Mixture Model For Image Segmentation Research Articles

A spatially constrained asymmetric Gaussian mixture model for image segmentation

The finite Gaussian mixture model (GMM) is a flexible and powerful tool for addressing many computer vision and pattern recognition problems. The Gaussian distribution is a probability distribution that is symmetric with respect to the mean. However, in many segmentation applications, the observed data obey an asymmetric distribution. Furthermore, the GMM is sensitive to imaging noise. To alleviate these issues, a new finite anisotropic asymmetric normal mixture model is presented in this paper. Note that GMM is a degraded case of our proposed model. First, the proposed model employs anisotropic spatial information to reduce the effect of imaging noise while preserving the details, such as edges, corners and slim structure objects. Second, the anisotropic spatial information is coupled into the skew normal distribution to fit the observed data obeying an asymmetric distribution. Then the modeling and estimation of the object intensity probability density function are proposed by using the anisotropic skew normal mixture model. The proposed model not only has the capability to fit the observed data obeying a non-symmetric distribution, but also can reduce the effect of noise while preserving the objects details. Finally, expectation maximization (EM) algorithm is adopted to estimate the model parameters in order to maximize the log-likelihood function. The experiment results on synthetic images and natural grayscale images demonstrate the superior performance of the proposed model compared with other state-of-the-art segmentation methods.

A Weighted Spatially Constrained Finite Mixture Model for Image Segmentation

Spatially Constrained Mixture Model (SCMM) is an image segmentation model that works over the framework of maximum a-posteriori and Markov Random Field (MAP-MRF). It developed its own maximization step to be used within this framework. This research has proposed an improvement in the SCMM’s maximization step for segmenting simulated brain Magnetic Resonance Images (MRIs). The improved model is named as the Weighted Spatially Constrained Finite Mixture Model (WSCFMM). To compare the performance of SCMM and WSCFMM, simulated T1-Weighted normal MRIs were segmented. A region of interest (ROI) was extracted from segmented images. The similarity level between the extracted ROI and the ground truth (GT) was found by using the Jaccard and Dice similarity measuring method. According to the Jaccard similarity measuring method, WSCFMM showed an overall improvement of 4.72%, whereas the Dice similarity measuring method provided an overall improvement of 2.65% against the SCMM. Besides, WSCFMM significantly stabilized and reduced the execution time by showing an improvement of 83.71%. The study concludes that WSCFMM is a stable model and performs better as compared to the SCMM in noisy and noise-free environments.

Non-local spatially varying finite mixture models for image segmentation

In this work, we propose a new Bayesian model for unsupervised image segmentation based on a combination of the spatially varying finite mixture models (SVFMMs) and the non-local means (NLM) framework. The probabilistic NLM weighting function is successfully integrated into a varying Gauss–Markov random field, yielding a prior density that adaptively imposes a local regularization to simultaneously preserve edges and enforce smooth constraints in homogeneous regions of the image. Two versions of our model are proposed: a pixel-based model and a patch-based model, depending on the design of the probabilistic NLM weighting function. Contrary to previous methods proposed in the literature, our approximation does not introduce new parameters to be estimated into the model, because the NLM weighting function is completely known once the neighborhood of a pixel is fixed. The proposed model can be estimated in closed-form solution via a maximum a posteriori (MAP) estimation in an expectation–maximization scheme. We have compared our model with previously proposed SVFMMs using two public datasets: the Berkeley Segmentation dataset and the BRATS 2013 dataset. The proposed model performs favorably to previous approaches in the literature, achieving better results in terms of Rand Index and Dice metrics in our experiments.

