Polar Representation Research Articles

Wireless Sensor Network-Based Localization Method Using TDOA Measurements in MPR

Localization is perhaps one of the most interesting research subjects in signal processing. Traditional localization methods rely on the prior information whether the source is located in the near-field or far-field. Since the prior knowledge is hard to obtain in practice, neither positioning nor bearing may not be able to provide reliable performance for both cases. The modified polar representation (MPR) is proposed to solve this contradictory problem in a uniform framework and eliminate the thresholding effect as the source range increases. The maximum likelihood estimator (MLE) in the state-of-art research realizes excellent performance reaching the Cramer-Rao lower bound (CRLB) but it is computation-complex and time-consuming. Besides, it has the possible divergence problem if the initial value is not close enough to the true value. This paper focuses on the localization problem using time difference of arrival measurements in MPR. Formulating it in a new form, we develop a two-step least squares (LS) estimator for the MPR model. The weighted total LS is applied in the first step and the weighted LS for the final solution, where the second step is based on the natural constraint of the unknowns. The proposed method is closed-form and able to reach CRLB in low noise power situation irrespective of the source range. The covariance is analyzed and proved to provide CRLB accuracy for Gaussian noise theoretically. Simulation supports our theoretical results and verifies the advocated performance that is comparable with MLE but simpler and computationally more efficient. It outperforms the classical closed-form solution.

General Analytical Modeling for Magnet Demagnetization in Surface Mounted Permanent Magnet Machines

This paper proposes an analytical model for the prediction of airgap magnetic field distribution for axial flux permanent magnet (AFPM) machine with partial magnet demagnetization. The AFPM machine geometry is first converted to a polar representation. Consequently, the subdomain model based on current sheet technique is developed. Then current sheet representation of PM is derived to consider the partial demagnetization using superposition principle. The back electromagnetic forces and cogging torque are obtained accordingly based on Maxwell's equations. The results show that the results of proposed approach agrees with that of finite-element method. The model is further validated by experiments under both healthy and demagnetized conditions, which can validate the proposed approach. Main contribution of the work is to consider the partial irreversible demagnetization. Moreover, the proposed method is applicable for both AFPM and radial flux permanent magnet machine.

An Effective Flux Weakening Control of a SyRM Drive Including MTPV Operation

A synchronous reluctance motor drive exhibits an inherent unlimited speed range capability; in fact, the maximum speed of this kind of machine is bounded only by mechanical limits. In order to exploit this peculiar characteristic of the drive while assuring the lowest power losses, a proper control algorithm has to be used. In particular, while the working speed is increasing, the control must be able to command the reluctance motor under the maximum torque per ampere condition at first, into the flux-weakening region, and then on the maximum torque per voltage trajectory. To this purpose, a novel voltage control loop is presented in this paper. It is combined with a field-oriented current control and profitably exploits a polar coordinate representation of the current reference to operate the reluctance machine in compliance with current and voltage rating constraints in all the different operating conditions. Additional merits of the proposed scheme are the ease of implementation and the simple design. The stability of the proposed control algorithm is proved through a small signal analysis and simulations and experimental tests confirm its effectiveness.

A cardioid-parametric model for the Magnus effect in baseballs

The Magnus effect is responsible for deflecting the trajectory of a spinning baseball. The deflection at the end of the trajectory can be estimated by simulating some similar trajectories or by clustering real paths; however, previous to this study, there are no reports for a detailed connection between the initial throw conditions and the resulting deflection by using. The only approximation about this is the PITCHf/x algorithm, which uses the kinematics equations. In this work, deflections from simulated spinning throws with random linear and angular velocities and spin axis parallel to the horizontal plane are analyzed in their polar representation. A cardioid function is proposed to express the vertical deflection as response of the angular velocity. This is based on both theoretical arguments from the ball movement equations and from the numerical solution of such equations. We found that the vertical deflection fits a cardioid model as function of the Magnus coefficient and the spin angle, for a set of trajectories with initial linear velocities symmetrically distributed around the direction of motion. A variation of the model can be applied to estimate the radial deflection whereas an extended model should be explored for trajectories with velocities asymmetrically distributed. The model is suitable for many applications: from video games to pitching machines. In addition, the model approaches to the results obatined with the kinematic equations, which serves as validation of the PITCHf/x algorithm.

