Spatially-Aware Gaussian Mixture Models for Structured Segmentation in Multispectral Satellite Imagery

Segmentation of clusters by template rotation expectation maximization

Gaussian-input Gaussian mixture model for representing density maps and atomic models.

The traditional Expectation-Maximization (EM) training of Gaussian Mixture Model (GMM) is essentially a batch mode procedure which requires the multiple data samples with the sufficient size to update the model parameters. This severely limits the deployment and adaptation of GMM in many real-time online systems since the newly observed data samples are expected to be incorporated into the system upon available via retraining the model. This paper presents a new online incremental EM training procedure of GMM, which aims to perform the EM training incrementally and so can adapt GMM online sample by sample. The proposed method is extended on two kinds of EM algorithms for GMM, namely, Split-and-Merge EM and the traditional EM. Experiments on both the synthetic data and a speech processing task show the advantages and efficiency of the new method.

One effective iterative method for estimating parameters in latent variable probabilistic models is the Expectation-Maximization (EM) algorithm, which finds extensive use in classification issues. A versatile probabilistic framework for modeling data from multiple Gaussian distributions, Gaussian Mixture Models (GMMs) employ EM for parameter estimation, which is explored in this article. Problems with class membership estimation (including means, covariances, and mixing coefficients) are the primary focus of this study. Starting with initial parameter estimations, estimating posterior probabilities in the E-step, and repeatedly updating model parameters in the M-step until convergence, the technique entails applying the EM algorithm on both synthetic and real-world datasets. In order to measure performance, we compare it to K-means and other baseline classifiers using measures like classification accuracy, Adjusted Rand Index (ARI), and log-likelihood progression. When data is distributed according to a multimodal Gaussian distribution, the findings show that EM-GMM provides better parameter estimation and better classification accuracy. Initialization procedures have a substantial effect on performance, as convergence study further shows. In addition to reiterating the EM algorithm's usefulness for probabilistic classification, this paper also describes its advantages and disadvantages and offers suggestions for improving its performance in settings with high-dimensional data and noise.

The accurate modeling of uncertain variables, such as wind power and load uncertainty, is an essential foundation for the planning operation and scheduling decisions in power systems. Currently, Gaussian mixture model (GMM) and Dirichlet process mixture model (DPMM) are the primary techniques used to characterize uncertainties in power systems, which are commonly solved by expectation-maximization (EM) algorithm. However, for the massive data of uncertain variables, the algorithm encounters challenges in accurately obtaining GMM and DPMM with a lower time consumption. To address this issue, we propose a method for GMM uncertainty modeling in power systems considering the mutual assistance of latent variables. Specifically, the GMM of uncertain variables is first constructed, and the conditional probability is employed to characterize the mutual assistance of latent variables. Then, an improved EM algorithm is developed to obtain the optimal GMM parameters, in which the expectation step (E-step) and maximization step (M-step) of the algorithm are revised using the conditional probability. Importantly, the closed-form solutions for GMM parameters are rederived in the revised E-step and M-step. Finally, the proposed uncertainty modeling method is compared with the traditional GMM and DPMM on actual wind power and load data from Australia. The proposed method performs the efficiency and accuracy in characterizing uncertainty.

The expectation-maximization (EM) algorithm is a popular approach for parameter estimation of finite mixture model (FMM). A drawback of this approach is that the number of components of the finite mixture model is not known in advance, nevertheless, it is a key issue for EM algorithms. In this paper, a penalized minimum matching distance-guided EM algorithm is discussed. Under the framework of Greedy EM, a fast and accurate algorithm for estimating the number of components of the Gaussian mixture model (GMM) is proposed. The performance of this algorithm is validated via simulative experiments of univariate and bivariate Gaussian mixture models.

The expectation maximisation (EM) algorithm is an iterative maximum likelihood procedure often used for estimating the parameters of a mixture model. Theoretically, increases in the likelihood function are guaranteed as the algorithm iteratively improves upon previously derived parameter estimates. The algorithm is considered to converge when all parameter estimates become stable and no further improvements can be made to the likelihood value. However, to reduce computational time, it is often common practice for the algorithm to be stopped before complete convergence using heuristic approaches. In this paper, we consider various stopping criteria and evaluate their effect on fitting Gaussian mixture models (GMMs) to patient length of stay (LOS) data. Although the GMM can be successfully fitted to positively skewed data such as LOS, the fitting procedure often requires many iterations of the EM algorithm. To our knowledge, no previous study has evaluated the effect of different stopping criteria on fitting GMMs to skewed distributions. Hence, the aim of this paper is to evaluate the effect of various stopping criteria in order to select and justify their use within a patient spell classification methodology. Results illustrate that criteria based on the difference in the likelihood value and on the GMM parameters may not always be a good indicator for stopping the algorithm. In fact we show that the values of the difference in the variance parameters should be used instead, as these parameters are the last to stabilise. In addition, we also specify threshold values for the other stopping criteria.

