Inverse Transformation Matrix Research Articles

Обобщение формулы Аккермана для некоторого класса многомерных динамических систем с векторным входом

A compact analytical formula is obtained that determines the entire set of solutions of the modal control problem for a wide class of multidimensional dynamical systems with vector input, where the number of states is divisible by the number of control inputs, and the controllability index is equal to the quotient of this division. This formula generalizes to systems with the vector input the Ackermann formula applied to multidimensional systems with scalar input. The basis to obtaining the generalized Ackermann formula lies in the original concepts of the Luenberger generalized canonical form and operations of the matrices block transposition. For the most convenient calculation of controller, the original system with vector input is reduced to the generalized Luenberger canonical form using the two successive similarity transformations. A lemma is proved that demonstrates the compact analytical form of the inverse transformation matrix. Transition equivalence makes it possible to obtain a complete countably infinite parametrized set of solutions to the modal control problem under consideration. Its parametrization is provided by selecting block coefficients of the matrix polynomial, which determinant corresponds to the given scalar characteristic polynomial. In cases, where the matrix polynomial involved in parametrization is not reduced to the multipliers, the generalized Ackermann formula contains solutions to the modal control problem that could not be obtained using the existing decomposition method. Examples are presented demonstrating both suitability of the proposed formula for analytical synthesis of modal controllers by state in systems with vector input and its advantages in comparison with the decomposition method

Geometric distortion assessment in 3T MR images used for treatment planning in cranial Stereotactic Radiosurgery and Radiotherapy.

Magnetic Resonance images (MRIs) are employed in brain Stereotactic Radiosurgery and Radiotherapy (SRS/SRT) for target and/or critical organ localization and delineation. However, MRIs are inherently distorted, which also impacts the accuracy of the Magnetic Resonance Imaging/Computed Tomography (MRI/CT) co-registration process. In this phantom-based study, geometric distortion is assessed in 3T T2-weighted images (T2WIs), while the efficacy of an MRI distortion correction technique is also evaluated. A homogeneous polymer gel-filled phantom was CT-imaged before being irradiated with 26 4-mm Gamma Knife shots at predefined locations (reference control points). The irradiated phantom was MRI-scanned at 3T, implementing a T2-weighted protocol suitable for SRS/SRT treatment planning. The centers of mass of all shots were identified in the 3D image space by implementing an iterative localization algorithm and served as the evaluated control points for MRI distortion detection. MRIs and CT images were spatially co-registered using a mutual information algorithm. The inverse transformation matrix was applied to the reference control points and compared with the corresponding MRI-identified ones to evaluate the overall spatial accuracy of the MRI/CT dataset. The mean image distortion correction technique was implemented, and resulting MRI-corrected control points were compared against the corresponding reference ones. For the scanning parameters used, increased MRI distortion (>1mm) was detected at areas distant from the MRI isocenter (>5cm), while median radial distortion was 0.76mm. Detected offsets were slightly higher for the MRI/CT dataset (0.92mm median distortion). The mean image distortion correction improves geometric accuracy, but residual distortion cannot be considered negligible (0.51mm median distortion). For all three datasets studied, a statistically significant positive correlation between detected spatial offsets and their distance from the MRI isocenter was revealed. This work contributes towards the wider adoption of 3T imaging in SRS/SRT treatment planning. The presented methodology can be employed in commissioning and quality assurance programmes of corresponding treatment workflows.

Perspective transformation based-initial value estimation for the speckle control points matching in an out-of-focus camera calibration using a synthetic speckle pattern.

Despite camera calibration methods using regular planar chessboard or circular marker array calibration targets having been widely used, the control point extraction accuracy is low if the image is defocused or if the noise level is high. Due to the noise robustness of digital image correlation (DIC) in speckle image matching, random speckle pattern is a better choice for camera calibration than chessboard or circular markers, if the imaging quality is low. The foremost process of this method is to conduct speckle control points matching DIC, where the initial value must be estimated close to the true value. It is challenging to provide accurate initial values for DIC if the difference of physical pixel scale is large between the reference image and the target image or if the target image is out-of-focus. To solve this problem, this work presents an efficient initial value estimation method for speckle control points matching using DIC, based on perspective transformation. Firstly, the four pairs of corners of the speckle regions in the reference image and target image are detected. Secondly, the target image is transformed to a new image that has the considerable size of pixel scale with the reference image, then four neighborhood points of the control point in the reference image and the corresponding points in the transformed new image are matched coarsely by fixed subset searching. Lastly, the matched points in the transformed target image are transformed back to the origin target image by the inverse perspective transformation matrix, then the initial value for DIC can be estimated by the matched four pairs of neighborhood points. Experiment results confirm the higher calibration accuracy delivered by the proposed method, rather than that of the chessboard or the circular marker array. Measurement precision is higher than the speckle pattern calibration method that uses SIFT-based initial value estimation.

