Orthogonal Iteration Algorithm Research Articles

RA-HOOI: Rank-adaptive higher-order orthogonal iteration for the fixed-accuracy low multilinear-rank approximation of tensors

In this paper, we propose a novel rank-adaptive higher-order orthogonal iteration (RA-HOOI) algorithm to solve the fixed-accuracy low multilinear-rank approximation of tensors. On the one hand, RA-HOOI relies on a greedy strategy to expand the subspace, which avoids computing the full SVD of the matricization of the input tensor. On the other hand, the new rank-adaptive strategy introduced in the RA-HOOI algorithm enables the obtained truncation to be more accurate. A series of numerical experiments related to synthetic and real-world tensors are carried out to show that the proposed RA-HOOI algorithm is comparable to state-of-the-art methods in terms of both accuracy and efficiency and performs better in certain situations.

Improved Tucker decomposition algorithm for noise suppression of 3D GPR data in road detection

AbstractThe echo data of ground‐penetrating radar (GPR) have a low signal‐to‐noise ratio. Denoising and interference suppression are important for improving the accuracy of underground target recognition and detection. In this paper, a new method of noise analysis and suppression of 3D GPR is proposed, transforming the problem of noise reduction into an optimization problem regarding a third‐order tensor. This method is improved with the following features; a bidimensional empirical mode decomposition (BEMD) algorithm is employed to decompose the 3D GPR noise. The main source of the noise is determined by computing the standard deviation of each component decomposed. For the shortcoming of the existing GPR denoising methods that reduce the dimension of 3D GPR data, the proposed approach can denoise 3D GPR data directly to avoid the loss of data caused by reducing the dimension. This preserves the desired signal and extracts noise through the Tucker decomposition of 3D GPR data. An improved high‐order orthogonal iteration algorithm is utilized to optimize the decomposition. The peak signal‐to‐noise ratio (PSNR) of the signal for each survey line is calculated to evaluate the effectiveness of noise reduction. Simulations and real data sets are provided to compare the performance of algorithms. The results show that the mean PSNR after noise suppression with our method is 8.915 dB and 16.458 dB higher than wavelet transform and singular value decomposition algorithms, respectively. This demonstrates that the proposed approach can better suppress 3D GPR noise and provides technical support for improving 3D GPR data quality and road detection accuracy.

Flexible On-Orbit Calibration for Monocular Camera and Laser Rangefinder Integrated Pose Measurement System

Owing to its low cost and ease of manufacture, integrated monocular space camera and laser rangefinders are commonly used in many space applications (i.e., pose measurement of non-cooperative targets). This and other composite systems estimate poses with high precision using a combination of high-resolution lateral visual and high-precision distance information. Notably, any system that is tested on ground must again receive precise on-orbit calibration because the accompanying spaceborne turntables and arms must be frequently manipulated to meet field-of-view and distance measurement requirements and require complicated realignments. To accommodate flexible multiple target calibration, this study proposed an on-orbit model that obtains accurate pose relationships jointly using the monocular camera and laser rangefinder. First, we invented a robust calibration model and derive its pose transformation matrix based on the given component positions. We then provided an improved (simplified) orthogonal iteration algorithm that optimizes the given matrix for calibration. The influences of different factors on calibration accuracy are quantitatively analyzed via simulations, and the new method’s performance is verified with real-world experiments. This system enables several novel and significant space and military applications.

Tensor dictionary learning for representing three-dimensional sound speed fields.

Ocean sound speed field (SSF) representation is often plagued with low resolution (i.e., the capability of explaining fine-scale fluctuations). This drawback, however, is inherent in a number of classical SSF basis functions, e.g., empirical orthogonal functions, Fourier basis functions, and more recent tensor-based basis functions learned via the higher-order orthogonal iterative algorithm. For two-dimensional depth-time SSF representation, recent attempts relying on dictionary learning have shown that fine-scale sound speed information can be well preserved by a large number of basis functions. They are learned from the historical data without imposing rigid constraints on their shapes, e.g., the orthogonal constraints. However, generalizing the dictionary learning idea to represent three-dimensional (3D) spatial ocean SSF is non-trivial, in terms of both problem formulation and algorithm development. It calls for integrating the dictionary learning framework and the tensor-based basis function learning framework, a recently proposed one that captures the 3D sound speed correlations well. To achieve this goal, we develop a 3D SSF-tailored tensor dictionary learning algorithm that learns a large number of tensor-based basis functions with flexible shapes in a data-driven fashion. Numerical results based on the South China Sea 3D SSF data have showcased the superiority of the proposed approach over the prior method.

