Single Gaussian Model Research Articles

Handling Device Heterogeneity and Orientation Using Multistage Regression for GMM Based Localization in IoT Networks

Location estimation of heterogeneous smart devices is needed for the Internet of Things (IoT) based location services. Device orientation and heterogeneity are the bottlenecks in accurate location estimation, which are not addressed together in the existing methods. Also, most of the state-of-the-art Received Signal Strength (RSS) based localization methods consider a single Gaussian model instead of a mixture of Gaussians. In this paper, we propose to solve both these issues with a combination of multistage linear regression and Gaussian Mixture Model (GMM) method. Additionally, the proposed method detects the malicious data in the IoT network and estimates the location in case of sensor faults. The performance of the proposed method is tested using Wi-Fi signals in an indoor environment.

An equity-credit hybrid model for asset correlations

Single factor Gaussian copula models are widely used to manage credit risk of loan portfolios, even driving how many large financial institutions are capitalised under Basel II/III. Under this formulation, the default correlation between two separate firms is directly explained by their asset correlation to a systematic factor, which can be estimated using either equity correlations or observed default rates, with the portfolio losses usually being simulated under a Gaussian copula model. Though it is widely accepted that the use of observed default rates or even equity returns to calibrate a single factor Gaussian copula model is likely to understate the tail risk. This paper proposes a Bayesian approach for a single factor Gaussian copula where the asset correlations are modelled using an inverse Wishart prior with the scale parameter calibrated to observed default rates and the degrees of freedom chosen using the in-sample continuous ranked probability score whilst the equity correlations are used to obtain the posterior distribution. The proposed hybrid model is shown to produce probabilistic forecasts of defaults with better out-of-sample performance than the standard single factor Gaussian copula even though it maintained low complexity and ease of implementation.

Estimation distribution algorithms on constrained optimization problems

Estimation distribution algorithm (EDA) is an evolution technique that uses sampling to generate the offspring. Most developed EDAs focus on solving the optimization problems which only have the constraints of variable boundaries. In this paper, EDAs are proposed for solving the constrained optimization problems (COPs) involving various types of constraints. In particular, a modified extreme elitism selection method is designed for EDAs to handle the constraints. This selection extrudes the role of some top best solutions to pull the mean vector of the Gaussian distribution towards these best solutions and makes EDAs form a primary evolutionary direction. The EDAs based on five different Gaussian distribution with this selection are evaluated using a set of benchmark functions and some engineering design problems. It is found that for solving these problems, the EDA that is based on a single multivariate Gaussian distribution model with the modified extreme elitism selection outperforms the other EDAs and some state-of-the-art techniques.

Research Progress on Accurate Pencil Beam Model for Heavy Ion Cancer Therapy

The heavy ion treatment planning system of Institute of Modern Physics(IMP), Chinese Academy of Sciences adopts single Gaussian model to depict the lateral dose distribution of pencil beam currently. Without taking secondary particles produced by heavy-ion pencil beam in medium into full consideration, the single Gaussian model is not accurate enough to describe the lateral dose distribution. In fact, an accurate pencil beam model should include the description of low dose envelope contributed by secondary particles. This work summarized the cause of formation, property, dose contribution, mathematic models and measuring methods of the low dose envelope laterally far away from the incident axis of a pencil beam. Moreover, the lateral dose distribution of heavy ion pencil beams with different energies were calculated by means of the Monte Carlo simulation method, based on the horizontal nozzle of the demonstration facility of heavy ion medical machine in the Wuwei heavy-ion therapy center, and thus the degree of coincidence between the simulated data and different mathematic models was investigated. The results verified that the triple Gaussian model was better than the single and double Gaussian models to depict the lateral dose distribution of heavy ion pencil beams, mentioned from existing papers. Thus, this work provides a basis for further developing practical and accurate pencil beam model for heavy ion cancer therapy.

Gaussian mixture 3D morphable face model

3D Morphable Face Models (3DMM) have been used in pattern recognition for some time now. They have been applied as a basis for 3D face recognition, as well as in an assistive role for 2D face recognition to perform geometric and photometric normalisation of the input image, or in 2D face recognition system training. The statistical distribution underlying 3DMM is Gaussian. However, the single-Gaussian model seems at odds with reality when we consider different cohorts of data, e.g. Black and Chinese faces. Their means are clearly different. This paper introduces the Gaussian Mixture 3DMM (GM-3DMM) which models the global population as a mixture of Gaussian subpopulations, each with its own mean. The proposed GM-3DMM extends the traditional 3DMM naturally, by adopting a shared covariance structure to mitigate small sample estimation problems associated with data in high dimensional spaces. We construct a GM-3DMM, the training of which involves a multiple cohort dataset, SURREY-JNU, comprising 942 3D face scans of people with mixed backgrounds. Experiments in fitting the GM-3DMM to 2D face images to facilitate their geometric and photometric normalisation for pose and illumination invariant face recognition demonstrate the merits of the proposed mixture of Gaussians 3D face model.