An Inverse Solution Algorithm for Industrial Robot

The inverse solution process of industrial robot is complex. Because the traditional matrix algorithm involves a lot of matrix operation, its process is complex. Numerical algorithms usually do not yield all the solutions, generally, the selection of initial value and the search algorithm have great influence on the convergence and accuracy. The geometric algorithms is simple and intuitionistic with simple expression and small computation. In this paper, a hybrid algorithm combining the geometric method and the inverse transformation matrix method is proposed for puma 560 industrial robots. The geometric algorithms is used to solve the first three joints and the matrix algorithm is used to obtain the final three joint angles. This paper introduces the inverse solution algorithm for this kind of robot in detail, and verifies the effectiveness of the proposed algorithm through matlab simulation.

High definition images transmission through single multimode fiber using deep learning and simulation speckles

Multimode fiber (MMF) plays a vital role in promoting the miniaturization of endoscope. However, real-time and high-definition imaging using the MMF that remains a challenging research. Traditional phase compensation and transmission matrix methods are affected by fiber shape and optical devices, which results in low imaging rate and accuracy. Deep learning can be used to construct the inverse transformation matrix (ITM, output to input) of the MMF. However, deep learning requires high similarity between sample sets. In this paper, we combine principal component analysis (PCA) method, deep learning based speckle classification (DLSC) and deep learning based image enhancement (DLIE) to improve imaging definition. To save experimental costs, we use the inverse-PCA method to obtain simulation speckles. The experimental results show that simulation speckles can be used for classification and image reconstruction of experimental speckles. With the difference between simulation and experimental speckles, which brings about low imaging definition. Therefore, we use the DLIE methods to further improve imaging definition. The experimental results show imaging capability with high definition for complex natural scenes, which may provide a feasible method for high definition images transmission through the MMF.

Research on image transmission mechanism through a multimode fiber based on principal component analysis

The real-time transmission of images through a multimode fiber (MMF) is still a challenging research work. One method completes image transmission by measuring and controlling the full complex field of the MMF. Another method uses artificial neural networks to train and construct the inverse transformation matrix of the MMF. However, the class of testing samples usually belongs to the same class used for the training. We propose a method that constructs the inverse transformation matrix of the MMF based on principal component analysis (PCA), which can reconstruct the grayscale images of natural scene at high frame rate and high resolution. Moreover, we use principal component analysis and support vector machine (PCA+SVM) to classify speckle patterns, and then images can be reconstructed based on the inverse transformation matrix of corresponding category. The PCA+SVM+PCA (PSP) method shows high reconstruction accuracy with few training samples. The proposed method demonstrates general imaging capability over a MMF lengths of 1 m, training time used to construct the inverse transformation matrix is short and the hardware requirements are low, which provides a feasible method for the MMF endoscope imaging.

Task design in APOS Theory

This paper discusses the role of task design in APOS Theory. The role played by the genetic decomposition in the theory and in task design is discussed. An example of a genetic decomposition for the concepts of inverse matrix transformation and inverse matrix is given. Tasks designed using this tool as a guide are exemplified as well as a description of their relationship to the genetic decomposition. In this way we provide insights about each task and the specific detailed construction it has as its aim. Therole of the tasks in the classroom is discussed since the combination of collaborative work of students in sequences of tasks and in group discussions are the foundation of APOS Theory’s potential to promote essential constructions needed for a deep learning of mathematical concepts.

Transmission of natural scene images through a multimode fibre

The optical transport of images through a multimode fibre remains an outstanding challenge with applications ranging from optical communications to neuro-imaging. State of the art approaches either involve measurement and control of the full complex field transmitted through the fibre or, more recently, training of artificial neural networks that however, are typically limited to image classes belong to the same class as the training data set. Here we implement a method that statistically reconstructs the inverse transformation matrix for the fibre. We demonstrate imaging at high frame rates, high resolutions and in full colour of natural scenes, thus demonstrating general-purpose imaging capability. Real-time imaging over long fibre lengths opens alternative routes to exploitation for example for secure communication systems, novel remote imaging devices, quantum state control processing and endoscopy.

The disturbance rejection of magnetically suspended inertially stabilized platform

In a magnetically suspended inertially stabilized platform, the yaw gimbal is suspended by the magnetic bearing, which can effectively isolate the external vibrations and disturbances. However, coupling torques and disturbance torques among gimbals still exist. Therefore, based on the cross feedback compensation, the output angles of gimbals are introduced as feedback variables, and the inverse coordinate transformation matrix is designed to compensate for the coupling torques. Furthermore, a disturbance observer is applied to inhibit the disturbance torque and simulations indicate that the disturbance observer can accurately estimate the disturbance torque. Consequently, the experimental results demonstrate that the cross feedback compensation can inhabit the coupling torques, and the disturbance observer greatly suppresses the external disturbance torques and improves the angular displacement precision of gimbals.

