3D Human Pose Estimation from a Monocular Image Using Model Fitting in Eigenspaces

Generally, there are two approaches for solving the problem of human pose estimation from monocular images. One is the learning-based approach, and the other is the model-based approach. The former method can estimate the poses rapidly but has the disadvantage of low estimation accuracy. While the latter method is able to accurately estimate the poses, its computational cost is high. In this paper, we propose a method to integrate the learning-based and model-based approaches to improve the estimation precision. In the learning-based approach, we use regression analysis to model the mapping from visual observations to human poses. In the model-based approach, a particle filter is employed on the results of regression analysis. To solve the curse of the dimensionality problem, the eigenspace of each motion is learned using Principal Component Analysis (PCA). Finally, the proposed method was estimated using the CMU Graphics Lab Motion Capture Database. The RMS error of human joint angles was 6.2 degrees using our method, an improvement of up to 0.9 degrees compared to the method without eigenspaces.

SOME RESIDUAL BOUNDS FOR APPROXIMATE EIGENVALUES AND APPROXIMATE EIGENSPACES

In this paper we consider approximate eigenvalues and approximate eigenspaces for the generalized Rayleigh quotient, and present some residual bounds. Our obtained bounds will improve the existing ones.

矢量水听器改进高分辨Eigenspace算法

针对传统高分辨方位谱估计算法在水声低信噪比环境下性能较差,且对相干源的方位估计性能显著下降的问题,本文在Eigenspace算法的基础上,提出了基于声矢量阵声压振速联合处理的Eigenspace-Wiener算法和空间平滑的Eigenspace-Wiener算法。本文将常规Eigenspace算法的推广应用于声矢量阵,采用维纳后置滤波算法,可以有效降低旁瓣;针对相干源,进行空间平滑处理后采用维纳后置滤波算法,可以增强解相干能力且抑制噪声。计算机仿真结果表明:Eigenspace-Wiener算法较Eigenspace算法旁瓣更低;空间平滑Eigenspace-Wiener算法相对于空间平滑MUSIC算法具有良好的相干目标分辨性能。

基于Eigenspace的面瘫判定系统

本文将特征空间分类方法应用于面瘫图像的判定。结合应用的特点 ,引入多特征空间分类 ,比较图像与它们到两个特征空间的投影之间的距离作出判定 ,并在系统中加入灰度图变换 ,脸部子区域分割 ,确定对称轴和输入向量计算等前处理步骤。实验证明 ,本文的改进提高了系统判定的正确性。

Robust multiple face tracking via mixture model

Based on particle filter framework,a robust tracker is proposed for tracking multiple faces of people moving in a scene.Although most existing algorithms are able to track human face well in controlled environments,they usually fail when human face appearance changes significantly or it is sheltered.To solve this problem,we propose a method using color,contour and texture information of human face together for tracking.Firstly,we use the color and contour model to track human faces in initial images and extract pixels belonging to human face color.Then these pixels are used to form a training set for setting up texture model on eigenspace representations.The two models then work together in following tracking.To reflect changes in human face appearance,update methods are also proposed for the two models including an adaptive-factor by which the texture model can be updated much more effectively when the human face's texture or rotation changes dramatically.Experiment results show that the proposed method is able to track human faces well under large appearance rotation changes,as well as in case of total occlusion by similar color objects.

Effect of Weather on the Spread of COVID-19 Using Eigenspace Decomposition

Since the end of 2019,the world has suffered from a pandemic of the disease called COVID-19.WHO reports show approximately 113M confirmed cases of infection and 2.5 M deaths.All nations are affected by this nightmare that continues to spread.Widespread fear of this pandemic arose not only from the speed of its transmission:a rapidly changing“normal life”became a fear for everyone.Studies have mainly focused on the spread of the virus,which showed a relative decrease in high temperature,low humidity,and other environmental conditions.Therefore,this study targets the effect of weather in considering the spread of the novel coronavirus SARS-CoV-2 for some confirmed cases in Iraq.The eigenspace decomposition technique was used to analyze the effect of weather conditions on the spread of the disease.Our theoretical findings showed that the average number of confirmed COVID-19 cases has cyclic trends related to temperature,humidity,wind speed,and pressure.We supposed that the dynamic spread of COVID-19 exists at a temperature of 130 F.The minimum transmission is at 120 F,while steady behavior occurs at 160 F.On the other hand,during the spread of COVID-19,an increase in the rate of infection was seen at 125%humidity,where the minimum spread was achieved at 200%.Furthermore,wind speed showed the most significant effect on the spread of the virus.The spread decreases with a wind speed of 45 KPH,while an increase in the infectious spread appears at 50 KPH.