Multilevel Gaussian graphical model for multilevel networks

Gaussian graphical models have become a popular tool to represent networks among variables such as genes. They use the conditional correlations from the joint distribution to describe the dependencies between gene pairs, and employ the precision matrix of the genes. Because of the sparse nature of the gene networks and small sample sizes in high dimensional genetic data, regularization approaches attracted much attention in aim at obtaining the shrinkage estimates of the precision matrix. However, existing methods have been focused on the Gaussian graphical model among genes; that is, they are only applicable to a single level Gaussian graphical model. It is known that pathways are not independent of each other because of shared genes and interactions among pathways. Developing multipathway analysis has been a challenging problem because of the complex dependence structure among pathways. By considering the dependency among pathways as well as the genes within each pathway, we propose a multilevel Gaussian graphical model (MGGM) in which one level describes the networks for genes and the other for pathways. We have developed a multilevel L1 penalized likelihood approach to achieve the sparseness on both levels. In addition, we have developed an iterative weighted graphical LASSO algorithm for MGGM. Our simulation results supported the advantages of our approach; our method estimated the network more accurately on the pathway level and sparser on the gene level. We also demonstrated the usefulness of our approach using a canine genes-pathways data set.

SU‐F‐T‐158: Experimental Characterization of Field Size Dependence of Dose and Lateral Beam Profiles of Scanning Proton and Carbon Ion Beams for Empirical Model in Air

Purpose:The Gaussian model for the lateral profiles in air is crucial for an accurate treatment planning system. The field size dependence of dose and the lateral beam profiles of scanning proton and carbon ion beams are due mainly to particles undergoing multiple Coulomb scattering in the beam line components and secondary particles produced by nuclear interactions in the target, both of which depend upon the energy and species of the beam. In this work, lateral profile shape parameters were fitted to measurements of field size dependence dose at the center of field size in air.Methods:Previous studies have employed empirical fits to measured profile data to significantly reduce the QA time required for measurements. From this approach to derive the weight and sigma of lateral profiles in air, empirical model formulations were simulated for three selected energies for both proton and carbon beams.Results:The 20%–80% lateral penumbras predicted by the double model for proton and single model for carbon with the error functions agreed with the measurements within 1 mm. The standard deviation between measured and fitted field size dependence of dose for empirical model in air has a maximum accuracy of 0.74% for proton with double Gaussian, and of 0.57% for carbon with single Gaussian.Conclusion:We have demonstrated that the double Gaussian model of lateral beam profiles is significantly better than the single Gaussian model for proton while a single Gaussian model is sufficient for carbon. The empirical equation may be used to double check the separately obtained model that is currently used by the planning system. The empirical model in air for dose of spot scanning proton and carbon ion beams cannot be directly used for irregular shaped patient fields, but can be to provide reference values for clinical use and quality assurance.

SU‐F‐T‐138: Commissioning and Evaluating Dose Computation Models for a Dedicated Proton Line Scanning Beam Nozzle in Eclipse Treatment Planning System

Purpose:In this study, we present an effective method to derive low dose envelope of the proton in‐air spot fluence at beam positions other than the isocenter to reduce amount of measurements required for planning commission. Also, we demonstrate commissioning and validation results of this method to the Eclipse treatment planning system (version 13.0.29) for a Sumitomo dedicated proton line scanning beam nozzle.Methods:The in‐air spot profiles at five beam‐axis positions (±200, ±100 and 0 mm) were obtained in trigger mode using a MP3 Water tank (PTW‐Freiburg) and a pinpoint ionization chamber (model 31014, PTW‐Freiburg). Low dose envelope (below 1% of the center dose) of the spot profile at isocenter was obtained by repeated point measurements to minimize dosimetry uncertainty. The double Gaussian (DG) model was used to fit and obtain optimal σ1, σ2 and their corresponding weightings through our in‐house MATLAB (Mathworks) program. σ1, σ2 were assumed to expand linearly along the beam axis from a virtual source position calculated by back projecting fitted sigmas from the single Gaussian (SG) model. Absolute doses in water were validated using an Advanced Markus chamber at the depth of 2cm with Pristine Peak (BP) R90d ranging from 5–32 cm for 10×10 cm2 scanned fields. The field size factors were verified with square fields from 2 to 20 cm at 2cm and before BP depth.Results:The absolute dose outputs were found to be within ±3%. For field size factor, the agreement between calculated and measurement were within ±2% at 2cm and ±3% before BP, except for the field size below 2×2 cm2.Conclusion:The double Gaussian model was found to be sufficient for characterizing the Sumitomo dedicated proton line scanning nozzle. With our effective double Gaussian fitting method, we are able to save significant proton beam time with acceptable output accuracy.