Automatic segmentation of corpus collasum using Gaussian mixture modeling and Fuzzy C means methods

Image segmentation has always been an important research direction in the field of images processing, however, due to the long cycle of algorithm, the image segmentation techniques have never been widely applied. According to the problem above, a image segmentation algorithm of Gaussian Mixture Model (GMM) based on Map/Reduce is proposed to improve the real-time performance. Firstly, the architecture of Hadoop image processing interface (Hipi) is presented to improve the ability of Map/Reduce to process small image. The K-means is present to generate the init value of Gaussian Mixture Model to avoid local optimal. Secondly, the cloud computational model of Map/Reduce is proposed to realize the parallel of GMM, and the fusion method of the sub-model for GMM is presented to keep the accuracy of segmentation. Finally, the experiment is carried out based on the cloud platform of aliyun. Results show the image segmentation algorithm of GMM based on Map/Reduce can greatly improve the real-time performance with keeping the accuracy of segmentation.

This article proposes the distribution similarity measure–based Gaussian mixtures model for the contact-state (CS) modelling in force-guided robotic assembly processes of flexible rubber parts. The wrench (Cartesian force and torque) signals of the manipulated object are captured for different states of the given assembly process. The distribution similarity measure–based Gaussian mixtures model CS modelling scheme is employed in modelling the captured wrench signals for different CSs. The proposed distribution similarity measure–based Gaussian mixtures model CS modelling scheme uses the Gaussian mixtures model in modelling the captured signals. The parameters of the Gaussian mixtures models are computed using expectation maximisation. The optimal number of Gaussian mixtures model components for each CS model is determined by considering the classification success rate as an index for the similarity measure between the distribution of the captured signals and the developed models. The optimal number of Gaussian mixtures model components corresponds to the highest classification success rate; hence, object elasticity variation would be accommodated by properly choosing the optimal number of Gaussian mixtures model components. The performance of the proposed distribution similarity measure–based Gaussian mixtures model CS modelling strategy is evaluated by a test stand composed of a KUKA lightweight robot doing peg-in-hole assembly processes for flexible rubber objects. Two rubber objects with different elasticity are considered for two experiments; in the first experiment, an elastic peg of 30 Shore A hardness is considered and that of the second experiment has hardness of 6 Shore A which is even softer than the one used in experiment 1. Employing the proposed distribution similarity measure–based Gaussian mixtures model CS modelling strategy excellent classification success rate was obtained for both experiments. However, more Gaussian mixtures model components are required for the softer one that gives a strong impression of the non-stationarity behaviour increment for softer materials. Comparison is performed with the available CS modelling schemes and the distribution similarity measure–based Gaussian mixtures model is shown to provide the best classification success rate performance with a reduced computational time.

To model manipulation tasks, we propose a novel method for learning manipulation skills based on the degree of motion granularity. Even though manipulation tasks usually consist of a mixture of fine-grained and coarse-grained movements, to the best of our knowledge, manipulation skills have so far been modeled without considering their motion granularity. To model such a manipulation skill, Gaussian mixture models (GMMs) have been represented using several well-known techniques such as principal component analysis, k-means, Bayesian information criterion, and expectation-maximization (EM) algorithms. However, in this GMM, there is a problem in that when a mixture of fine-grained and coarse-grained movements is modeled as a GMM, fine-grained movements tend to be poorly represented. To resolve this issue, we measure a continuous degree of motion granularity for every time step of a manipulation task from a GMM. Then, we remodel the GMM by weighting a conventional k-means algorithm with motion granularity. Finally, we also estimate the parameters of the GMM by weighting the conventional EM with motion granularity. To validate our proposed method, we evaluate the GMM estimated using our proposed method by comparing it with those estimated by different GMMs in terms of inference, regression, and generalization using a robot arm that performs two daily tasks, namely decorating a very small area and passing through a narrow tunnel.

