Translation Matrices Research Articles

T-matrix method for closely adjacent obstacles

This paper presents a novel method to calculate the T-matrix for two non-spherical obstacles positioned close to each other, where the individual circumscribed spheres intersect. This is achieved by translating the obstacles coordinate systems, using translation matrices for spherical vector waves. The new circumscribing spheres enables the obstacles to be positioned close to each other. A new total T-matrix of the two-obstacle system can then be calculated using methods for composite particles, i.e., the superposition T-matrix method. This total T-matrix will generally be larger than the original ones, depending on the sizes of the circumscribing spheres used in the coordinate translation procedure. However, it is shown that the total T-matrix can be truncated after transformation to a common origin, without degrading the accuracy. The total truncated T-matrix is only slightly larger than the original individual ones. The method is demonstrated for electromagnetic scattering simulations of two metallic disks, closely adjacent to each other.

ProjFE: Prediction of fuzzy entity and relation for knowledge graph completion

A growing number of tasks about knowledge graph completion have been studied and improved recently, but most of them use translation matrices or reflect known entity to other space, always focusing on improving the method of translating known entities and relations. Differing from current works, our paper employs a combination operator instead of the translation matrix to avoid massive calculations, and takes fuzzy membership degree into consideration in the predicting process to enhance accuracy of projection. Hence, we propose a method called ProjFE to predict the missing parts of triplets for knowledge graph completion. This model uses fuzzy combination operators to combine the fuzzy known entities and relations. Score function is employed to access to a descending order of the correct candidates after combination, where the target entity is the top one. What is more, we use sigmoid and ReLU activation functions for evaluations, which could alleviate some undesirable gradient problems in the training process. It is worth noting that our method ProjFE tends to have a relatively smaller parameter size than some existing models. Besides, our model is proved to perform better in terms of Mean Rank.

Quantitative motion detection of in-hand objects for robotic grasp manipulation

In an actual grasp operation, grasp accidents (slant, rolling, turning over, and dropping) of in-hand objects occur frequently. Quantitative motion detection of in-hand objects is critical to optimize the grasp configuration and to improve the stability and dexterity of a grasp manipulation. In this article, an innovative method for quantitative measurement of the motions of in-hand objects is presented. Firstly, the slip information at object–finger interface between adjacent states is detected by three omnidirectional slip sensors; next, singular value decomposition method is applied to calculate the rotation and translation matrices according to the relative coordinate changes extracted from the slip information. Finally, Euler angles and the linear displacements which illustrate the motion of in-hand objects are quantitatively measured from the translation matrix and the rotation matrix, and the continuous motion track can be further established. Experiment results show that the proposed method is effective in detecting multiple motion information of in-hand objects.

KINEMATIC AND DYNAMIC ANALYSIS OF MULTIBODY SYSTEMS USING THE KRONECKER PRODUCT

This paper employ Khang’s definition of the partial derivative of a matrix with respect to a vector and the Kronecker product to define translational and rotational Hessian matrices. With these definitions, the generalized velocities in the expression of a linear acceleration or an angular acceleration are collected into a quadratic term. The relations of Jacobian and Hessian matrices in relative motion are then established. A new matrix form of Lagrange’s equations showing clearly the quadratic term of generalized velocities is also introduced.

Improved Generalized Single-Source Tangential Equivalence Principle Algorithm with Contact-Region Modeling Method for Array Structures

An improved generalized single-source tangential equivalence principle algorithm (GSST-EPA) is proposed for analyzing array structures with connected elements. In order to use the advantages of GSST-EPA, the connected array elements are decomposed and computed by a contact-region modeling (CRM) method, which makes that each element has the same meshes. The unknowns of elements can be transferred onto the equivalence surfaces by GSST-EPA. The scattering matrix in GSST-EPA needs to be solved and stored only once due to the same meshes for each element. The shift invariant of translation matrices is also used to reduce the computation of near-field interaction. Furthermore, the multilevel fast multipole algorithm (MLFMA) is used to accelerate the matrix-vector multiplication in the GSST-EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed method.

Unique and concise system translation matrices for evaluating optical aberration variations.

New unique and concise translation matrices are derived for evaluating the aberration variations of conceptual and real lenses when the paraxial marginal and chief ray paths are arbitrarily changed. They are helpful in investigating the general behaviors of lenses and optimizing the balanced aberrations of lens components in prime and zoom lenses. These new matrices, with a dimension of 9×9 for monochromatic aberrations and a dimension of 4×4 for chromatic aberrations, are derived based on our earlier algorithms of which four cases with distinct translation factors and matrices are required according to the relationships of the original and new positions of the object and pupil; otherwise, division-by-zero errors or insufficient numerical accuracy will be encountered. As a comparison, the new matrices have several advantages. First, by introducing four meaningful equivalent optical invariants, multiplying the old matrices, and simplifying the new matrices, they have concise expressions to significantly reduce the calculation time. Second, they are unique and always accurate to apply for all kinds of object and pupil positions without suffering any mathematical problems, i.e., four separated algorithms are no longer necessary. Third, due to the unique property, the component contributions of original aberrations to new aberrations can be directly evaluated and analyzed.