基于改进的单高斯背景模型检测算法的研究

基于改进的单高斯背景模型检测算法的研究

Robust point matching method for multimodal retinal image registration

In this paper, motivated by the problem of multimodal retinal image registration, we introduce and improve the robust registration framework based on partial intensity invariant feature descriptor (PIIFD), then present a registration framework based on speed up robust feature (SURF) detector, PIIFD and robust point matching, called SURF–PIIFD–RPM. Existing retinal image registration algorithms are unadaptable to any case, such as complex multimodal images, poor quality, and nonvascular images. Harris-PIIFD framework usually fails in correctly aligning color retinal images with other modalities when faced large content changes. Our proposed registration framework mainly solves the problem robustly. Firstly, SURF detector is useful to extract more repeatable and scale-invariant interest points than Harris. Secondly, a single Gaussian robust point matching model is based on the kernel method of reproducing kernel Hilbert space to estimate mapping function in the presence of outliers. Most importantly, our improved registration framework performs well even when confronted a large number of outliers in the initial correspondence set. Finally, multiple experiments on our 142 multimodal retinal image pairs demonstrate that our SURF–PIIFD–RPM outperforms existing algorithms, and it is quite robust to outliers.

Improving Estimation of Distribution Algorithm on Multimodal Problems by Detecting Promising Areas.

In this paper, a novel multiple sub-models maintenance technique, named maintaining and processing sub-models (MAPS), is proposed. MAPS aims to enhance the ability of estimation of distribution algorithms (EDAs) on multimodal problems. The advantages of MAPS over the existing multiple sub-models based EDAs stem from the explicit detection of the promising areas, which can save many function evaluations for exploration and thus accelerate the optimization speed. MAPS can be combined with any EDA that adopts a single Gaussian model. The performance of MAPS has been assessed through empirical studies where MAPS is integrated with three different types of EDAs. The experimental results show that MAPS can lead to much faster convergence speed and obtain more stable solutions than the compared algorithms on 12 benchmark problems.

Moving Target Detection Based on Double Model

In order to overcome the problem that the single-Gauss model is poor of anti-interference and Gaussian Mixture model is poor of real-time, we present the double modeling algorithm of moving target detection. We use three frame difference method to distinguish the invariant region and complex region in background. And then we use single-Gauss modeling to model the invariant background while the complex region of background would be modeled with Gaussian Mixture modeling. It is more effective than the single-Gauss model and more efficient than the Gaussian Mixture model .The experimental results show that the improved algorithm is superior to the traditional single Gauss model or Gaussian Mixture model. It can detect moving target more quickly and accurately, with good robustness and real-time.

Research on Algorithm of Video Segmentation Based on Self-Adaptive Single Gaussian Model

Single Gaussian background modeling is often used in the static scene. In order to overcome the deficiency of the traditional single Gaussian background subtraction method, an improved adaptive background modeling algorithm was proposed. First, the number of each pixel in the image determined as foreground that were as the parameters of each pixel update rate were counted respectively. So the original fixed update rate was transformed into the dynamic update rate changing with the parameter. In this way, the phenomena of ghosting and shelling was suppressed effectively in the traditional single model of Gauss. Finally, foreground objects were obtained by using the method of shadow removal based on morphological reconstruction. The experimental results indicate that the algorithm can quickly and accurately establish and update the background model, and extract the moving object effectively. Compared with existing approaches, experimental results with different real scenes demonstrate the robustness of the proposed method.

基于改进的单高斯背景模型运动目标检测算法

基于改进的单高斯背景模型运动目标检测算法

Persian Sign Language Recognition Using Radial Distance and Fourier Transform

This paper provides a novel hand gesture recognition method to recognize 32 static signs of the Persian Sign Language (PSL) alphabets. Accurate hand segmentation is the first and important step in sign language recognition systems. Here, we propose a method for hand segmentation that helps to build a better vision based sign language recognition system. The proposed method is based on YCbCr color space, single Gaussian model and Bayes rule. It detects region of hand in complex background and non-uniform illu mination. Hand gesture features are extracted by radial distance and Fourier t ransform. Finally, the Euclidean distance is used to compute the similarity between the input signs and all training feature vectors in the database. The system is tested on 480 posture images of the PSL, 15 images for each 32 signs. Experimental results show that our approach is capable to recognize all 32 PSL alphabets with 95.62% recognition rate.