Pose estimation of camera based on weighted accelerated orthogonal iterative algorithm

Pose estimation of camera based on weighted accelerated orthogonal iterative algorithm

Generalized Liquid Association Analysis for Multimodal Data Integration

Multimodal data are now prevailing in scientific research. One of the central questions in multimodal integrative analysis is to understand how two data modalities associate and interact with each other given another modality or demographic variables. The problem can be formulated as studying the associations among three sets of random variables, a question that has received relatively less attention in the literature. In this article, we propose a novel generalized liquid association analysis method, which offers a new and unique angle to this important class of problems of studying three-way associations. We extend the notion of liquid association from the univariate setting to the sparse, multivariate, and high-dimensional setting. We establish a population dimension reduction model, transform the problem to sparse Tucker decomposition of a three-way tensor, and develop a higher-order orthogonal iteration algorithm for parameter estimation. We derive the nonasymptotic error bound and asymptotic consistency of the proposed estimator, while allowing the variable dimensions to be larger than and diverge with the sample size. We demonstrate the efficacy of the method through both simulations and a multimodal neuroimaging application for Alzheimer’s disease research. Supplementary materials for this article are available online.

Federated Tensor Decomposition-Based Feature Extraction Approach for Industrial IoT

Data in modern industrial applications and data science present multidimensional progressively, the dimension and the structural complexity of these data are becoming extremely high, which renders existing data analysis methods and machine learning algorithms inadequate to the extent. In addition, high-dimensional data in actual scenarios often share some common latent components and patterns, it is necessary and significant to analyze such data in an associative manner, rather than treating them independently. Considering the problem of data islands and data privacy that is prevalent in the industry. In this article, we propose the first joint high-order orthogonal iterative (J-HOOI) algorithm for simultaneous tensor decomposition and federated tensor decomposition (FTD) model for feature extraction and dimension reduction of high-dimensional industrial data under the federated learning framework. Moreover, we also develop a secure federated computation process based on the J-HOOI method. Using this method, multiple participants iteratively calculate the local factor matrices and transfer the local information to the parameter server, which aggregates the local information to generate the globally updated factor matrices. Finally, each client generates globally compressed features by projecting local data onto these common potential spaces. We have demonstrated with real-world industrial datasets that our approach is similar to a centralized training model in decomposition accuracy and classification accuracy while respecting privacy.

A Monocular Vision Relative Displacement Measurement Method Based on Bundle Adjustment Optimization and Quadratic Function Correction

In order to meet the requirements of high-precision target displacement measurement, this paper proposed a measurement method based on monocular vision measurement system by which the advantages of simple structure, convenient debugging, easy to install and calibrate is recognized. This method first uses the bundle adjustment algorithm with conditional constraints to optimize the solution results of the orthogonal iterative algorithm, then calculates the relative poses of the optimization results, finally establishes an error correction model to perform secondary optimization on the relative poses. The experimental results show that the method proposed in this paper can reduce more than 54% average error of displacement measurement results, and the error between the final displacement measurement results and the actual displacement values is controlled at 0.4mm level, which proves that the method has good practical value.

Accelerative and Weighted Camera Pose Estimation Based on Extended Orthogonal Iterative Algorithm

The camera pose estimation algorithm is typically more based on reference points and less on the linear information in the image.In this paper,based on the extended orthogonal iteration,an accelerative and weighted camera pose estimation algorithm based on the combination of point and line segments is proposed to ensure a good anti-interference and real-time performance of the algorithm.The algorithm considers the sum of the weighted collinearity error and the weighted coplanarity error as the error function.The weight coefficients are determined by the depth information and the re-projection error of the initial value.In addition,the algorithm accelerates the iterative process and reduces the time complexity of the iteration process dramatically from O(n)to O(1).The simulation results demonstrate that the algorithm can suppress the interference of abnormal points and reduce the calculation time.The calculation accuracy of the rotation matrix is 51.69%higher than that of the traditional orthogonal iterative algorithm,and the calculation accuracy of the translation vector is increased by 51.21%.Furthermore,the calculation time after the acceleration is reduced by 47.11%.The physical experiment shows that the algorithm can make full use of the detected reference points and reference line information,improve the calculation accuracy,reduce the cumulative error,and has high practical application value.