Convex Relaxation Methods for Unified Near-Field and Far-Field TDOA-Based Localization

This paper develops two convex relaxation solutions for the unified localization of a signal source using time difference of arrival measurements, regardless of whether the source is in the near field for coordinate positioning or in the far field for the direction of arrival estimation. The previous study on unified estimation only derived an iterative solution, which is sensitive to initialization. Albeit a coarse initialization was supplied to start the iteration, it may not be sufficient to ensure convergence to the global solution especially when the source is close to the sensors. The proposed solutions come from two novel formulations for optimization, one using the weighted least squares with the modified polar representation of the source position as variable and the other applying fractional programming with the Cartesian coordinate representation instead. Both the optimization problems are solved by first performing semidefinite relaxation and then tightening the relaxed problem by including a set of second-order cone constraints. The two formulations are created from different approaches. Nevertheless, we are able to prove that both the formulations reduce to solving exactly the same mixed semidefinite/second-order cone program and thus establish their equivalence. Furthermore, the proposed solution method is extended to the more practical scenario when sensor position errors are present. The results from both the simulated and real experiments show that the proposed method achieves almost the same performance of the iterative maximum likelihood estimator under ideal initialization.

A Polar Representation for Complex Interval Numbers

The present work defines the basic elements for the introduction to the Study of Complex variables under the mathematical interval context with the goal of using it as a foundation for the understanding of pure mathematical problems, associating the mathematical interval to support the results. The present article contributes to the complex interval theory taking into consideration Euler’s Identity and redefining the polar representation of interval complex numbers. In engineering, the present article could be used as a subsidy for many applications where complex variable theory is applicable and requires accurate results.

Accurate Heart Rate Monitoring Method During Physical Exercise From Photoplethysmography Signal

Photoplethysmography (PPG) is mainly used to find skin blood flow. Volumetric change of blood flow indicates cardiac rhythm, due to that there is a possibility to monitor the heart rate (HR) from PPG signals. PPG sensors can be implemented in wrist band or smart watch. HR monitoring during physical exercise can give helpful information regarding physical fitness tracking features like calorie measurement, sleep tracking, counting steps and help the trainer to achieve their training goals. Body movements during physical exercise produces noise content in PPG signal. This noise content is generally called as moving artifact. Monitoring accurate heart rate from PPG signal is a challenging task. Nowadays there are many methods are proposed to improve the HR monitoring from PPG signals. This paper is envisaged to develop a method to detect accurate HR without any complexity. The proposed work consists of two steps: 1) extraction of PPG signal from the observed PPG by sparse method and2) HR estimation. The main advantage of sparse method is the proper reconstruction of signals from small number of highly noisy elementary signals. This method eliminates the need of accelerometer reading and uses only two PPG signals, which results less complexity. Estimation of HR through the phase information, which provided by the polar representation of PPG signal. The proposed method results in an average absolute error of 1.00 BPM and average relative error of 0.85 BPM using 2 PPG signals compared to existing methods.

Intelligent Diagnosis of V-Type Marine Diesel Engines Based on Multifeatures Extracted From Instantaneous Crankshaft Speed

This paper presents an intelligent combustion fault diagnosis approach for V-type marine diesel engines with uneven firing intervals based on the instantaneous crankshaft speed (ICS). First, experimental ICSs of a 16-cylinder marine diesel engine under normal and different degrees of fault conditions are investigated to obtain the most sensitive fault features. A new polar representation method named cyclic-polar-map (CPM) is proposed to effectively demonstrate the fault features. The quantitative radii of the CPM are used to indicate the location and degree of fault. Then, a support vector machine (SVM)-based intelligent fault diagnosis system is developed for automatically detecting the combustion faults with the features extracted from the proposed CPM and the frequency analysis of ICS. In addition, for the SVM training set is not always available in practice, a dynamic model of the crankshaft system is developed to simulate different fault patterns. Finally, the efficiency of the proposed intelligent diagnosis approach is validated by experimental data. The results show that the proposed SVM-based intelligent diagnosis system using both CPM features and frequency domain features of the ICS can obtain good accuracies under different fault degrees at various speed and load conditions.

Investigating the Role of Charge-Altering Post-Translational Modifications on Tau Peptide Conformational Ensembles using Polarizable Molecular Dynamics Simulations