Dynamic integration and online evaluation of vision‐based lane detection algorithms

Lane detection techniques have been widely studied in the last two decades and applied in many advance driver assistance systems. However, the development of a robust lane detection system, which can deal with various road conditions and efficiently evaluate its detection results in real time, is still of great challenge. In this study, a vision-based lane detection system with dynamic integration and online evaluation is proposed. To increase the robustness of the lane detection system, the integration system dynamically processes two lane detection modules. First, a primary lane detection module is designed based on the steerable filter and Hough transform algorithm. Then, a secondary algorithm, which combines the Gaussian mixture model for image segmentation and random sample consensus for lane model fitting, will be activated when the primary algorithm encounters a low detection confidence. To detect the colour and line style of the ego lanes and evaluate the lane detection system in real time, a lane sampling and voting technique is proposed. By combining the sampling and voting system system with prior lane geometry knowledge, the evaluation system can efficiently recognise the false detections. The system works robustly in various complex situations (e.g. shadows, night, and lane missing scenarios) with a monocular camera.

A Rough Set Bounded Spatially Constrained Asymmetric Gaussian Mixture Model for Image Segmentation.

Accurate image segmentation is an important issue in image processing, where Gaussian mixture models play an important part and have been proven effective. However, most Gaussian mixture model (GMM) based methods suffer from one or more limitations, such as limited noise robustness, over-smoothness for segmentations, and lack of flexibility to fit data. In order to address these issues, in this paper, we propose a rough set bounded asymmetric Gaussian mixture model with spatial constraint for image segmentation. First, based on our previous work where each cluster is characterized by three automatically determined rough-fuzzy regions, we partition the target image into three rough regions with two adaptively computed thresholds. Second, a new bounded indicator function is proposed to determine the bounded support regions of the observed data. The bounded indicator and posterior probability of a pixel that belongs to each sub-region is estimated with respect to the rough region where the pixel lies. Third, to further reduce over-smoothness for segmentations, two novel prior factors are proposed that incorporate the spatial information among neighborhood pixels, which are constructed based on the prior and posterior probabilities of the within- and between-clusters, and considers the spatial direction. We compare our algorithm to state-of-the-art segmentation approaches in both synthetic and real images to demonstrate the superior performance of the proposed algorithm.

Image segmentation model based on adaptive adjustment of global and local information

ABSTRACTIn this article, an adaptive mixture model for image segmentation that synthesizes both global information and local information using a new adaptive balance function has been proposed. Given the variety of possible image characteristics that may have to be processed, the proposed model can adaptively adjust the weighting to drive curve evolution trends and states. In this way, the intensity information of weak boundaries and complex backgrounds can be extracted more precisely, thus enabling the model to produce better results for low‐contrast images and complex structures. In addition, a Gaussian filtering process has been added to the model to smooth and standardize the level set function, and a parameter has been introduced to speed up the curve evolution. A penalty term is also used to eliminate the need for complex re‐initialization procedures. Experimental results for various kinds of images efficiently demonstrate the good performance of the proposed model in terms of both speed and accuracy. © 2016 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 26, 179–187, 2016

A spatially constrained generative asymmetric Gaussian mixture model for image segmentation

Accurate image segmentation is an essential step in image processing, where Gaussian mixture models with spatial constraint play an important role. Nevertheless, most methods suffer from one or more challenges such as limited robustness to noise, over-smoothness for segmentations, and lack of flexibility to fit the observed data. To address these issues, in this paper, we propose a generative asymmetric Gaussian mixture model with spatial constraint for image segmentation. The asymmetric distribution is modified to be easily incorporated the spatial information. Then our asymmetric model can be constructed based on the posterior and prior probabilities of within-cluster and between-cluster. Based on the Kullback-Leibler divergence, we introduce two pseudo-likelihood quantities which consider the neighboring priors of within-cluster and between-cluster. Finally, we derive an expectation maximization algorithm to maximize the approximation of the data log-likelihood. We compare our algorithm with state-of-the-art segmentation approaches to demonstrate the superior performance of the proposed algorithm.

