空间约束层次加权Gamma混合模型的SAR图像分割

Hierarchically weighted Gamma mixture model with spatial constraint for SAR image segmentation

目的合成孔径雷达(SAR)图像中像素强度统计分布呈现出复杂的特性,而传统混合模型难以建模非对称、重尾或多峰等特性的分布。为了准确建模SAR图像统计分布并得到高精度分割结果,本文提出一种利用空间约束层次加权Gamma混合模型(HWGa MM)的SAR图像分割算法。方法采用Gamma分布的加权和定义混合组份;考虑到同质区域内像素强度的差异性和异质区域间像素强度的相似性,采用混合组份加权和定义HWGa MM结构。采用马尔可夫随机场(MRF)建模像素空间位置关系,利用中心像素及其邻域像素的后验概率定义混合权重以将像素邻域关系引入HWGa MM,构建空间约束HWGa MM,以降低SAR图像内固有斑点噪声的影响。提出算法结合M-H(Metropolis-Hastings)和期望最大化算法(EM)求解模型参数,以实现快速SAR图像分割。该求解方法避免了M-H算法效率低的缺陷,同时克服了EM算法难以求解Gamma分布中形状参数的问题。结果采用3种传统混合模型分割算法作为对比算法进行分割实验。拟合直方图结果表明本文算法具有准确建模复杂统计分布的能力。在分割精度上,本文算法比基于高斯混合模型(GMM)、Gamma分布和Gamma混合模型(Ga MM)分割算法分别提高33%,29%和9%。在分割时间上,本文算法虽然比GMM算法多64 s,但与基于Gamma分布和Ga MM算法相比较分别快600 s和420 s。因此,本文算法比传统M-H算法的分割效率有很大的提高。结论提出一种空间约束HWGa MM的SAR图像分割算法,实验结果表明提出的HWGa MM算法具有准确建模复杂统计分布的能力,且具有较高的精度和效率。

Objective The development of synthetic aperture radar(SAR)technology has resulted in the generation of highresolution SAR images under all weather conditions and time periods.SAR images are widely used in many fields,such as disaster monitoring and ocean science.SAR image segmentation is a crucial step in image processing.The statistical modelbased SAR segmentation algorithm is popular for its statistical distribution of homogeneous regions in SAR images with specific regularity.However,the statistical distribution of pixel intensities in high-resolution SAR images can be asymmetric,heavy-tailed,or multi-modal.Traditional mixture models use the weighted sum of components to model the statistical distribution of pixel intensities in SAR image segmentation.The components of mixture models are defined by probability density functions to mainly model the statistical distribution of homogeneous regions.The components can be Gaussian,student’s,or Gamma distribution in the Gaussian mixture model(GMM),student’s mixture model,and gamma mixture model(Ga MM),respectively.However,these components fail to model the complicated distribution of pixel intensities in SAR images.To address the problem,this study proposes a SAR image segmentation algorithm that is based on a hierarchically weighted Gamma mixture model(HWGa MM)with spatial constraint.Method A mixture model is defined by the weighted sum of its components to model the statistical distribution of pixel intensities.Its components are usually defined by the probability distribution,which results in the difficulty of modeling the complicated distribution of homogeneous regions in SAR images.To accurately model the asymmetric,heavy-tailed,or multi-modal distribution of pixel intensities,the proposed algorithm uses the HWGa MM to model the statistical distribution of pixel intensities in SAR images.The component of the HWGa MM is defined by the weighted sum of Gamma distributions,which represent the element used to model the statistical distribution of local homogeneous regions.As a result of the differences in pixel intensities in the same region and the similarities of pixel intensities in different regions for high-resolution SAR images,the HWGa MM is defined by the weighted sum of the components.The hierarchy of the HWGa MM can be expressed as follows.The basic layer is the element,i.e.,Gamma distribution,which is used to model the statistical distribution of local homogeneous regions.The second layer is the component,which is the weighted sum of elements to mainly model the statistical distribution of homogeneous regions.The top layer is the HWGa MM,which is the weighted sum of components to model the statistical distribution of SAR images.The spatial relation of pixels is modeled by a Markov random field to reduce the influence of image noise.The spatial relation of pixels is introduced to the HWGa MM by defining the weight of components by the posterior probabilities of the pixels and neighboring pixels.Such introduction can improve the robustness of the proposed algorithm and prevent the increase in the complexity of model parameter estimation.In this work,SAR image segmentation is realized by estimating the model parameters through the combination of the Metropolis-Hastings(M-H)algorithm and expectation maximization(EM)algorithm.The traditional M-H algorithm usually suffers from poor efficiency because of its sampling for every model parameter in each iteration.The EM algorithm cannot easily estimate the shape parameter of a Gamma distribution because the shape parameter is included in the gamma function.To address such problem,the proposed algorithm uses the M-H algorithmin simulating the posterior distribution of the shape parameter and the EM algorithm in estimating the scale parameter and element weight.The method of parameter estimation overcomes the drawback of the EM algorithm and achieves higher efficiency than the M-H algorithm.Result Segmentation experiments are carried out on simulated and real SAR images,and the results are analyzed qualitatively and quantitatively to verify the feasibility and effectiveness of the proposed algorithm.The proposed algorithm is compared with the GMM-based,Gamma distribution-based,and Ga MM-based segmentation algorithms to highlight its advantages.The results of the fitting histograms reveal that the HWGa MM can accurately model the complicated distribution of pixel intensities.The segmentation accuracy can be calculated from the confusion matrix to quantitatively evaluate the proposed algorithm.The segmentation accuracies of the proposed algorithm are33%,29%,and 9%higher than those of the GMM-based,Gamma distribution-based,and Ga MM-based segmentation algorithms,respectively.The segmentation time of the proposed algorithm is 64 s faster than that of GMM-based segmentation algorithm but is 600 s and 420 s slower than that of the gamma distribution-and Ga MM-based segmentation algorithms,respectively.Conclusion This work proposes an SAR image segmentation algorithm that is based on a spatially constrained HWGa MM.The proposed HWGa MM can model the complicated distribution of pixel intensities.The proposed segmentation algorithm also has higher accuracy than other relevant methods.Although the efficiency of the proposed algorithm is lower than that of the EM-based segmentation algorithm,it is much higher than that of the M-H-based segmentation algorithm.