A feature extraction and correspondence algorithm for laser range finder with sensor uncertainty

This paper presents a feature extraction and correspondence algorithm which employs a novel feature transform. Unlike conventional approaches such as Hough Transform, we employ a robust but simple approach to extract the geometrical feature under real dynamic world conditions. Multi-threshold segmentation and the split-and-merge method are employed to interpret geometrical features such as edge, concave corners, convex corners, and segments in a unified framework. The features are represented by feature tree (F-Tree) so as to compactly represent the environments and some important properties of the F-Tree are discussed in this paper. To demonstrate the validity of the approach, we show the actual experiment results which are based on real Laser Range Finder data and real time analysis. The comparative study with Hough Transform shows the advantages and the high performance of the proposed algorithm.

An Eigenspace Method for Detecting Space-Time Disease Clusters with Unknown Population-Data

Space-time disease cluster detection assists in conducting disease surveillance and implementing control strategies.The state-of-the-art method for this kind of problem is the Space-time Scan Statistics(SaTScan)which has limitations for non-traditional/non-clinical data sources due to its parametric model assumptions such as Poisson orGaussian counts.Addressing this problem,an Eigenspace-based method called Multi-EigenSpot has recently been proposed as a nonparametric solution.However,it is based on the population counts data which are not always available in the least developed countries.In addition,the population counts are difficult to approximate for some surveillance data such as emergency department visits and over-the-counter drug sales,where the catchment area for each hospital/pharmacy is undefined.We extend the population-based Multi-EigenSpot method to approximate the potential disease clusters from the observed/reported disease counts only with no need for the population counts.The proposed adaptation uses an estimator of expected disease count that does not depend on the population counts.The proposed method was evaluated on the real-world dataset and the results were compared with the population-based methods:Multi-EigenSpot and SaTScan.The result shows that the proposed adaptation is effective in approximating the important outputs of the population-based methods.

Seismic Data Quality Control and Interpolation Using Principal Component Analysis

Commonly, seismic data processing procedures, such as stacking and prestack migration, require the ability to detect bad traces/shots and restore or replace them by interpolation, particularly when the seismic observations are noisy or there are malfunctioned components in the recording system. However, currently available trace/shot interpolation methods in the spatial or Fourier domain must deal with requirements such as evenly sampled traces/shots, infinite bandwidth of the signals, and linear seismic events. In this paper, we present a novel method, termed the E-S (eigenspace seismic) method, using principal component analysis (PCA) of the seismic signal to address the issue of reliable detection or interpolation of bad traces/shots. The E-S method assumes the existence of a correlation between the observed seismic entities, such as trace or shot gathers, making it possible to estimate one of these entities from all others for interpolation or seismic quality control. It first transforms a trace (or shot) gather into an eigenspace using PCA. Then in the eigenspace, it treats every trace as a point with its loading scores of PCA as its coordinates. Simple linear, bilinear, or cubic spline 1 dimensional (1D) interpolation is used to determine PCA loading scores for any arbitrary coordinate in the eigenspace, which are then used to construct an interpolated trace for the desired position in physical space. This E-S method works with either regular or irregular sampling and, unlike various other published methods, it is well-suited for band-limited seismic records with curvilinear reflection events. We developed related algorithms and applied these to processed synthetic and offshore seismic survey data with or without simulated noises to demonstrate their performance. By comparing the interpolated and observed seismic traces, we find that the E-S method can effectively assess the quality of the trace, and restore poor quality data by interpolation. The successful processing of synthetic and real data using the E-S method presented in this approach will be widely applicable to seismic trace/shot interpolation and seismic quality control.

A SUBARRAY-SYNTHESIS BASED 2D DOA ESTIMATION METHOD

In some satellite communications, we need to perform Direction Of Arrival (DOA) angle estima- tion under the restriction that the number of receivers is less than that of the array elements in an array antenna. To solve the conundrum, a method named subarray-synthesis-based Two-Dimensional DOA (2D DOA) angle estimation is proposed. In the method, firstly, the array antenna is divided into a series of subarray antennas based on the total number of receivers; secondly, the subarray antennas’ output covariance matrices are esti- mated; thirdly, an equivalent covariance matrix is synthesized based on the subarray output covariance matri- ces; then 2D DOA estimation is performed. Monte Carlo simulations showed that the estimation method is ef- fective.

On Monotone Eigenvectors of a Max-<i>T </i>Fuzzy Matrix

The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices in the max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra have been presented in previous papers. In this paper, we investigate the monotone eigenvectors in a max-T algebra, list some particular properties of the monotone eigenvectors in max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra, respectively, and illustrate the relations among eigenspaces in these algebras by some examples.

Performance Analysis on Output SINR of Robust Two-Stage Beamforming

In this paper, we present a theoretical analysis of the output signal-to-interference-plus-noise ratio (SINR) for eigen-space beamformers so as to investigate the performance degradation caused by large pointing errors. For the sake of reducing such performance loss, a robust scheme, which consists of two cascaded signal processors, is proposed for adaptive beamformers. In the first stage, an algorithm possessing time efficiency is developed to adjust the direc-tion-of-arrival (DOA) estimate of the desired source. Based the achieved DOA estimate, the second stage provides an eigenspace beamformer combined with the spatial derivative constraints (SDC) to further mitigate the cancellation of the desired signal. Analysis and numerical results have been conducted to verify that the proposed scheme yields a better robustness against pointing errors than the conventional approaches.

