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. 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. 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. 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.