Aggregation of amyloidogenic proteins, such as the amyloid β-peptide, microtubule-binding protein tau, and α-synuclein, is linked to a number of human diseases. Amyloidogenic proteins unfold, aggregate, and self-assemble into highly stable, insoluble fibrils characterized by cross-β structure. Despite having unique primary sequences, these amyloidogenic proteins all undergo similar conformational changes, from disordered and only partially structured, to highly ordered in the fibril form. The forces driving such changes in structure are not completely characterized and a better understanding is needed to potentially combat a wide range of diseases that are currently incurable. In this study, we performed molecular dynamics simulations with the Drude polarizable protein force field to gain a better understanding of protein aggregation. We previously found that the explicit representation of electronic polarization was required to delineate mutation-specific unfolding pathways of the amyloid β-peptide. Building upon those findings, here we explore the impact of charge-altering post-translational modifications (PTMs) on the dynamics of tau, the protein that forms intracellular, neurofibrillary tangles in Alzheimer's disease. PTMs like acetylation of lysine and phosphorylation of serine and threonine are known to induce tau aggregation, but the underlying molecular mechanism remains unknown. By studying fragments of tau harboring these PTMs, we sought to gain novel insights into how changes in charge caused by PTMs shift the conformational ensembles of fragments of the tau protein. Polarizable simulations of these charge-altering PTMs shed light on how electrostatic interactions, including those between permanent and induced dipoles, affect side-chain properties, salt bridges, water and ion interactions, and changes in secondary structure.

Polar Transformation on Image Features for Orientation-Invariant Representations

The choice of image feature representation plays a crucial role in the analysis of visual information. Although vast numbers of alternative robust feature representation models have been proposed to improve the performance of different visual tasks, most existing feature representations [e.g., handcrafted features or convolutional neural networks (CNNs)] have a relatively limited capacity to capture the highly orientation-invariant (rotation/reversal) features. The net consequence is suboptimal visual performance. To address these problems, this study adopts a novel transformational approach, which investigates the potential of using polar feature representations. Our low level consists of a histogram of oriented gradient, which is then binned using annular spatial bin-type cells applied to the polar gradient. This gives gradient binning invariance for feature extraction. In this way, the descriptors have significantly enhanced orientation-invariant capabilities. The proposed feature representation, called orientation-invariant histograms of oriented gradients , is capable of accurately processing visual tasks (e.g., facial expression recognition). In the context of the CNN architecture, we propose two polar convolution operations, referred to as full polar convolution and local polar convolution, and use these to develop polar architectures for the CNN orientation-invariant representation. Experimental results show that the proposed orientation-invariant image representation, based on polar models for both handcrafted features and deep learning features, is both competitive with state-of-the-art methods and maintains compact representation on a set of challenging benchmark image datasets.

Solution and Analysis of TDOA Localization of a Near or Distant Source in Closed Form

Point positioning and direction of arrival (DOA) localization require separate estimators, depending on whether the source is near or distant from the sensors. The use of modified polar representation (MPR) for the source location enables the integration of the two estimators together and eliminates the knowledge needed if the source is in the near-field or far-field. The previous work on MPR only provides an iterative implementation of the maximum likelihood estimator (MLE) initialized by a coarse semidefinite relaxation (SDR) solution. This paper proposes a formulation for time difference of arrival (TDOA) localization of a 2-D or 3-D source in MPR that would lead to a closed-form solution through the minimization of a quadratic function with a quadratic constraint. Two techniques, the successive unconstrained minimization (SUM) and the generalized trust region subproblem (GTRS), are applied to solve the optimization. Detailed analysis in the first order for mean-square and in the second order for estimation bias is performed for both methods. The theoretical results illustrate that the closed-form solution from each of the methods provides the Cramer–Rao lower bound performance for Gaussian noise. The GTRS solution has better accuracy than the SUM solution when the source signal is arriving at an azimuth or elevation angle close to zero, 90 $^\circ$ , or 180 $^\circ$ or when the measurement noise level is large. They yield comparable performance with the MLE albeit having less complexity and avoiding possible divergence behavior. They outperform the closed-form solutions from the literature in angle estimation and have smaller bias.

Automatic Feature-Based Point Cloud Alignment and Inspection

3D scanning is a non-contact geometric inspection technique that has potential applications in many industrial sectors. Compared to coordinate measuring machines, 3D scanning is able to acquire high-density sampling of an entire part in a relatively short time without fixturing. In practice, point clouds, which are the output of 3D scanning, must be aligned with the base-truth CAD model before calculating the point-wise deviation. Existing methods accomplish this task by determining the optimal transformation that maximizes the overlap between the point cloud and base-truth CAD model. However, these methods do not consider the problem from a geometric dimensioning and tolerancing (GD&T) perspective. Specifically, dimensional errors are not quantified in reference to the established datum features. In this work, a new scheme is proposed to automatically align the datum features of 2D shapes based on point clouds via a polar coordinate representation. From the result of the new alignment scheme, the point-wise deviation is evaluated through the deviation distribution to differentiate manufacturing and measurement errors. The proposed scheme is applied in three case studies, in which the sample shapes to be inspected are generated by adding random errors to their nominal models to mimic measurement errors in physical experiments. The result illustrates the effectiveness and efficiency of the proposed scheme in automatic shape alignment based on datum features and in subsequent detection of point-wise deviation.