Spectral Imagery Tensor Decomposition for Semantic Segmentation of Remote Sensing Data through Fully Convolutional Networks

This work aims at addressing two issues simultaneously: data compression at input space and semantic segmentation. Semantic segmentation of remotely sensed multi- or hyperspectral images through deep learning (DL) artificial neural networks (ANN) delivers as output the corresponding matrix of pixels classified elementwise, achieving competitive performance metrics. With technological progress, current remote sensing (RS) sensors have more spectral bands and higher spatial resolution than before, which means a greater number of pixels in the same area. Nevertheless, the more spectral bands and the greater number of pixels, the higher the computational complexity and the longer the processing times. Therefore, without dimensionality reduction, the classification task is challenging, particularly if large areas have to be processed. To solve this problem, our approach maps an RS-image or third-order tensor into a core tensor, representative of our input image, with the same spatial domain but with a lower number of new tensor bands using a Tucker decomposition (TKD). Then, a new input space with reduced dimensionality is built. To find the core tensor, the higher-order orthogonal iteration (HOOI) algorithm is used. A fully convolutional network (FCN) is employed afterwards to classify at the pixel domain, each core tensor. The whole framework, called here HOOI-FCN, achieves high performance metrics competitive with some RS-multispectral images (MSI) semantic segmentation state-of-the-art methods, while significantly reducing computational complexity, and thereby, processing time. We used a Sentinel-2 image data set from Central Europe as a case study, for which our framework outperformed other methods (included the FCN itself) with average pixel accuracy (PA) of 90% (computational time ∼90s) and nine spectral bands, achieving a higher average PA of 91.97% (computational time ∼36.5s), and average PA of 91.56% (computational time ∼9.5s) for seven and five new tensor bands, respectively.

Flexible Three-Dimensional Reconstruction via Structured-Light-based Visual Positioning and Global Optimization.

Three-dimensional (3D) reconstruction using line structured light vision system commonly cooperates with motion restraint devices, such as parallel guide rail push-broom devices. In this study, we propose a visual positioning method to eliminate the motion constraint. An extended orthogonal iteration algorithm for visual positioning is proposed to obtain the precise position of the line structured light binocular camera system during movement. The algorithm uses the information acquired by the binocular camera, and produces a better positioning accuracy than the traditional vision localization algorithm. Furthermore, a global optimization method is proposed to calculate the poses of the camera relative to the world coordinate system at each shooting position. This algorithm effectively reduces the error accumulation and pose drift during visual positioning, and 3D information of the surface can be measured via the proposed free-moving line structured light vision system. The simulation and physical experiments performed herein validate the proposed method and demonstrate the significant improvement in the reconstruction accuracy: when the test distance is 1.5 m, the root mean square error of the point cloud is within 0.5 mm.

An orthogonal iteration pose estimation algorithm based on an incident ray tracking model

Although the pinhole imaging model prevails among current pose estimation algorithms, this idealized model gradually shows its limitation and inaccuracy, especially in harsh environments. In recent years, a few generic imaging models have been proposed to replace the dominant pinhole one. Among them, the camera model, named the incident ray tracking model, has proved to be superior. This model consists of mappings between pixels on the image and straight lines in 3D space. Based on the incident ray tracking camera model, a pose estimation algorithm, which can be called the perspective-ray-based orthogonal iteration (PROI), is proposed in this paper. The proposed algorithm introduces the popular orthogonal iteration algorithm into the incident ray tracking model. In this method, the object space collinearity error is expressed by a more accurate perspective ray instead of the traditional line of sight. The orthogonal rotation matrices are computed by an iterative algorithm and the iterative initial value is given in a weak perspective model. Experiment results on the pose estimation with better accuracy and efficiency by PROI have shown the superiority of the proposed method compared with the best currently employed optimization algorithms.