Flexible system of multiple RGB-D sensors for measuring and classifying fruits in agri-food Industry

The productivity of the agri-food sector experiences continuous and growing challenges that make the use of innovative technologies to maintain and even improve their competitiveness a priority. In this context, this paper presents the foundations and validation of a flexible and portable system capable of obtaining 3D measurements and classifying objects based on color and depth images taken from multiple Kinect v1 sensors. The developed system is applied to the selection and classification of fruits, a common activity in the agri-food industry. Being able to obtain complete and accurate information of the environment, as it integrates the depth information obtained from multiple sensors, this system is capable of self-location and self-calibration of the sensors to then start detecting, classifying and measuring fruits in real time. Unlike other systems that use specific set-up or need a previous calibration, it does not require a predetermined positioning of the sensors, so that it can be adapted to different scenarios. The characterization process considers: classification of fruits, estimation of its volume and the number of assets per each kind of fruit. A requirement for the system is that each sensor must partially share its field of view with at least another sensor. The sensors localize themselves by estimating the rotation and translation matrices that allow to transform the coordinate system of one sensor to the other. To achieve this, Iterative Closest Point (ICP) algorithm is used and subsequently validated with a 6 degree of freedom KUKA robotic arm. Also, a method is implemented to estimate the movement of objects based on the Kalman Filter. A relevant contribution of this work is the detailed analysis and propagation of the errors that affect both the proposed methods and hardware. To determine the performance of the proposed system the passage of different types of fruits on a conveyor belt is emulated by a mobile robot carrying a surface where the fruits were placed. Both the perimeter and volume are measured and classified according to the type of fruit. The system was able to distinguish and classify the 95% of fruits and to estimate their volume with a 85% of accuracy in worst cases (fruits whose shape is not symmetrical) and 94% of accuracy in best cases (fruits whose shape is more symmetrical), showing that the proposed approach can become a useful tool in the agri-food industry.

Method to automatically register scattered point clouds based on principal pose estimation

Three dimensional (3-D) modeling is important in applications ranging from manufacturing to entertainment. Multiview registration is one of the crucial steps in 3-D model construction. The automatic establishment of correspondences between overlapping views, without any known initial information, is the main challenge in point clouds registration. An automatic registration algorithm is proposed to solve the registration problem of rigid, unordered, scattered point clouds. This approach is especially suitable for registering datasets that are lacking in features or texture. In general, the existing techniques exhibit significant limitations in the registration of these types of point cloud data. The presented method automatically determines the best coarse registration results by exploiting the statistical technique principal component analysis and outputs translation matrices as the initial estimation for fine registration. Then, the translation matrices obtained from coarse registration algorithms are used to update the original point cloud and the optimal translation matrices are solved using an iterative algorithm. Experimental results show that the proposed algorithm is time efficient and accurate, even if the point clouds are partially overlapped and containing large missing regions.

A Truncated Singular Value Decomposition Enhanced Nested Complex Source Beam Method

This work presents a novel matrix compression algorithm to improve the computational efficiency of the nested complex source beam (NCSB) method. The algorithm is based on the application of the truncated singular value decomposition (TSVD) to the multilevel aggregation, translation, and disaggregation operations in NCSB. In our implementation, the aggregation/disaggregation matrices are solved by the truncated far-field matching, which is based on the directional far-field radiation property of the complex source beams (CSBs). Furthermore, the translation matrices are obtained according to the beam width of CSBs. Due to the high directivity of the radiation patterns of CSBs, all the far-field related interaction matrices are low-ranked. Therefore, TSVD can be employed and a new set of equivalent sources can be constructed by a linear combination of the original CSBs. It is proved that the radiation power of the new sources is proportional to the square of the corresponding singular values. This provides a theoretical guideline to drop the insignificant singular vectors in the calculation. In doing so, the efficiency of the original NCSB method can be much improved while a reasonably good accuracy is maintained. Several numerical tests are conducted to validate the proposed method.

The Error Control of Mixed-Form Fast Multipole Algorithm Based on the High-Order Multipole Rotation

In this letter, the mixed-form fast multipole algorithm (MF-FMA) with feasible error controllability is implemented through high-order multipole rotation that can make the translation matrices very sparse. The saving of both storage and CPU time makes it attainable to increase the number of harmonics in the middle frequency regime, thus shifting up the transition region of MF-FMA. Consequently, the broadband accuracy of the MF-FMA can be improved significantly.