Geometric representation of polarization for a general three-dimensional optical field

On the basis of previous work in this area, we propose a new geometric representation of polarization for a general three-dimensional (3D) optical field. This representation is based on the characteristic and eigenvalue decompositions of the 3 × 3 coherency matrix, which is appropriate for all 3D polarized optical fields, including totally polarized, partially polarized and totally un-polarized optical fields. Based on this representation method, the degree of polarization for an arbitrary 3D optical field can be characterized by a unique point located on a spatial equilateral triangle. Correspondingly, the 3D state of polarization can be illustrated by the 3D distribution maps of polarization ellipse quantitatively.

Note on [formula omitted]-polar fuzzy graph representation of concept lattice: How to really compute [formula omitted]-polar fuzzy concepts

Singh (2018) claims to propose an extension of formal concept analysis for handling multi-polar information. For this setting he invents an algorithm. The aim of this note is two-fold: First, we show that Singh’s algorithm is inefficient, since it is a direct generalization of one of the least efficient algorithms known in formal concept analysis, and strictly speaking, the algorithm is incorrect. Second, we are reminded that many algorithms already exist which can be used instead. This is because Singh’s setting is already covered by a more general and well established framework of formal fuzzy concept analysis.

Lightlike shell solitons of extremal space-time film

New exact solution class of Born—Infeld type nonlinear scalar field model is obtained. The variational principle of this model has a specific form which is characteristic for extremal four-dimensional hypersurface or hyper-film in five-dimensional space-time. Obtained solutions are singular solitons propagating with speed of light and having energy, momentum, and angular momentum which can be calculated for explicit conditions. Such solitons will be called the lightlike ones. The soliton singularity has a form of moving two-dimensional surface or shell. The lightlike soliton can have a set of tubelike singular shells with the appropriate cavities. A twisted lightlike soliton is considered. It is notable that its energy is proportional to its angular momentum in high-frequency approximation. A case with one tubelike cavity is considered. In this case the soliton shell is diffeomorphic to a cylindrical surface with threads by multifilar helix. The shell transverse size of the appropriate finite energy soliton can be converging to zero at infinity. The ideal gas of such lightlike solitons with minimal twist parameter is considered in a finite volume. Explicit conditions provide that the angular momentum of each soliton in the volume equals Planck constant. The equilibrium energy spectral density for the solitons is obtained. It has the form of Planck distribution in some approximation. A beam of the twisted lightlike solitons is considered. The representation of arbitrary polarization for the beam with the twisted lightlike solitons is discussed. It is shown that the effect of mechanical angular momentum transfer to absorbent by the circularly polarized beam can be provided. This effect is well known for photon beam. Thus the soliton solution which have determinate likeness with photon is obtained in particular.

3D shape classification and retrieval based on polar view

This paper presents a novel approach for classifying and retrieving 3D shapes. We first propose a new polar view based strategy that, by using 360-degree projection, effectively reflects the internal structure and key features of a 3D shape. Specifically, the point cloud of the 3D shape is mapped to a two-dimensional (2D) plane, and the polar view representation is obtained by the maximum depth of the point cloud. Projecting 3D point clouds into a 2D plane enables us to use sufficient image data for training, and the process also takes advantage of both image-based and 3D shape-based methods. We propose a convolutional neural network (CNN) that is trained by using only a single polar view of a 3D shape to obtain the polar view representation (PVR) and realize the classification and retrieval of 3D shapes. Experiments on standard datasets, such as ModelNet10 and ModelNet40, show that our method outperforms state-of-the-art methods on 3D shape classification and retrieval.