The results of comprehensive monitoring of anthropogenic impact on some coastal water areas of the Black Sea are presented. Multispectral satellite imagery and sea truth hydrooptical and hydroacoustical data acquired aboard research vessels are used as the main information sources. In the course of monitoring, more than 300 multispectral Resurs-P, GeoEye, WorldView, Landsat, Sentinel-2 and other satellite images of water areas near the cities of Sevastopol and Gelendzhik were systematized and analyzed. For processing the multispectral satellite imagery, we use an approach based on the calculation and analysis of distributions of relative variability characteristics of the backscattering signal in different regions of the electromagnetic spectrum (“color indices”). The sea truth measurements, which were carried out using a SIPO9 light attenuation index spectral meter and an ADCP acoustic Doppler profilometer, allowed us to detect submerged pollutant plumes and validate the results of satellite data processing. By using the suggested methods, we found and quantified the characteristics of intensive anthropogenic impacts due to submerged outfalls in the coastal waters near Sevastopol and Gelendzhik. Processing the multispectral satellite imagery and sea-truth data revealed several disruptions in the outfall collectors located in these coastal waters.

Surface water maps are useful in a variety of disciplines from climate change analysis to water resource management. Multispectral satellite imagery can be used to derive such surface water maps using a variety of image processing methods. The medium resolution Sentinel-2 multispectral satellite imagery catalogue is currently used extensively for surface water mapping. The quality and accuracy of these maps produced from Sentinel-2 imagery can vary greatly depending on the method applied to classify the image pixels into land or water. Thus far, there has not been a consensus on which method produces the highest accuracy surface water maps, warranting a direct comparison to assess these methods in a wide range of geographic settings. Here we show that among some of the most commonly applied surface water mapping methods (NDWI, MNDWI, AWEI_SH, AWEI_NSH, AWEI_BOTH, SVM, RT, MLC, and KNN) that no single method produced the most accurate maps across the four locations studied, but AWEI_NSH performed the best overall across the four locations, and SVM was the best performing machine learning technique. Rather, each method's performance was shown to depend on the objects present in the image (e.g., built-up, shadows, vegetated shorelines, narrow waterbodies, etc.) and how successfully the method was able to classify those objects properly. This is in-line with current understanding of spectral index methods' performance, and we provide recommendations to aid remote sensing data users in choosing a suitable method based on their image's characteristics. Using these recommendations, we hope that the quality of surface water maps derived from multispectral satellite imagery will be improved for all disciplines that utilize such data by allowing users to choose the method that is best fit to the application.

In this letter, we investigate the semitied Gaussian mixture models for robust learning and adaptation of robot manipulation tasks. We make use of the spatial and temporal correlation in the data by tying the covariance matrices of the mixture model with common synergistic directions/basis vectors, instead of estimating full covariance matrices for each cluster in the mixture. This allows the reuse of the discovered synergies in different parts of the task having similar coordination patterns. We extend the approach to task-parameterized and hidden semi-Markov models for autonomous adaptation to changing environmental situations. The planned movement sequence from the model is smoothly followed with a finite horizon linear quadratic tracking controller. Experiments to encode whole body motion data in simulation, followed by valve opening and pick-and-place via obstacle avoidance tasks with the Baxter robot, show improvement over standard Gaussian mixture models with much less parameters and better generalization ability.

Mixture modeling using elliptical distributions promises enhanced robustness, flexibility, and stability over the widely employed Gaussian mixture model (GMM). However, existing studies based on the elliptical mixture model (EMM) are restricted to several specific types of elliptical probability density functions, which are not supported by general solutions or systematic analysis frameworks; this significantly limits the rigor in the design and power of EMMs in applications. To this end, we propose a novel general framework for estimating and analyzing the EMMs, achieved through the Riemannian manifold optimization. First, we investigate the relationships between Riemannian manifolds and elliptical distributions, and the so established connection between the original manifold and a reformulated one indicates a mismatch between these manifolds, a major cause of failure of the existing optimization for solving general EMMs. We next propose a universal solver that is based on the optimization of a redesigned cost and prove the existence of the same optimum as in the original problem; this is achieved in a simple, fast and stable way. We further calculate the influence functions of the EMM as theoretical bounds to quantify robustness to outliers. Comprehensive numerical results demonstrate the ability of the proposed framework to accommodate EMMs with different properties of individual functions in a stable way and with fast convergence speed. Finally, the enhanced robustness and flexibility of the proposed framework over the standard GMM are demonstrated both analytically and through comprehensive simulations.