Fast re-parameterisation of Gaussian mixture models for robotics applications

Autonomous navigation and picture compilation tasks require robust feature descriptions or models. Given the non Gaussian nature of sensor observations, it will be shown that Gaussian mixture models provide a general probabilistic representation allowing analytical solutions to the update and prediction operations in the general Bayesian filtering problem. Each operation in the Bayesian filter for Gaussian mixture models multiplicatively increases the number of parameters in the representation leading to the need for a re-parameterisation step. A computationally efficient re-parameterisation step will be demonstrated resulting in a compact and accurate estimate of the true distribution.

Estimation of signals in colored non gaussian noise based on Gaussian Mixture models

Non-Gaussianity of signals/noise often results in significant performance degradation for systems, which are designed using the Gaussian assumption. So non-Gaussian signals/noise require a different modelling and processing approach. In this paper, we discuss a new Bayesian estimation technique for non-Gaussian signals corrupted by colored non Gaussian noise. The method is based on using zero mean finite Gaussian Mixture Models (GMMs) for signal and noise. The estimation is done using an adaptive non-causal nonlinear filtering technique. The method involves deriving an estimator in terms of the GMM parameters, which are in turn estimated using the EM algorithm. The proposed filter is of finite length and offers computational feasibility. The simulations show that the proposed method gives a significant improvement compared to the linear filter for a wide variety of noise conditions, including impulsive noise. We also claim that the estimation of signal using the correlation with past and future samples leads to reduced mean squared error as compared to signal estimation based on past samples only.

Task-driven adaptive statistical compressive sensing of gaussian mixture models

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific sensing protocols specifically and jointly designed for classification and reconstruction. A two-step adaptive sensing paradigm is developed, where online sensing is applied to detect the signal class in the first step, followed by a reconstruction step adapted to the detected class and the observed samples. The approach is based on information theory, here tailored for Gaussian mixture models (GMMs), where an information-theoretic objective relationship between the sensed signals and a representation of the specific task of interest is maximized. Experimental results using synthetic signals, Landsat satellite attributes, and natural images of different sizes and with different noise levels show the improvements achieved using the proposed framework when compared to more standard sensing protocols. The underlying formulation can be applied beyond GMMs, at the price of higher mathematical and computational complexity. © 1991-2012 IEEE.

An optimisation of Gaussian mixture models for integer processing units

This paper investigates sub-integer implementations of the adaptive Gaussian mixture model (GMM) for background/foreground segmentation to allow the deployment of the method on low cost/low power processors that lack Floating Point Unit (FPU). We propose two novel integer computer arithmetic techniques to update Gaussian parameters. Specifically, the mean value and the variance of each Gaussian are updated by a redefined and generalised "round'' operation that emulates the original updating rules for a large set of learning rates. Weights are represented by counters that are updated following stochastic rules to allow a wider range of learning rates and the weight trend is approximated by a line or a staircase. We demonstrate that the memory footprint and computational cost of GMM are significantly reduced, without significantly affecting the performance of background/foreground segmentation.

Incremental learning of temporally-coherent gaussian mixture models

In this paper we address the problem of learning Gaussian Mixture Models (GMMs) incrementally. Unlike previous approaches which universally assume that new data comes in blocks representable by GMMs which are then merged with the current model estimate, our method works for the case when novel data points arrive oneby- one, while requiring little additional memory. We keep only two GMMs in the memory and no historical data. The current fit is updated with the assumption that the number of components is fixed, which is increased (or reduced) when enough evidence for a new component is seen. This is deduced from the change from the oldest fit of the same complexity, termed the Historical GMM, the concept of which is central to our method. The performance of the proposed method is demonstrated qualitatively and quantitatively on several synthetic data sets and video sequences of faces acquired in realistic imaging conditions

Incremental learning of temporally-coherent Gaussian mixture models

In this paper we address the problem of learning Gaussian Mixture Models (GMMs) incrementally. Unlike previous approaches which universally assume that new data comes in blocks representable by GMMs which are then merged with the current model estimate, our method works for the case when novel data points arrive one- by-one, while requiring little additional memory. We keep only two GMMs in the memory and no historical data. The current fit is updated with the assumption that the number of components is fixed which is increased (or reduced) when enough evidence for a new component is seen. This is deducedfrom the change from the oldest fit of the same complexity, termed the Historical GMM, the concept of which is central to our method. The performance of the proposed method is demonstrated qualitatively and quantitatively on several synthetic data sets and video sequences of faces acquired in realistic imaging conditions.

Overfitting Bayesian mixture models with an unknown number of components

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

Speeded up Gaussian mixture model algorithm for background subtraction

Adaptive Gaussian Mixture Models (GMM) have been one of the most popular and successful approaches to perform foreground segmentation on multimodal background scenes. However, the good accuracy of the GMM algorithm comes at a high computational cost. An improved GMM technique was proposed by Zivkovic to reduce computational cost by minimizing the number of modes adaptively. In this paper, we propose a modification to his adaptive GMM algorithm that further reduces execution time by replacing expensive floating point computations with low cost integer operations. To maintain accuracy, we derive a heuristic that computes periodic floating point updates for the GMM weight parameter using the value of an integer counter. Experiments show speedups in the range of 1.33 - 1.44 on standard video datasets where a large fraction of pixels are multimodal.