Conforming shear-locking-free four-node rectangular finite element of moderately thick plate

AbstractAn outline of the modified Mindlin plate theory, which deals with bending deflection as a single variable, is presented. Shear deflection and cross-section rotation angles are functions of bending deflection. A new four-node rectangular finite element of moderately thick plate is formulated by utilizing the modified Mindlin theory. Shape functions of total (bending+shear) deflections are defined as a product of the Timshenko beam shape functions in the plate longitudinal and transversal direction. The bending and shear stiffness matrices, and translational and rotary mass matrices are specified. In this way conforming and shear-locking-free finite element is obtained. Numerical examples of plate vibration analysis, performed for various combinations of boundary conditions, show high level of accuracy and monotonic convergence of natural frequencies to analytical values. The new finite element is superior to some sophisticated finite elements incorporated in commercial software.

Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having three joints, each either revolute or prismatic and each with selectable compliance. The geometry of the mechanism and the location of the compliance frame relative to the mechanism base are each arbitrary but specified. Necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. We show that, for an appropriately constructed serial mechanism having at least one revolute joint, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. For each type of three-joint combination, requirements on the redundant mechanism geometry are identified for the realization of every point planar elastic behavior at a given location, just by changing the mechanism configuration and the joint compliances.

Domain decomposition scheme with equivalence spheres for the analysis of aircraft arrays in a large-scale range

we propose a domain decomposition scheme for solving scattering problem from multi-objects distribution in a large-scale range. Each sub-object is enclosed by an equivalence sphere. The scheme is composed of the equivalence process and translation process. In the equivalence process, the scattering fields from the sub-object are produced by the equivalence mode currents on the equivalence sphere. The equivalence mode currents are the current expansion of the body of revolution (BoR) basis functions, which are transformed from the current expansion of the Rao–Wilton-Glisson (RWG) basis functions. The multilevel fast multipole algorithm (MLFMA) is employed to accelerate the equivalence process. In the translation process, the mode translation matrices are obtained based on the BoR basis functions and the coordinate conversion method for computing the interactions among the equivalence spheres. The adaptive cross algorithm (ACA) is used to accelerate the evaluation of mode translation matrices. The proposed approach is very efficient for analysis of the objects distributed in a large-scale range. Numerical results demonstrate that the approach provides significant improvements in terms of memory requirements.

Design and Verification of Novel Low-Cost MR-Guided Small-Animal Stereotactic System

Stereotactic systems have been used for decades to position surgical instruments in important preclinical and clinical studies. We developed and verified a low-cost magnetic-resonance-guided system for accurate preclinical stereotactic operations on small animals. The system consists of both commercially available and custom components, including in-house software written in MATLAB to register coordinate spaces. The software registers target the image-space coordinates from magnetic resonance imaging to the physical space through a rigid-body transform. The transform uses singular value decomposition to determine rotation and translation matrices that are optimal in a least squares sense. Needle positioning and core biopsy studies were performed to verify the accuracy of the system. The needle positioning study demonstrated a sub-millimeter positioning error of 0.294 ± 0.156 mm while using a 26 s gauge Hamilton needle. Biopsy studies demonstrated >94 % success in accessing sub-millimeter stereotactic targets embedded in agarose gel phantoms. These favorable results confirm that despite its relatively low hardware cost (US$18,730) and easy assembly, the system is able to consistently access stereotactic targets on the spatial scale of a small animal.

Two-dimensional analytical modeling of a linear variable filter for spectral order sorting.

A two-dimensional thin film thickness model based on the geometry of a commercial coater which can calculate more effectively the profiles of linear variable filters (LVFs) has been developed. This is done by isolating the substrate plane as an independent coordinate (local coordinate), while the rotation and translation matrices are used to establish the coordinate transformation and combine the characteristic vector with the step function to build a borderline which can conclude whether the local mask will block the deposition or not. The height of the local mask has been increased up to 40 mm in the proposed model, and two-dimensional simulations are developed to obtain a thin film profile deposition on the substrate inside the evaporation chamber to achieve the specific request of producing a LVF zone width in a more economical way than previously reported [Opt. Express23, 5102 (2015)OPEXFF1094-408710.1364/OE.23.005102].

