## 2 Algorithm Based on Human Visual System
### The Theory of Frequency-Domain in the First Stage  
Most existing significant target detection method is through detecting abnormal patterns in the image, namely, its difference with other parts of the image. Through defining and controlling insignificant areas, namely those easily overlooked by human eye attention mechanism, methods of frequency domain can distinguish the significant target.  
In the model based on frequency-domain, we assume that a natural image consists of several salient and many so-called regular regions. All of these entities (whether distinct or not) may be considered as visual stimuli that compete for attention in the visual cortex. Then, the image is divided into many patches (at a particular scale), some of which are distinctive, while others are quite homogenous. These regular patches are identified as repeated patterns, which correspond to non-saliency. Then suppress them through several different operations in frequency-domain. These kinds of methods (e.g., SR, PFT, HFT) essentially suppress regular regions through suppress amplitude spectrum of the regular regions, thereby producing the pop-out of the salient objects. Here follows the expression in mathematics of these methods.  
First we introduce the related definition. Given an image \(f(x,y)\), it was first transformed into the frequency domain: \(f(x,y)\overset{F}{\rightarrow}F(f)(u,v)\). The amplitude \(A(u,v)=|F(f)|\) and phase \(P(u,v)=angle(F(f))\) spectra are calculated, and then the log amplitude spectrum is obtained: \(L(u,v)=log(A(u,v))\).  
The operation in amplitude spectrum of SR method is defined as [5].  
\[A_{SR}(u,v)=L(u,v)-L(u,v)\times h_{n}(f) \tag{1}\]  
where \(h_{n}(f)\) is a n \(\times\) n matrix defined by:  
\[h_{n}(f)=\frac{1}{n^{2}}\begin{pmatrix}1&1&\cdots&1\\ 1&1&\cdots&1\\ \vdots&\vdots&\ddots&\vdots\\ 1&1&\cdots&1\end{pmatrix} \tag{2}\]  
In PFT reconstruction, amplitude spectrum is abandoned which means \(A_{PFT}(u,v)=1\)[6]. For HFT method, a gaussian kernel \(h_{G}\) is employed to suppress spikes in amplitude spectrum [7]:\[A_{HFT}(u,v)=|F(f(x,y))|\times h_{G} \tag{3}\]  
The resulting processed amplitude spectrum A (\(A_{SR}\) for SR, 1 for PFT and \(A_{HFT}\) for HFT) and the original phase spectrum are combined to compute the inverse transform, which in turn, yields the saliency map [6]:  
\[S=F^{-1}\left\{A(u,v)e^{i\times P(u,v)}\right\} \tag{4}\]  
In order to improve the visual display of saliency, we define saliency map hereafter as Equation (5), where g is the parameter to adjust gray level of the saliency map. For convenience, here we set g to be 10.  
\[S=g\times\left|F^{-1}\left\{  
samples which belong to the salient regions of the first a few pictures. Considering that the target shape may have a slight change in the process of moving as a result of the change of direction and attitude, we could update the training set to make the classifier more intelligent. This process adds true and false target of the testing image into the training set respectively.  
After the above preparation, we define the centers of salient areas obtained in the Section 2.2 as the suspected target centers and use the SVM classifier to classify these pixels with its \(16\times 16\) neighbors. Attributed to SVM classifier successful separations of target from clutters, the accuracy can be improved to a satisfactory degree.