Algorithm for pose estimation based on objective function with uncertainty-weighted measuring error of feature point cling to the curved surface.

This paper is concerned with the anisotropic and non-identical gray distribution of feature points clinging to the curved surface, upon which a high precision and uncertainty-resistance algorithm for pose estimation is proposed. Weighted contribution of uncertainty to the objective function of feature points measuring error is analyzed. Then a novel error objective function based on the spatial collinear error is constructed by transforming the uncertainty into a covariance-weighted matrix, which is suitable for the practical applications. Further, the optimized generalized orthogonal iterative (GOI) algorithm is utilized for iterative solutions such that it avoids the poor convergence and significantly resists the uncertainty. Hence, the optimized GOI algorithm extends the field-of-view applications and improves the accuracy and robustness of the measuring results by the redundant information. Finally, simulation and practical experiments show that the maximum error of re-projection image coordinates of the target is less than 0.110 pixels. Within the space 3000 mm×3000 mm×4000 mm, the maximum estimation errors of static and dynamic measurement for rocket nozzle motion are superior to 0.065° and 0.128°, respectively. Results verify the high accuracy and uncertainty attenuation performance of the proposed approach and should therefore have potential for engineering applications.

Complete Initial Solutions for Iterative Pose Estimation From Planar Objects

Camera pose estimation from the image of a planar object has important applications in photogrammetry and computer vision. In this paper, an efficient approach to find the initial solutions for iterative camera pose estimation using coplanar points is proposed. Starting with homography, the proposed approach provides a least-squares solution for absolute orientation, which has a relatively high accuracy and can be easily refined into one optimal pose that locates local minima of the according error function by using Gauss-Newton scheme or Lu’s orthogonal iteration algorithm. In response to ambiguities that exist in pose estimation from planar objects, we propose a novel method to find initial approximation of the second pose, which is different from existing methods in its concise form and clear geometric interpretation. Thorough testing on synthetic data shows that combined with currently employed iterative optimization algorithm, the two initial solutions proposed in this paper can achieve the same accuracy and robustness as the best state-of-the-art pose estimation algorithms, while with a significant decrease in computational cost. Real experiment is also employed to demonstrate its performance.

A novel algorithm for pose estimation based on generalized orthogonal iteration with uncertainty-weighted measuring error of feature points

In this paper, we investigate the effect of anisotropic and correlated non-identical distributions of feature points’ gray level on pose estimation in stereo vision system. The generalized orthogonal iteration (GOI) algorithm for pose estimation with uncertainty-weighted measuring error of feature target is proposed. In this method, the inverse covariance matrix is applied to describe the uncertainty of feature points, and weighted contribution of uncertainty to the error objective function is analysed. By transforming the uncertainty into the covariance-weighted data space, a novel objective function based on spatial collinear error is constructed. The orthogonal iterative algorithm is extended to stereo vision system for pose estimation and the GOI algorithm is deduced, by which the optimized solution to a novel objective function is given. Finally, simulation and actual experimental results show high accuracy and strong robustness of the proposed approach, and should therefore, have potential for a variety of engineering applications.

High precision and fast estimation of position and attitude measurement for space targets

In this paper, a high accuracy and fast speed position and attitude estimation algorithm of space targets is proposed. The central idea of the proposed algorithm is to solve the pose estimation problem with fast speed, high accuracy and noise-resistance by designing an improved orthogonal iteration algorithm with optimized absolute orientation solution. The predominant advantage of this technique is that it avoids the poor convergence or convergence failure problem caused by the weak perspective projection. By selecting the closed-form solution to initialize parameters, this algorithm improves the accuracy with negligible additional computational time. The proposed technique only needs to observe the targets at different orientations that unknown to observers, and the objective function of the collinearity error based on object space is established, thus the estimated parameters can be subsequently computed. Simulation and field experiment are conducted simultaneously.Results show that the algorithm we proposed performs higher accuracy and faster speed than the current employed algorithms, and the noise-resistance also outperforms others in experiment. The maximum estimation relative error of three euler angles doesn’t exceed 0.38%. This technique is very significant for high accuracy solution of position and attitude measurement for space target.

