Thanh Minh Nguyen

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

Robust Student's-t Mixture Model With Spatial Constraints and Its Application in Medical Image Segmentation

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An Extension of the Standard Mixture Model for Image Segmentation

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.

Gaussian-Mixture-Model-Based Spatial Neighborhood Relationships for Pixel Labeling Problem

Finite mixture model based on the Students-t distribution, which is heavily tailed and more robust than Gaussian, has recently received great attention for image segmentation. A new finite Students-t mixture model (SMM) is proposed in this paper. Existing models do not explicitly incorporate the spatial relationships between pixels. First, our model exploits Dirichlet distribution and Dirichlet law to incorporate the local spatial constrains in an image. Secondly, we directly deal with the Students-t distribution in order to estimate the model parameters, whereas, the Students-t distributions in previous models are represented as an infinite mixture of scaled Gaussians that lead to an increase in complexity. Finally, instead of using expectation maximization (EM) algorithm, the proposed method adopts the gradient method to minimize the higher bound on the data negative log-likelihood and to optimize the parameters. The proposed model is successfully compared to the state-of-the-art finite mixture models. Numerical experiments are presented where the proposed model is tested on various simulated and real medical images.

Bounded generalized Gaussian mixture model

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 real-time ellipse detection based on edge grouping

In this paper, we present a new algorithm for pixel labeling and image segmentation based on the standard Gaussian mixture model (GMM). Unlike the standard GMM where pixels themselves are considered independent of each other and the spatial relationship between neighboring pixels is not taken into account, the proposed method incorporates this spatial relationship into the standard GMM. Moreover, the proposed model requires fewer parameters compared with the models based on Markov random fields. In order to estimate model parameters from observations, instead of utilizing an expectation-maximization algorithm, we employ gradient method to minimize a higher bound on the data negative log-likelihood. The performance of the proposed model is compared with methods based on both standard GMM and Markov random fields, demonstrating the robustness, accuracy, and effectiveness of our method.

A Nonsymmetric Mixture Model for Unsupervised Image Segmentation

Abstract The generalized Gaussian mixture model (GGMM) provides a flexible and suitable tool for many computer vision and pattern recognition problems. However, generalized Gaussian distribution is unbounded. In many applications, the observed data are digitalized and have bounded support. A new bounded generalized Gaussian mixture model (BGGMM), which includes the Gaussian mixture model (GMM), Laplace mixture model (LMM), and GGMM as special cases, is presented in this paper. We propose an extension of the generalized Gaussian distribution in this paper. This new distribution has a flexibility to fit different shapes of observed data such as non-Gaussian and bounded support data. In order to estimate the model parameters, we propose an alternate approach to minimize the higher bound on the data negative log-likelihood function. We quantify the performance of the BGGMM with simulations and real data.

A Robust Fuzzy Algorithm Based on Student's t-Distribution and Mean Template for Image Segmentation Application

In this paper, we present a efficient algorithm for real-time ellipse detection. Unlike Hough transform algorithm that is computationally intense and requires a higher dimensional parameter space, our proposed method reduces the computational complexity significantly, and accurately detects ellipses in realtime. We present a new method of detecting arc-segments from the image, based on the properties of ellipse. We then group the arc-segments into elliptical arcs in order to estimate the parameters of the ellipse, which are calculated using the least-square method. Our method has been tested and implemented on synthetic and real-world images containing both complete and incomplete ellipses. The performance is compared to existing ellipse detection algorithms, demonstrating the robustness, accuracy and effectiveness of our algorithm.

Multiresolution Based Gaussian Mixture Model for Background Suppression

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 Students 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.

Synthetic Aperture Radar Image Segmentation by Modified Student's t-Mixture Model

Fuzzy c-means (FCM) with spatial constraints has been considered as an effective algorithm for image segmentation. Students t-distribution has come to be regarded as an alternative to Gaussian distribution, as it is heavily tailed and more robust for outliers. In this letter, we propose a new algorithm to incorporate the merits of these two approaches. The advantages of our method are as follows: First, we incorporate the local spatial information and pixel intensity value by considering the labeling of an image pixel influenced by the labels in its immediate neighborhood. Second, we introduce additional parameter a to control the extent of this influence. The larger a indicates heavier extent of influence in the neighborhoods. Finally, we utilize a mean template instead of the traditional hidden Markov random field (HMRF) model for estimation of prior probability. Compared with HMRF, our method is simple, easy and fast to implement. Experimental results on synthetic and real images demonstrate the improved robustness and effectiveness of our approach.