Objective

2

The development of synthetic aperture radar (SAR) technology has resulted in the generation of high-resolution 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 model-based 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 (GaMM)

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 (HWGaMM) with spatial constraint.

Method

2

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 HWGaMM to model the statistical distribution of pixel intensities in SAR images. The component of the HWGaMM 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 HWGaMM is defined by the weighted sum of the components. The hierarchy of the HWGaMM 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 HWGaMM

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 HWGaMM 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 algorithm in 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

2

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 GaMM-based segmentation algorithms to highlight its advantages. The results of the fitting histograms reveal that the HWGaMM 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 are 33%

29%

and 9% higher than those of the GMM-based

Gamma distribution-based

and GaMM-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 GaMM-based segmentation algorithms

respectively.

Conclusion

2

This work proposes an SAR image segmentation algorithm that is based on a spatially constrained HWGaMM. The proposed HWGaMM 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.