SU‐F‐T‐405: Development of a Rapid Cardiac Contouring Tool Using Landmark‐Driven Modeling

Purpose:This study aims to develop a tool to rapidly delineate cardiac substructures for use in dosimetry for large‐scale clinical trial or epidemiological investigations. The goal is to produce a system that can semi‐automatically delineate nine cardiac structures to a reasonable accuracy within a couple of minutes.Methods:The cardiac contouring tool employs a Most Similar Atlas method, where a selection criterion is used to pre‐select the most similar model to the patient from a library of pre‐defined atlases. Sixty contrast‐enhanced cardiac computed tomography angiography (CTA) scans (30 male and 30 female) were manually contoured to serve as the atlas library. For each CTA 12 structures were delineated. Kabsch algorithm was used to compute the optimum rotation and translation matrices between the patient and atlas. Minimum root mean squared distance between the patient and atlas after transformation was used to select the most‐similar atlas. An initial study using 10 CTA sets was performed to assess system feasibility. Leave‐one patient out method was performed, and fit criteria were calculated to evaluate the fit accuracy compared to manual contours.Results:For the pilot study, mean dice indices of .895 were achieved for the whole heart, .867 for the ventricles, and .802 for the atria. In addition, mean distance was measured via the chord length distribution (CLD) between ground truth and the atlas structures for the four coronary arteries. The mean CLD for all coronary arteries was below 14mm, with the left circumflex artery showing the best agreement (7.08mm).Conclusion:The cardiac contouring tool is able to delineate cardiac structures with reasonable accuracy in less than 90 seconds. Pilot data indicates that the system is able to delineate the whole heart and ventricles within a reasonable accuracy using even a limited library. We are extending the atlas sets to 60 adult males and females in total.

Realization of point planar elastic behaviors using revolute joint serial mechanisms having specified link lengths

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having only revolute joints, each with selectable compliance. The link lengths of the mechanism and the location of the compliant frame relative to the mechanism base are arbitrary but specified. The realizability of a given compliant behavior is investigated, and necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. These realization conditions are interpreted in terms of geometric relationships among the joints. We show that, for an appropriately sized 3R serial mechanism, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. Requirements on mechanism geometry to realize every particle planar elastic behavior at a given location just by changing the mechanism configuration are also identified.

Stereo kamera sisteminde aykırılık haritaları yardımıyla nesne uzaklıklarının tespit edilmesi

In this study, it is intended to detect various objects’ depths consequently distances from parallel camera plane with stereo camera system. In the established test setup, there are two fixed cameras for capturing left and right image and a computer for processing the images. After cameras were placed fixedly, they were calibrated with chessboard. Subsequently calibration; the intrinsic parameters, essential and fundamental matrices, rotation and translation matrices between left and right cameras were occurred. Then rectification process performed to the images which captured from left and right cameras. Accordingly, depth map and knowledge of distance has been obtained. It is possible to use the depth knowledge process in many fields involved robot and vehicle distance detect systems to handicapped distance determination.

Simple image intensity compensation (SIMIC) method prior to application of distortion correction algorithms in brain diffusion Tensor Magnetic Resonance Imaging: Validation test for two cost functions of distortion correction algorithms

The purpose of this study is to design a simple image intensity compensation SIMIC method prior to the application of a variety of cost functions for distortion correction in diffusion tensor imaging DTI. The synthetic dataset consists of each direction of diffusion weighted imaging DWI made by multiplication of nondiffusion weighted image b = 0 image and tensor matrices. We added the effects of patient motion and eddy current distortion using translation, rotation, scaling and shearing matrices. We calculated the b = 0 image of each direction from original DTI, inversely. A co-registration method was applied to the extracted b = 0 images of each direction based on the original b = 0 image and then, the transformation matrices were generated and the original DTI were transformed using this transformation matrix. For the DTI distortion correction, two kinds of cost functions, normalized mutual information NMI and normalized cross-correlation NCC, were used. Visual assessments and quantitative measurements were used to evaluate the results. When using the NMI as a cost function, the quantitative results showed no significant differences between NMI and NMI with SIMIC method. However, there are significant differences compared with using the NCC as a cost function. Our study showed cost function for image distortion correction with SIMIC method improved the results both quantitatively and in terms of qualitative accuracy. This method may be helpful for DTI analysis and helpful for increasing accuracy. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 328-33, 2015

Medical Image Registration Based on Inertia Matrix and Iterative Closest Point

The closest iterative point algorithm (ICP) is widely used in medical image registration. But there exist some problems in the following aspects. First, due to its heavily computational load, it has a time-consuming process and a low registration efficiency. Second, due to the fact that it heavily depends on whether the initial rotation and translation matrices of the floating point set can be exactly extracted, it often traps in the local optimum and even fails to register images. In addition, due to the complexity of medical images, it is difficult to automatically extract the salutary feature points. In this paper, by computing the coordinate inertia matrices of the reference and floating images, the rotation angles are obtained and referred to as the initial rotation parameters of ICP for image registration. The edges of the reference and floating images are detected by the edge convolution kernel so-called B-spline gradient operator (BSGO) and then the binarization images involving the feature points are acquired. The experimental results reveal that, this proposed method has a fairly simple implementation, a low computational load, a fast registration and good alignment accuracy. Also, It can efficiently avoid trapping in the local optimum and cater to both mono-modality and multi-modality image registrations.