ECM算法的多视SAR影像分割

多视SAR影像像素强度通常建模为Gamma分布,其形状参数为常数(视数)。实验表明,多视SAR影像分割时,设Gamma分布的形状参数为变量可取得更好的分割结果。由于Gamma分布中形状参数以Gamma函数的形式出现,利用EM算法求解时无法获得形状参数的解析解。为此,本文提出了一种基于Expectation/Conditional Maxinnization(ECM)算法的多视SAR影像分割方法。利用ECM算法估计最大化后验概率条件下的Gamma分布参数及表征最优多视SAR影像分割的标号场实现。采用模拟和真实多视SAR影像验证提出算法。实验结果表明,Gamma分布的形状和尺度参数均能快速收敛到稳态值,且以此得到各同质区域的Gamma分布曲线可以很好地拟合其直方图。通过对分割结果的定性和定量分析,可知提出算法具有有效性和可行性,且优于EM算法。

ECM-based segmentation for multi-look SAR image

The intensities of pixels in images of multi-look Synthetic Aperture Radar (SAR) are usually modeled by gamma distribution. To obtain a segmentation result, the parameters that indicate the distributions should be estimated. However, traditional expectation maximization (EM) algorithm cannot approach the shape parameter through taking partial derivation of the likelihood probability. Thus, to solve this problem, the shape parameter should be made equal to the number of looks, and only the scale parameter should be estimated. Nevertheless, the conclusion is obtained under the assumption that a pixel is constructed by infinite scattering units, which is impossible especially in highresolution SAR images. Apparently, that assumption is unreasonable and will lead to inaccurate estimation of the corresponding parameters. Moreover, gamma distribution with fixed-shape parameter cannot completely describe the characteristics of intensity distribution in multilook SAR images. Thus, this paper proposes a scheme for solving the parameter based on Expectation/Conditional Maximization (ECM) algorithm and develops a new segmentation algorithm for multi-look SAR images. First, the neighborhood system on the label field is considered, and Markov random field model is employed to define prior distribution. Then, intensities in each homogeneous region of a multilook SAR image are modeled by gamma distribution, in which both shape and scale parameters are considered as variables. Finally, the gamma distribution along with the prior distribution constructs the posterior distribution, on which purpose it should be maximized. In this paper, Metropolis-Hastings algorithm is used as a random sampling method in estimating the marginal posterior probability model and changing the labels of each pixel. However, the estimation of the shape parameter remains a problem because it cannot be solved through partial derivation. ECM algorithm introduces the Newton iterative method to approach the real value of parameters, which cannot be directly solved from an equation. Therefore, shape parameter is evaluated by ECM algorithm, and all variables are obtained ultimately. The proposed algorithm is applied to simulated and real multi-look SAR images. Experimental results show that the proposed method can accurately estimate shape and scale parameters of gamma distribution. The proposed algorithm''s user, product, and total accuracies, and kappa coefficient are all higher than those of the EM algorithm''s, and the estimated values of the algorithm are much closer to the real values. The proposed algorithm can estimate the parameters of gamma distribution and the corresponding reality of the label field under the circumstance of maximized posteriori probability. Experiments on simulated and real multi-look SAR image verify the effectiveness and feasibility of the proposed algorithm, and the shape and scale parameters of gamma distribution can quickly converge to their stable state in a considerably short time. The ECM algorithm introduced in this paper can estimate the value of the shape parameter in gamma distribution, which is treated as the number of looks in the traditional EM algorithm. Thus, the connections between different looks are included in the distribution, and the corresponding segmentation results are improved.