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry

A high‐order local transmitting boundary is developed to model the propagation of elastic waves in unbounded domains. This transmitting boundary is applicable to scalar and vector waves, to unbounded domains of arbitrary geometry and to anisotropic materials. The formulation is based on a continued‐fraction solution of the dynamic‐stiffness matrix of an unbounded domain. The coefficient matrices of the continued fraction are determined recursively from the scaled boundary finite element equation in dynamic stiffness. The solution converges rapidly over the whole frequency range as the order of the continued fraction increases. Using the continued‐fraction solution and introducing auxiliary variables, a high‐order local transmitting boundary is formulated as an equation of motion with symmetric and frequency‐independent coefficient matrices. It can be coupled seamlessly with finite elements. Standard procedures in structural dynamics are directly applicable for evaluating the response in the frequency and time domains. Analytical and numerical examples demonstrate the high rate of convergence and efficiency of this high‐order local transmitting boundary. Copyright © 2007 John Wiley & Sons, Ltd.     

Object‐oriented finite element analysis of thermo‐hydro‐mechanical (THM) problems in porous media

The design, implementation and application of a concept for object‐oriented in finite element analysis of multi‐field problems is presented in this paper. The basic idea of this concept is that the underlying governing equations of porous media mechanics can be classified into different types of partial differential equations (PDEs). In principle, similar types of PDEs for diverse physical problems differ only in material coefficients. Local element matrices and vectors arising from the finite element discretization of the PDEs are categorized into several types, regardless of which physical problem they belong to (i.e. fluid flow, mass and heat transport or deformation processes). Element (ELE) objects are introduced to carry out the local assembly of the algebraic equations. The object‐orientation includes a strict encapsulation of geometrical (GEO), topological (MSH), process‐related (FEM) data and methods of element objects. Geometric entities of an element such as nodes, edges, faces and neighbours are abstracted into corresponding geometric element objects (ELE–GEO). The relationships among these geometric entities form the topology of element meshes (ELE–MSH). Finite element objects (ELE–FEM) are presented for the local element calculations, in which each classification type of the matrices and vectors is computed by a unique function. These element functions are able to deal with different element types (lines, triangles, quadrilaterals, tetrahedra, prisms, hexahedra) by automatically choosing the related element interpolation functions. For each process of a multi‐field problem, only a single instance of the finite element object is required. The element objects provide a flexible coding environment for multi‐field problems with different element types. Here, the C++ implementations of the objects are given and described in detail. The efficiency of the new element objects is demonstrated by several test cases dealing with thermo‐hydro‐mechanical (THM) coupled problems for geotechnical applications. Copyright © 2006 John Wiley & Sons, Ltd.     

Polygon‐based contact resolution for superquadrics

The representation of discrete objects in the discrete element modelling is a fundamental issue, which has a direct impact on the efficiency of discrete element implementation and the dynamic behaviour of particulate systems. Disks and spheres are the most commonly used geometric shapes due to their geometric simplicity and computational efficiency, but they are unable to provide resistance to rolling motion. For this reason, some non‐circular/spherical objects, such as polygons/polyhedrons, superquadrics, or the clustering of disks/spheres to form irregular shapes, are introduced. When superquadrics are used as discrete elements, the bottleneck of contact resolution is associated with the searching for intersections of two non‐linear functions, which is a very expensive operation and may sometimes fail in finding the solution. In this work, an efficient and robust algorithm is proposed for contact resolution of 2D superquadrics, in which any superquadric is approximated with a convex polygon through adaptive sampling; then by clipping two polygons, an efficient linear algorithm is performed to search for intersections and overlap area of the polygons; the contact forces and directions are determined by employing a newly established corner/corner contact model. It is important to highlight that the proposed methodology can also be extended to general non‐circular discrete object cases. The performance of the algorithm is demonstrated via numerical examples. Copyright © 2005 John Wiley & Sons, Ltd.     

Locking in the incompressible limit for the element‐free Galerkin method

Volumetric locking (locking in the incompressible limit) for linear elastic isotropic materials is studied in the context of the element‐free Galerkin method. The modal analysis developed here shows that the number of non‐physical locking modes is independent of the dilation parameter (support of the interpolation functions). Thus increasing the dilation parameter does not suppress locking. Nevertheless, an increase in the dilation parameter does reduce the energy associated with the non‐physical locking modes; thus, in part, it alleviates the locking phenomena. This is shown for linear and quadratic orders of consistency. Moreover, the biquadratic order of consistency, as in finite elements, improves the locking behaviour. Although more locking modes are present in the element‐free Galerkin method with quadratic consistency than with standard biquadratic finite elements. Finally, numerical examples are shown to validate the modal analysis. In particular, the conclusions of the modal analysis are also confirmed in an elastoplastic example. Copyright © 2001 John Wiley & Sons, Ltd.     

A singular‐value decomposition (SVD)‐based generalized finite difference (GFD) method for close‐interaction moving boundary flow problems

In this paper, we present a study on a singular‐value decomposition (SVD)‐based generalized finite difference (GFD) method and a nodal selection scheme for moving body/boundary flow problems formulated on a hybrid Cartesian cum meshfree grid system. The present study shows that the SVD‐based method is more robust and accurate than the conventional least‐squares‐based GFD scheme. A nodal selection scheme is also introduced to overcome the problem of numerical instability associated with the clustering of computational nodes. Such nodal clustering occurs dynamically when moving bodies or boundaries approach within close proximity of each other, resulting in the overlap of their meshfree grids. The nodal scheme is applied to close‐interaction flow problems as exemplified by the squeezing action of a circular cylinder through a very narrow slot and the close proximity bypass interaction of two oscillating circular cylinders. Copyright © 2008 John Wiley & Sons, Ltd.     

Parallel efficient mesh motion using radial basis functions with application to multi‐bladed rotors

Radial basis functions are used to provide a solution to the problem of mesh motion for unsteady aerodynamic simulation. The method is independent of connectivity and produces high‐quality meshes, but is expensive for large meshes in its full form. Hence, the efficiency of the technique has been greatly improved here by reducing the number of surface points used to define deformations of the surface, and the minor error in position that this implies at other surface points is corrected with a simple decaying perturbation, thus splitting the method into a primary basis function method and a secondary local correction method. This means that the exact surface is retained, but the mesh motion is significantly faster, while splitting the motion into two stages allows both the methods to work on appropriate problems given their relative strengths. An example deformation for a 5×10⁶ cell helicopter rotor mesh with an exaggerated cyclic pitch motion shows excellent mesh quality, thus validating a scheme that is also simple, robust and readily parallelized. Copyright © 2009 John Wiley & Sons, Ltd.