Face and Hand Shape Segmentation Using Statistical Skin Detection for Sign Language Recognition

An accurate face and hand segmentation is the first and important step in sign language recognition systems. In this paper, we propose a method for face and hand segmentation that helps to build a better vision based sign language recognition system. The method proposed is based on YCbCr color space, single Gaussian model, Bayes rule and morphology operations. It detects regions of face and hands in complex background and non-uniform illumination. This method tested on 700 posture images of the sign language that are performed with one hand or both hands. Experimental results show that our method has achieved a good performance for images with complex background.

Features modeling with an α-stable distribution: Application to pattern recognition based on continuous belief functions

The aim of this paper is to show the interest in fitting features with an α-stable distribution to classify imperfect data. The supervised pattern recognition is thus based on the theory of continuous belief functions, which is a way to consider imprecision and uncertainty of data. The distributions of features are supposed to be unimodal and estimated by a single Gaussian and α-stable model. Experimental results are first obtained from synthetic data by combining two features of one dimension and by considering a vector of two features. Mass functions are calculated from plausibility functions by using the generalized Bayes theorem. The same study is applied to the automatic classification of three types of sea floor (rock, silt and sand) with features acquired by a mono-beam echo-sounder. We evaluate the quality of the α-stable model and the Gaussian model by analyzing qualitative results, using a Kolmogorov–Smirnov test (K–S test), and quantitative results with classification rates. The performances of the belief classifier are compared with a Bayesian approach.

Detection of moving objects with a moving camera using non-panoramic background model

This paper presents a fast and reliable method for moving object detection with moving cameras (including pan---tilt---zoom and hand-held cameras). Instead of building large panoramic background model as conventional approaches, we construct a small-size background model, whose size is the same as input frame, to decrease computation time and memory storage without loss of detection performance. The small-size background model is built by the proposed single spatio-temporal distributed Gaussian model and this can solve false detection results arising from registration error and background adaptation problem in moving background. More than the proposed background model based on spatial and temporal information, several pre- and post-processing methods are adopted and organized systematically to enhance the detection performances. We evaluate the proposed method with several video sequences under difficult conditions, such as illumination change, large zoom variation, and fast camera movement, and present outperforming detection results of our algorithm with fast computation time.

Very large fMRI study using the IMAGEN database: Sensitivity–specificity and population effect modeling in relation to the underlying anatomy

In this paper we investigate the use of classical fMRI Random Effect (RFX) group statistics when analyzing a very large cohort and the possible improvement brought from anatomical information. Using 1326 subjects from the IMAGEN study, we first give a global picture of the evolution of the group effect t-value from a simple face-watching contrast with increasing cohort size. We obtain a wide activated pattern, far from being limited to the reasonably expected brain areas, illustrating the difference between statistical significance and practical significance. This motivates us to inject tissue-probability information into the group estimation, we model the BOLD contrast using a matter-weighted mixture of Gaussians and compare it to the common, single-Gaussian model. In both cases, the model parameters are estimated per-voxel for one subgroup, and the likelihood of both models is computed on a second, separate subgroup to reflect model generalization capacity. Various group sizes are tested, and significance is asserted using a 10-fold cross-validation scheme. We conclude that adding matter information consistently improves the quantitative analysis of BOLD responses in some areas of the brain, particularly those where accurate inter-subject registration remains challenging.

A hierarchical naive Bayesian network classifier embedded GMM for textural image

To address several problems in high-dimensional textures feature space and the deficiencies of the single Gaussian distribution for remote sensing data, this paper proposes a hierarchical naive Bayesian network classifier embedded in a Gaussian mixture model for high-dimensional textural image classification. High-dimensional features are grouped by the model on the basis of the correlations between them. In this way, the high-dimensional problem is decomposed into multiple problems of lower dimension. At the same time, for each group of features, a Gaussian mixture model is applied to simulate the data distribution in feature space for land covers, which fits the “original” data distribution better than a single Gaussian model. The Gaussian mixture model is embedded as a child node into a naive Bayesian network, and then the final classification result is obtained within the naive Bayesian network classifier framework. Experimental results for the classification of Landsat ETM+ and QuickBird image textures demonstrated that the classification accuracy of this method is better than that of a traditional Bayesian network classifier and some other classical classifiers. Comparing with the method dealing with original high-dimensional features, it is also more efficiency and effectiveness with fewer demand of sample size and lower time complexity.