融入邻域作用的高斯混合分割模型及简化求解

目的 基于高斯混合模型（GMM）的图像分割方法易受噪声影响，为此采用马尔可夫随机场（MRF）将像素邻域关系引入GMM，提高算法抗噪性。针对融入邻域作用的高斯混合分割模型结构复杂、参数估计困难，难以获得全局最优分割解等问题，提出一种融入邻域作用的高斯混合分割模型及其简化求解方法。方法 首先，构建融入邻域作用的GMM。为了提高GMM的抗噪性，采用MRF建模混合模型权重系数的先验分布。然后，利用贝叶斯理论建立图像分割模型，即品质函数；由于品质函数中参数较多（包括权重系数，均值，协方差）、函数结构复杂，导致参数求解困难。因此，将品质函数中的均值和协方差定义为权重系数的函数，由此简化模型结构并方便其求解；虽然品质函数中仅包含参数权重系数，但结构比较复杂，难以求得参数的解析式。最后，采用非线性共轭梯度法（CGM）求解参数，该方法仅需利用品质函数值和参数梯度值，降低了参数求解的复杂性，并且收敛快，可以得到全局最优解。结果 为了有效而准确地验证提出的分割方法，分别采用本文算法和对比算法对合成图像和高分辨率遥感图像进行分割实验，并定性和定量地评价和分析了实验结果。实验结果表明本文方法的有效抗噪性，并得到很好的分割结果。从参数估计结果可以看出，本文算法有效简化了模型参数，并获得全局最优解。结论 提出一种融入邻域作用的高斯混合分割模型及其简化求解方法，实验结果表明，本文算法提高了算法的抗噪性，有效地简化了模型参数，并得到全局最优参数解。本文算法对具有噪声的高分辨率遥感影像广泛适用。

Gaussian mixture model with neighbor relationship for image segmentation and simplified solving method

Objective The development of remote sensing technology has improved the resolution of remote sensing images. Thus, high-resolution remote sensing image segmentation has become a major research topic in remote sensing image processing. Geometrical details in high-resolution remote sensing images are more obvious than those in moderate resolution images, but the improvement in spatial resolution increases the spectral similarity between different classes and spectral differences of the same class. This phenomenon leads to the reduction in the statistical separability of different classes, which involves many segmentation errors. Gaussian mixture model (GMM) is a method of modeling statistical distribution of data and is successfully applied to image segmentation. Modeling based on GMM image segmentation method presents some advantages and a simple structure. However, GMM only considers the effect of pixel itself on segmentation and is sensitive to image noise. The robustness of GMM is improved by introducing neighbor relationship into GMM using Markov random field (MRF). MRF-based GMM image segmentation methods using standard expectation maximization (EM) lead to a computational problem in estimating parameters, as EM fails to obtain the global solution of segmentation model. In this study, an image segmentation method is proposed to solve the above-mentioned problem in high-resolution remote sensing image segmentation. Method The proposed remote sensing image segmentation method combines GMM based on MRF and nonlinear conjugate gradient method (CGM). In the algorithm, GMM is used to model the statistical distribution of pixel intensity in a remote sensing image. The components of GMM are Gaussian distributions, which model the statistical distribution of pixel intensity of each homogeneous area. The MRF introduces the neighbor relationship into the GMM to reduce the noise effect. In other words, the prior distribution of weight coefficient of GMM is modeled by the MRF. The segmentation model, namely, the quality function, is built by combining GMM with prior distribution of GMM weight coefficient on the basis of Bayesian theory. The quality function includes a large number of parameters, such as weight coefficient, mean, and covariance, and possesses a fairly complicated structure. The problem results in difficulty in solving the model parameters. Therefore, the proposed algorithm defines the mean and covariance as the functions of weight coefficient depending on their relationships, thereby minimizing multiple parameters to only one. Although the quality function now involves only one parameter, its structure is still complicated. For solving the parameter, a nonlinear CGM is designed for estimation. This method only uses the value of the quality function and parameter gradient and reduces the complexity of the parameter solution. At the same time, its convergence is fast and the global optimal solution can be obtained. The loss function is defined as the negative quality function to obtain the optimal segmentation, and the formula derivation of gradient of weight coefficient can be calculated easily using the said function. Result Segmentation experiments are conducted using the proposed algorithm, GMM-CGM algorithm, and spatially variable finite mixture model (SVFMM). In testing the noise resistance of the proposed algorithm, salt-and-pepper noise is added in synthetic and high-resolution remote sensing images. Segmentation results demonstrate that the proposed algorithm effectively improves the noise resistance and obtain better results than those of the compared algorithms. Comparing the estimating parameters shows that the proposed algorithm can derive the global solution whereas the compared algorithms can obtain only the local solution. The overall accuracy and Kappa coefficient are calculated from confusion matrix and are compared with those of the compared algorithms to quantitatively evaluate the proposed algorithm. The accuracy values demonstrate that the proposed algorithm can achieve more precise segmentation results than those of the compared algorithms. Conclusion This study proposes a high-resolution remote sensing image segmentation method that combines GMM based on MRF with nonlinear CGM. The proposed approach is promising and effective and presents ideal results but still needs improvement. Nonlinear CGM method exhibits many other functions that can be used to estimate the model parameters. Other parameter estimation methods that can conveniently and accurately obtain the optimal solution will be used in future works.