New Permanent Magnet Synchronous Motor Current Sensing Phase Delay Compensation Method

This paper presents a method that can improve the performance of permanent magnet synchronous motor current control by minimizing the measured current phase delay caused by the Low Pass Filter(LPF) used to cut off the noises that flowed in when feedback currents are measured. Although existing methods that change the Cutoff Frequency of the LPF can minimize phase delays during high speed rotations, their noise cutoff effects are much lower and this may lead to the decline of control performance. Therefore, in this study, an algorithm that can compensate current phase delays through relatively simple calculations from the synchronous motor d-q axis coordinate transformation matrix and the inverse transformation matrix is proposed and the validity of the proposed method is verified by comparing the waveform of the calculated current with the waveform of actual currents through simulations and experiments.

Optimum Linear Block Precoding for Multi-Point Cooperative Transmission with Per-Antenna Power Constraints

Using cyclic prefix (CP), the transmission schemes, orthogonal frequency-division multiplexing (OFDM), single carrier block transmission, and time reversal, can be unified as linear block precoding. Considering frequency-selective channels, this paper studies linear block precoding for CP-based multi-point transmission with per-antenna power constraints (PAPCs) under capacity maximization and mean-square-error (MSE) minimization criteria. We show that, the optimal precoders for both criteria could be, but not necessarily, in the form of OFDM transmission (i.e., an inverse discrete fourier transformation (IDFT) matrix multiplying a complex diagonal matrix). Based on the optimal precoder structure, the two problems are simplified to two matrix-free optimization problems for which we prove strong duality holds. Moreover, it is shown that the dual problems can be equivalent to two unconstrained convex optimization problems. Efficient optimum precoding algorithms are proposed for both problems. Simulation results show that the maximum capacity (or minimum MSE) in the PAPC case almost coincides with that in the sum power constraint (SPC) case when the power budgets for each antenna are equal, but a capacity (or MSE) gap exists between the two power constraint cases when the power budgets for each antenna are different.

A moment-based approach for deskewing rotationally symmetric shapes

The covariance matrix of a pattern is composed by its second order central moments. For a rotationally symmetric shape, its covariance matrix is a scalar identity matrix. In this work, we apply this property to restore the skewed shape of rotational symmetry. The relations between the skew transformation matrix and the covariance matrices of original and skewed shapes are derived. By computing the covariance matrix of the skewed shape and letting the covariance matrix of the original shape be a scalar identity matrix, the skew transformation matrix can be solved. Then, the rotationally symmetric shape can be recovered by multiplying the inverse transformation matrix with the skewed shape. The method does not rely on continuous contours and is robust to noise, because only the second-order moments of the input shape are required. Experimental results are also presented.

Inverse Dynamic Analysis of Mechanical Systems Using the Velocity Transformation Technique

This paper presents a method for the inverse dynamic anlaysis of mechanical systems. Actuating forces(or torques) depending on the driving constraints are analyzed in the relative coordinate space using the velocity transformation technique. A systematic method to compose the inverse velocity transformation matrix, which is used to determine the joint reaction forces, is proposed. Two examples are taken to verify the method developed here.

Vectorcardiogram synthesized from a 12-lead ECG: Superiority of the inverse Dower matrix

Vectorcardiographic (VCG) criteria for the diagnosis of, for example, myocardial infarction and right ventricular hypertrophy, are superior to the corresponding 12-lead ECG criteria. Contour and rotation of the QRS loops are important parts of these VCG criteria that have no direct counterpart in the 12-lead ECG. Therefore, attempts have been made to synthesize VCGs from 12-lead ECGs for diagnostic purposes. Visual comparison of QRS loops from the Frank VCG and three different synthesized VCGs was made by three independent observers to determine which method produces the most Frank-like QRS loops. The inverse transformation matrix of Dower proved to be the best method of synthesis. Normal limits for some clinically important measurements in VCG interpretation were calculated for this synthesis method and the Frank VCG.

A triangular bending element based on an energy-orthogonal free formulation

A new Kirchhoff triangular plate-bending element with nine degrees of freedom is derived. The assumed shape functions are nonconforming and consist of a complete quadratic expansion complemented by three cubic modes that are energy-orthogonal to the quadratic expansion. The derivation is based on the free formulation of Bergan and Nygård, which satisfies the conditions of invariance and the patch test. An explicit expression is obtained for the inverse transformation matrix required in this formulation, which makes the stiffness computations extremely efficient. The aspect ratio sensitivity of the element under cylindrical bending modes can be lessened by scaling the higher-order stiffness through coefficients determined by a superlinear patch test technique. Numerical experiments indicate that the new element outperforms previously derived 9-dof triangular elements based on displacement modes.

Simplified relativistic force transformation equation

A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic force on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and show that the constant of proportionality in Coulomb’s law is equal to the speed of light squared times the constant of proportionality in the Biot-Savart law. All is done with simple vector algebra without using four vectors, tensors, or Maxwell’s equations. The simplification results from the fact that when one takes the usual force transformation law: F′=A (U)F, and rewrites it using the inverse transformation matrix, as F=A−1(U)F′, the resulting expression is more simple because A−1(U) is linear in the velocity, U but A (U) is not.