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A valid unsupervised and multiscale segmentation of synthetic aperture radar (SAR) imagery is proposed by a combination GA-EM of the Expectation Maximization (EM) algorith with the genetic algorithm (GA). The mixture multiscale autoregressive (MMAR) model is introduced to characterize and exploit the scale-to-scale statistical variations and statistical variations in the same scale in SAR imagery due to radar speckle, and a segmentation method is given by combining the GA algorithm with the EM algorithm. This algorithm is capable of selecting the number of components of the model using the minimum description length (MDL) criterion. Our approach benefits from the properties of the Genetic and the EM algorithm by combination of both into a single procedure. The population-based stochastic search of the genetic algorithm (GA) explores the search space more thoroughly than the EM method. Therefore, our algorithm enables escaping from local optimal solutions since the algorithm becomes less sensitive to its initialization. Some experiment results are given based on our proposed approach, and compared to that of the EM algorithms. The experiments on the SAR images show that the GA-EM outperforms the EM method.

In recent years, SAR imaging has been rapidly gaining prominence in applications such as remote sensing, surface surveillance and automatic target recognition. For these applications, the segmentation of various categories of clutter is quite important, and this segmentation can play a key role in the subsequent analysis for target detection, recognition and image compression. Because of the nature of the SAR instrument, SAR images contain speckle noise, complicating the segmentation of SAR images. Several different segmentation methods especially designed for SAR data have been proposed. One approach to deal with the speckle is to use a multiscale approach, which exploits the coherent nature of SAR imagery formation. In particular, we build on the idea of characterizing and exploiting the scale-to-scale statistical variations and statistical variations in the same scale in SAR imagery due to radar speckle [

This paper is organized as follows. In the next section, we will describe quadtree interpretation of SAR imagery and its MMAR Modeling. In Section 3, we will propose a hybrid method based on the GA algorithm and EM algorithm for MMAR model. In Section 4, we will present the experimental results. In Section 5, we will present a short conclusion concerning our algorithm.

The starting point for our model development is a multiscale sequence _{L}_{L}_{−1}, …, _{0} of SAR images, where _{L}_{0} correspond to the coarsest and finest resolution images, respectively. The resolution varies dyadically between images at successive scales. More precisely, we assume that the finest scale image _{0} has a resolution of ^{M}_{m}^{−}^{m}×^{−}^{m}N^{m}δ^{m}δ_{m}^{m}^{m}_{m}_{m}_{−1}. This indicates that quadtree is natural for the mapping. Each node _{m}_{m}

In this paper, we focus on a specific class of multiscale models, namely mixture multiscale autoregressive models [_{k}_{i}_{i}_{s}_{k}

In Bayesian unsupervised segmentation using parametric estimation, the problem of segmentation is based on the model identification. The most commonly used estimator is the ML estimator, which is solved by the classical EM algorithms [

The posterior probability for a pixel _{0} to belong to class _{s,k}_{k}_{,0} − _{k,}_{1}_{k,p}X^{p}

In this step, _{s,k}_{k}_{,0}, _{k}_{,1}, ⋯,_{k},_{p}^{i}

The estimates of the parameters are then obtained by iterating the four steps until convergence. Parameters _{k}

The main goal of interweaving GA with the EM algorithm is to utilize the properties of both algorithms. Similar to the method in [

In the following section, the framework of the GA-EM algorithm is presented:
_{end}_{end}_{min} ← min(_{min} ← argmin_{MDL}_{min}| ≠ _{end}_{min}|
else
_{end}_{end}_{min}) until convergence of the log likelihood is reached
end

The best evaluation value achieved during the evolution process is stored in MDL_{min} and the corresponding individual in _{min}, where |_{min}|denotes the number of components used for this model.

Each individual is composed of two parts. The first part uses binary encoding, where the length of this part is determined by the maximal number of allowed components _{max} Each of these bits is related to a particular component. If a bit is set to zero, then its associated component is omitted for modeling the mixture, while setting the bit to one includes the component. The second part uses floating point value encoding to encode the _{k,j}_{k}_{max} components. Due to the switching mechanism of the components among the individuals during evolution of the GA, the components weight _{k}

The crossover operator selects two parent individuals randomly from the population _{c}_{c}M_{max}} within the first part of the individual and exchanges the value of the genes to the right of this position between both individuals for the first part with its associated parameters in the second part.

For selection, the (^{m}

If more components model the data points in a similar manner, some of their parameters are forced to mutate. This similarity is measured using the correlation coefficient. If the correlation coefficient is above the threshold, one of both components is randomly selected and added to the candidate set for mutation. Once the candidate set for enforced mutation is complete, a binary value is sampled from a uniform distribution for each candidate. According to this value, either the candidate component is removed by resetting the corresponding bit in the first part of the individual.

The mutation operator inverts the binary value of each gene in the first part of the individuals with the mutation probability _{m}

After the number of SAR imagery regions is detected and the model parameters are estimated, SAR image segmentation is performed by classifying pixels. The Bayesian classifier is utilized for implementing classification. That is to say, to attribute at each

To demonstrate the segmentation performance of our proposed algorithm, we applied it to two complex SAR images of 200×200 pixel resolution size, consisting of woodlands and cornfields [see _{i}_{max} =15 for the EM and the GA-EM algorithm. The parameter setting for the GA-EM is _{m}_{c}_{max} components. The selected model is the one that achieves the lowest MDL value within the set of obtained candidate models. The termination condition of both algorithms is reached when the relative log likelihood drops below 0.001.

We combine the GA algorithm with the EM algorithm (denoted as GA-EM) and apply it to the segmentation of SAR image based on the MMAR model of SAR imagery. This kind of algorithm leads to a great improvement in ML parameter estimation and is less sensitive to initialization compared to the standard EM algorithm. Experimental results show that the GA-EM algorithm gives better results than the classical EM algorithm in the quality of the segmented image.

This work is supported in part by the National Natural Science Foundation of China (No. 60375003), the Aeronautics and Astronautics Basal Science Foundation of China (No. 03I53059), the Tianjin Natural Science Foundation, the Science Foundation of Tianjin University of Technology (2006BA15).

Sequence of three multiresolution SAR images mapped onto a quadtree.

(a) Original SAR image. (b) Segmented image from EM algorithm. (c) Segmented image from GA-EM algorithm.

Percentage of pixels that are correctly segmented using EM and GA-EM algorithm.

EM | GA-EM | |
---|---|---|

82 | 93 | |

79 | 95 |