Double Gaussian mixture model for image segmentation with spatial relationships

In this paper, we present a finite mixture model based on a Gaussian distribution for image segmentation. There are four advantages to the proposed model. First, compared with the standard Gaussian mixture model (GMM), the proposed model effectively incorporates spatially relationships between the pixels using a Markov random field (MRF). Second, the proposed model is similar to GMM, but has a simple representation and is easier to implement than some existing models based on MRF. Third, the contextual mixing proportion of the proposed model is explicitly modelled as a probabilistic vector and can be obtained directly during the inference process. Finally, the expectation maximization algorithm and gradient descent approach are used to maximize the log-likelihood function and infer the unknown parameters of the proposed model. The performance of the proposed model at image segmentation is compared with some state-of-the-art models on various synthetic noisy grayscale images and real-world color images.

A Spatially Correlated Mixture Model for Image Segmentation

A Spatially Correlated Mixture Model for Image Segmentation

A finite mixture model for detail-preserving image segmentation

We present a new finite mixture model for image segmentation. Firstly, in order to take into account the spatial dependencies in an image, existing mixture models use a constant temperature parameter (β) throughout the image for every label. The constant value of β reduces the impact of noise in homogeneous regions but negatively affects segmentation along the border of two regions. We propose a new way to use a different value of β throughout the image. Secondly, in order to incorporate the correlation between each center pixel and its neighboring pixels, the existing mixture model gives the same importance to all pixels in a neighborhood window. We assign different weights to different pixels appearing in the window, which is based on the fact that the clique strength should be reduced with distance. Thirdly, our model is based on the Student's-t distribution, which is heavily tailed and more robust than the Gaussian. We exploit the Dirichlet distribution and Dirichlet law to incorporate the spatial relationships between pixels in an image. Finally, the expectation maximization (EM) algorithm is adopted to maximize the data log-likelihood and to optimize the parameters. The performance is compared to other existing models based on the model-based techniques, demonstrating the superiority of the proposed model for image segmentation.

Fast and Robust Spatially Constrained Gaussian Mixture Model for Image Segmentation

In this paper, a new mixture model for image segmentation is presented. We propose a new way to incorporate spatial information between neighboring pixels into the Gaussian mixture model based on Markov random field (MRF). In comparison to other mixture models that are complex and computationally expensive, the proposed method is fast and easy to implement. In mixture models based on MRF, the M-step of the expectation-maximization (EM) algorithm cannot be directly applied to the prior distribution ${\pi_{ij}}$ for maximization of the log-likelihood with respect to the corresponding parameters. Compared with these models, our proposed method directly applies the EM algorithm to optimize the parameters, which makes it much simpler. Experimental results obtained by employing the proposed method on many synthetic and real-world grayscale and colored images demonstrate its robustness, accuracy, and effectiveness, compared with other mixture models.

A Nonsymmetric Mixture Model for Unsupervised Image Segmentation

Finite mixture models with symmetric distribution have been widely used for many computer vision and pattern recognition problems. However, in many applications, the distribution of the data has a non-Gaussian and nonsymmetric form. This paper presents a new nonsymmetric mixture model for image segmentation. The advantage of our method is that it is simple, easy to implement, and intuitively appealing. In this paper, each label is modeled with multiple D-dimensional Student's t-distribution, which is heavily tailed and more robust than Gaussian distribution. Expectation-maximization algorithm is adopted to estimate model parameters and to maximize the lower bound on the data log-likelihood from observations. Numerical experiments on various data types are conducted. The performance of the proposed model is compared with that of other mixture models, demonstrating the robustness, accuracy, and effectiveness of our method.

Dirichlet Gaussian mixture model: Application to image segmentation

Gaussian mixture model based on the Dirichlet distribution (Dirichlet Gaussian mixture model) has recently received great attention for modeling and processing data. This paper studies the new Dirichlet Gaussian mixture model for image segmentation. First, we propose a new way to incorporate the local spatial information between neighboring pixels based on the Dirichlet distribution. The main advantage is its simplicity, ease of implementation and fast computational speed. Secondly, existing Dirichlet Gaussian model uses complex log-likelihood function and require many parameters that are difficult to estimate. The total parameters in the proposed model lesser and the log-likelihood function have a simpler form. Finally, to estimate the parameters of the proposed Dirichlet Gaussian mixture model, a gradient method is adopted to minimize the negative log-likelihood function. Numerical experiments are conducted using the proposed model on various synthetic, natural and color images. We demonstrate through extensive simulations that the proposed model is superior to other algorithms based on the model-based techniques for image segmentation.