An effective computer aided diagnosis model for pancreas cancer on PET/CT images

Background and objective: Pancreas cancer is a digestive tract tumor with high malignancy, which is difficult for diagnosis and treatment at early time. To this end, this paper proposes a computer aided diagnosis (CAD) model for pancreas cancer on Positron Emission Tomography/Computed Tomography (PET/CT) images.Methods: There are three essential steps in the proposed CAD model, including (1) pancreas segmentation, (2) feature extraction and selection, (3) classifier design, respectively. First, pancreas segmentation is performed using simple linear iterative clustering (SLIC) on CT pseudo-color images generated by the gray interval mapping (GIP) method. Second, dual threshold principal component analysis (DT-PCA) is developed to select the most beneficial feature combination, which not only considers principal features but also integrates some non-principal features into a new polar angle representation. Finally, a hybrid feedback-support vector machine-random forest (HFB-SVM-RF) model is designed to identify normal pancreas or pancreas cancer and the key is to use 8 types of SVMs to establish the decision trees of RF.Results: The proposed CAD model is tested on 80 cases of PET/CT data (from General Hospital of Shenyang Military Area Command) and achieves the average pancreas cancer identification accuracy of 96.47%, sensibility of 95.23% and specificity of 97.51%, respectively. In addition, the proposed pancreas segmentation method is also evaluated using a public dataset with 82 3D CT scans from the National Institutes of Health (NIH) Clinical Center and its performance is found to surpass other methods, with a mean Dice coefficient of 78.9% and Jaccard index of 65.4%.Conclusions: Collectively, contrast experiments in 10-fold cross validation demonstrate the efficiency and accuracy of the proposed CAD model as well as its performance advantages as compared with related methods.

Analytical method for the transformation of Zernike polynomial coefficients for scaled, rotated, and translated pupils.

Zernike polynomials provide an excellent metric basis for characterizing the wavefront aberrations of human eyes and optical systems. Since the Zernike expansion is dependent on the size, position, and orientation of the pupil in which the function is defined, it is often necessary to transform the Zernike coefficients between different pupils. An analytic method of transforming the Zernike coefficients for scaled, rotated, and translated pupils is proposed in this paper. The normalized coordinate transformation functions between the polar coordinates of the transformed pupil and the Cartesian coordinates of the original pupil are given. Based on the Cartesian and polar representations of Zernike polynomials, the coefficients' transformation matrix can be derived directly and conveniently. The first 36 terms of standard Zernike polynomials are used to validate the proposed method. For different types of transformation, transformation rules of individual Zernike terms are systematically analyzed, revealing how individual terms of the original pupil transform into terms of the transformed pupil. Numerical examples are presented to demonstrate the validity of the proposed method. Further application of the proposed method to the alignment of pupil-decentered off-axis optical systems is discussed.

Automatic Plaque Detection in IVOCT Pullbacks Using Convolutional Neural Networks.

Coronary heart disease is a common cause of death despite being preventable. To treat the underlying plaque deposits in the arterial walls, intravascular optical coherence tomography can be used by experts to detect and characterize the lesions. In clinical routine, hundreds of images are acquired for each patient, which require automatic plaque detection for fast and accurate decision support. So far, automatic approaches rely on classic machine learning methods and deep learning solutions have rarely been studied. Given the success of deep learning methods with other imaging modalities, a thorough understanding of deep learning-based plaque detection for future clinical decision support systems is required. We address this issue with a new data set consisting of in vivo patient images labeled by three trained experts. Using this data set, we employ the state-of-the-art deep learning models that directly learn plaque classification from the images. For improved performance, we study different transfer learning approaches. Furthermore, we investigate the use of Cartesian and polar image representations and employ data augmentation techniques tailored to each representation. We fuse both representations in a multi-path architecture for more effective feature exploitation. Last, we address the challenge of plaque differentiation in addition to detection. Overall, we find that our combined model performs best with an accuracy of 91.7%, a sensitivity of 90.9%, and a specificity of 92.4%. Our results indicate that building a deep learning-based clinical decision support system for plaque detection is feasible.

A Different Polar Representation for Generalized and Generalized Dual Quaternions

In this paper, we present a new polar representation for generalized quaternions and generalized dual quaternions. In this different polar form representation, as in the Cayley–Dickson form, a generalized quaternion and a generalized dual quaternion are represented by a pair of complex numbers and dual complex numbers, respectively. But here, for a generalized quaternion, these two complex numbers coincide with a complex modulus and a complex argument which are calculated from an arbitrary generalized quaternion and for a generalized dual quaternion these two dual complex numbers coincide with a dual complex modulus and a dual complex argument which are calculated from an arbitrary generalized dual quaternion in Cayley–Dickson form. It is known that a unit generalized quaternion and unit generalized dual quaternion correspond to a rotation and a screw operator in 4-dimensional generalized space \(E_{\alpha \beta }^{4}\), respectively. By the help of this kind of polar form of a generalized quaternion and a generalized dual quaternion, a generalized rotation and a screw operator in 4-dimensional generalized space can be written in a product of two generalized rotation operators and screw operators in 2 and 3 dimensional generalized spaces, respectively. One of these operators is in the 2-dimensional generalized space \(E_{\alpha \beta }^{2}\) spanned by the vectors 1 and i and the other is in the 3-dimensional space \(E_{\alpha \beta }^{3}\) spanned by the vectors 1, j and k.