An Improved Orthogonal Iterative Algorithm for Monocular Camera Pose Estimation

In this paper, we focus on the classical perspective-n-point(PnP) problem in monocular camera pose estimation and propose an improved orthogonal iterative algorithm. The key idea is to integrate the steps in each iteration, and extract the repetitive calculation of each iteration. The repetitive computation in each iteration can be abstracted and done before iteration process. The computational complexity of each iteration is reduced from toO(n) to O(1) . So that, more iterations can be done in a short time and the accuracy is improved as well. The simulation results and real experiments results show the efficiency and accuracy of our entry accepted iterative algorithms, our algorithm can maintain high pose estimation accuracy. This algorithm is more likely to converge to correct pose in a short run time, which makes it more applicable for real time applications.

Improved system calibration for specular surface measurement by using reflections from a plane mirror.

In this paper, we introduce a flexible and simple system calibration method for specular surface metrology based on the combination of reflection rays determined by the varied points on a screen and reflection images of a plane mirror without fiducials placed at three different locations. This calibration procedure involves three steps. The camera is first calibrated based on plane patterns. Then the reflection ray directions are measured via correspondence matching. The last calibration step is the pose estimation by the orthogonal iteration algorithm and reflections in a plane mirror. Basically, the concept of replacing the coordinates of the camera center with the reflection ray can alleviate the trouble of imaging aberration. Then global optimization can be operated with the orthogonal projection defined by the reflection ray, providing precise initial values for the process of bundle adjustment, compared to the classical calibration approach directly using the local optimization algorithm. Simulations and experiments both demonstrate the validity, efficiency, and robustness of the proposed improved method. In the simulations, the proposed method achieves the absolute errors of the camera parameters within 3 pixels and the relative errors of the screen pose are below 0.5% when the noise level is 0.6 pixel. Furthermore, the calibration method shows strong anti-noise ability, relying on the application of the reflection rays and the global optimization before the final bundle adjustment. In addition, the reconstruction accuracy in our experiment improves by 60.11% by the proposed method compared with the calibration procedure, which only utilizes the bundle adjustment optimization. In general, this novel calibration method can make the measurement achieve high accuracy and robustness at a low cost and with a simple setup, providing an efficient, economical, and flexible approach for a phase measuring deflectometry system in practical situations.

Visual Measurement of the Racket Trajectory in Spinning Ball Striking for Table Tennis Player

A high-speed monocular vision system is established to track the racket trajectory for estimating the spinning ball initiated by a human. A new fast and robust method is proposed to extract the feature sequence of a racket's pose during the process of striking. Considering the complexity of the working environment and fast movement of the racket, a novel corner extraction algorithm with good robustness and high efficiency is presented, which mainly consists of two parts, i.e., target segmentation and line detection. Then PnP-based algorithm is adopted to get the rough pose of the racket, which is then optimized by orthogonal iteration algorithm to guarantee the orthogonality of the racket's orientation matrix. In order to classify the spinning mode of the ball with a higher accuracy, the racket's movement is represented by the sequence of normal vector of the racket's surface. Experiments are thoroughly conducted to verify the effectiveness of the proposed method.

基于序列正交迭代算法的立体视觉定位

For the intelligent vehicle autonomous visual navigation need to get real-time,accurate,robust their own location information,a robust,efficient and accurate stereo visual localization algorithm is proposed.A new direct P3 Ppose estimation with RANSAC was proposed to obtain matching inliers and initial motion parameters and greatly improve accuracy.Then a new motion parameters optimization method was proposed based on sequence orthogonal iterative algorithm for general camera models.Recent Nframes motion and structure parameters of stereo camera were rapidly optimized online.Compared with bundle adjustment,the speed and robust of the proposed method greatly enhanced,and the proposed method could attain global convergence.The outdoor real experiments show this method has high accuracy,good robustness and high computing speed in localization that can meet the high performance requirement of navigation localization.