Fast estimation of Gaussian mixture models for image segmentation

The expectation maximization algorithm has been classically used to find the maximum likelihood estimates of parameters in probabilistic models with unobserved data, for instance, mixture models. A key issue in such problems is the choice of the model complexity. The higher the number of components in the mixture, the higher will be the data likelihood, but also the higher will be the computational burden and data overfitting. In this work, we propose a clustering method based on the expectation maximization algorithm that adapts online the number of components of a finite Gaussian mixture model from multivariate data or method estimates the number of components and their means and covariances sequentially, without requiring any careful initialization. Our methodology starts from a single mixture component covering the whole data set and sequentially splits it incrementally during expectation maximization steps. The coarse to fine nature of the algorithm reduce the overall number of computations to achieve a solution, which makes the method particularly suited to image segmentation applications whenever computational time is an issue. We show the effectiveness of the method in a series of experiments and compare it with a state-of-the-art alternative technique both with synthetic data and real images, including experiments with images acquired from the iCub humanoid robot.

An Extension of the Standard Mixture Model for Image Segmentation

Standard gaussian mixture modeling (GMM) is a well-known method for image segmentation. However, the pixels themselves are considered independent of each other, making the segmentation result sensitive to noise. To reduce the sensitivity of the segmented result with respect to noise, Markov random field (MRF) models provide a powerful way to account for spatial dependences between image pixels. However, their main drawback is that they are computationally expensive to implement, and require large numbers of parameters. Based on these considerations, we propose an extension of the standard GMM for image segmentation, which utilizes a novel approach to incorporate the spatial relationships between neighboring pixels into the standard GMM. The proposed model is easy to implement and compared with MRF models, requires lesser number of parameters. We also propose a new method to estimate the model parameters in order to minimize the higher bound on the data negative log-likelihood, based on the gradient method. Experimental results obtained on noisy synthetic and real world grayscale images demonstrate the robustness, accuracy and effectiveness of the proposed model in image segmentation, as compared to other methods based on standard GMM and MRF models.

A finite mixture model for image segmentation

In this paper, we propose a model for image segmentation based on a finite mixture of Gaussian distributions. For each pixel of the image, prior probabilities of class memberships are specified through a Gibbs distribution, where association between labels of adjacent pixels is modeled by a class-specific term allowing for different interaction strengths across classes. We show how model parameters can be estimated in a maximum likelihood framework using Mean Field theory. Experimental performance on perturbed phantom and on real benchmark images shows that the proposed method performs well in a wide variety of empirical situations.

A Class-Adaptive Spatially Variant Mixture Model for Image Segmentation

We propose a new approach for image segmentation based on a hierarchical and spatially variant mixture model. According to this model, the pixel labels are random variables and a smoothness prior is imposed on them. The main novelty of this work is a new family of smoothness priors for the label probabilities in spatially variant mixture models. These Gauss-Markov random field-based priors allow all their parameters to be estimated in closed form via the maximum a posteriori (MAP) estimation using the expectation-maximization methodology. Thus, it is possible to introduce priors with multiple parameters that adapt to different aspects of the data. Numerical experiments are presented where the proposed MAP algorithms were tested in various image segmentation scenarios. These experiments demonstrate that the proposed segmentation scheme compares favorably to both standard and previous spatially constrained mixture model-based segmentation.

A Spatially Constrained Mixture Model for Image Segmentation

Gaussian mixture models (GMMs) constitute a well-known type of probabilistic neural networks. One of their many successful applications is in image segmentation, where spatially constrained mixture models have been trained using the expectation-maximization (EM) framework. In this letter, we elaborate on this method and propose a new methodology for the M-step of the EM algorithm that is based on a novel constrained optimization formulation. Numerical experiments using simulated images illustrate the superior performance of our method in terms of the attained maximum value of the objective function and segmentation accuracy compared to previous implementations of this approach.