Structural uncertainty quantification of Reynolds-Averaged Navier–Stokes closures for various shock-wave/boundary layer interaction flows

Accurate prediction of Shock-Wave/Boundary Layer Interaction(SWBLI)flows has been a persistent challenge for linear eddy viscosity models.A major limitation lies in the isotropic representation of the Reynolds stress,as assumed under the Boussinesq approximation.Recent studies have shown promise in improving the prediction capability for incompressible separation flows by perturbing the Reynolds-stress anisotropy tensor.However,it remains uncertain whether this approach is effective for SWBLI flows,which involve compressibility and discontinuity.To address this issue,this study systematically quantifies the structural uncertainty of the anisotropy for oblique SWBLI flows.The eigenspace perturbation method is applied to perturb the anisotropy tensor predicted by the Menter Shear–Stress Transport(SST)model and reveal the impacts of anisotropy on the prediction of quantities of interest,such as separation and reattachment positions,wall static pressure,skin friction,and heat flux.The results demonstrate the potential and reveal the challenges of eigenspace perturbation in improving the SST model.Furthermore,a detailed analysis of turbulent characteristics is performed to identify the source of uncertainty.The findings indicate that eigenspace perturbation primarily affects turbulent shear stress,while the prediction error of the SST model is more related to turbulent kinetic energy.

Image Region Selection and Ensemble for Face Recognition

In this paper, a novel framework for face recognition, namely Selective Ensemble of Image Regions （SEIR）, is proposed. In this framework, all possible regions in the face image are regarded as a certain kind of features. There are two main steps in SEIR： the first step is to automatically select several regions from all possible candidates; the second step is to construct classifier ensemble from the selected regions. An implementation of SEIR based on multiple eigenspaces, namely SEME, is also proposed in this paper. SEME is analyzed and compared with eigenface, PCA ＋ LDA, eigenfeature, and eigenface ＋ eigenfeature through experiments. The experimental results show that SEME achieves the best performance.

Voice conversion using structured Gaussian mixture model in cepstrum eigenspace

A new methodology of voice conversion in cepstrum eigenspace based on structured Gaussian mixture model is proposed for non-parallel corpora without joint training. For each speaker, the cepstrum features of speech are extracted, and mapped to the eigenspace which is formed by eigenvectors of its scatter matrix, thereby the Structured Gaussian Mixture Model in the EigenSpace （SGMM-ES） is trained. The source and target speaker＇s SGMM-ES are matched based on Acoustic Universal Structure （AUS） principle to achieve spectrum transform function. Experimental results show the speaker identification rate of conversion speech achieves 95.25%, and the value of average cepstrum distortion is 1.25 which is 0.8% and 7.3% higher than the performance of SGMM method respectively. ABX and MOS evaluations indicate the conversion performance is quite close to the traditional method under the parallel corpora condition. The results show the eigenspace based structured Gaussian mixture model for voice conversion under the non-parallel corpora is effective.

Maximization of the sum of the trace ratio on the Stiefel manifold, I: Theory

We are concerned with the maximization of tr（V T AV）/tr（V T BV）＋tr（V T CV） over the Stiefel manifold {V ∈ R m×l ｜ V T V = Il} （l 〈 m）, where B is a given symmetric and positive definite matrix, A and C are symmetric matrices, and tr（. ） is the trace of a square matrix. This is a subspace version of the maximization problem studied in Zhang （2013）, which arises from real-world applications in, for example, the downlink of a multi-user MIMO system and the sparse Fisher discriminant analysis in pattern recognition. We establish necessary conditions for both the local and global maximizers and connect the problem with a nonlinear extreme eigenvalue problem. The necessary condition for the global maximizers offers deep insights into the problem, on the one hand, and, on the other hand, naturally leads to a self-consistent-field （SCF） iteration to be presented and analyzed in detail in Part II of this paper.

Maximization of the sum of the trace ratio on the Stiefel manifold, II: Computation

The necessary condition established in Part I of this paper for the global maximizers of the maximization problem max V tr（VTAV）/tr（VTBV）＋tr（VTCV）over the Stiefel manifold{V∈Rm×l ｜VTV=Il}（l〈m）,naturally leads to a self-consistent-field（SCF）iteration for computing a maximizer.In this part,we analyze the global and local convergence of the SCF iteration,and show that the necessary condition for the global maximizers is fulfilled at any convergent point of the sequences of approximations generated by the SCF iteration.This is one of the advantages of the SCF iteration over optimization-based methods.Preliminary numerical tests are reported and show that the SCF iteration is very efficient by comparing with some manifold-based optimization methods.