# Research on Building Target Detection Based on High-Resolution Optical Remote Sensing Imagery
## 2 Data and Methodology
### Methodology
#### 2.2.2 Diffusion-Based Saliency Model
To improve the reliability of foreground detection and the overall quality of the saliency region segmentation, the distribution metric of super-pixel \(v_{i}\) relative to the center of mass of the compactness-based saliency map \(S_{com}\) is defined as Equation (12). \[\mathbf{dm}(i)=\frac{\sum_{j=1}^{N}m_{ij}\cdot n_{j}\cdot\lVert b_{j}-us \rVert}{\sum_{j=1}^{N}m_{ij}\cdot n_{j}}, \tag{12}\]  
where \(m_{ij}\) is the spatial distance similarity measure of a pair of super-pixels \(v_{i}\) and \(v_{j}\), defined as \(m_{ij}=a_{ij}\cdot\exp(-\lVert b_{i}-b_{j}\rVert/\sigma^{2})\). \(\mu\)s \(=[\mu s^{x},\mu s^{y}]\) is the center of mass of the compactness-based saliency map \(S_{com}\). \(us\) is calculated in the same way as Equation (9). \[ \begin{array}{l}\mu s^{x}=\frac{\sum_{i=1}^{N}S_{com}(i)\cdot n_{i}\cdot b_{ j}^{x}}{\sum_{i=1}^{N}S_{com}(i)\cdot n_{i}}\\ \mu s^{y}=\frac{\sum_{i=1}^{N}S_{com}(i)\cdot n_{i}\cdot b_{j}^{x}}{\sum_{i=1 }^{N}S_{com}(i)\cdot n_{i}}\end{array}  \tag{13}\]  
Combining the Lab color space distance \(\mathbf{Id}\) and the distribution metric \(\mathbf{dm}\) to define the local contrast, the N-dimensional column vector \(\mathbf{lc}\) is obtained, as shown in Equation (14). \[\mathbf{lc}(i)=\mathbf{Id}(i)\cdot(1-Norm(\mathbf{dm}(i))). \tag{14}\]  
The local contrast \(\mathbf{lc}\) saliency map [16] tends to highlight the boundaries rather than the entire region. The \(\mathbf{lc}\) saliency map is propagated using a manifold ranking algorithm to obtain an N-dimensional column vector \(S_{loc}=Norm((\mathbf{D}-\alpha\mathbf{W})^{-1}\mathbf{lc})\). First, after the image is super-pixel segmented, a preliminary saliency map is generated using the algorithm of Reference [17] with background seeds and a modified manifold ranked diffusion model. The method uses the boundary super-pixel nodes of the experimental image as background seeds to rank the other super-pixel regions. The saliency maps of the four boundary priors are constructed by taking the upper boundary, lower boundary, left boundary and right boundary, respectively. The saliency map using the left boundary prior \(S_{l}\) is represented as Equation (15). \[S_{l}(i)=1-Norm(\mathbf{f}^{*}(i))\ \ \ \ \ \ i=1,2,\ldots,N, \tag{15}\]  
where \(i\) is the subscript of the super-pixel node in the experimental image and \(Norm(\mathbf{f}^{*}(i))\) represents the normalized vector of \(\mathbf{f}^{*}\). Similarly, the saliency map \(S_{r}\) for the right boundary prior, the saliency map \(S_{t}\) for the top boundary prior, and the saliency map \(S_{b}\) for the bottom boundary prior are obtained. The saliency maps of the four boundary priors are integrated to obtain the saliency map: \(S_{blq}(i)=S_{l}(i)\times S_{r}(i)\times S_{t}(i)\times S_{b}(i)\). The compactness-based, local contrast-based, and boundary prior-based saliency maps are fused, and the fusion results are shown in Equation (16). \[S_{init}=Norm(\varepsilon_{com}S_{com}+\varepsilon_{loc}S_{loc}+\varepsilon_{ bd}S_{bl}), \tag{16}\]  
where \(\varepsilon\) represents the weights of the calculation results of the three saliency maps. In this paper, Edge Boxes proposed in Reference [18] is chosen to generate saliency objects from edges. This algorithm outputs the number of bounding boxes and the score of each bounding box, but the number of generated bounding boxes is large, resulting in a large computational effort. According to Reference [19], the outliers with too large or too small sizes of the bounding boxes are removed, and then the bounding boxes of the regions without high saliency within the boxes are removed. For each super-pixel node, the average score is calculated from the scores of the screened bounding boxes, which is calculated as Equation (17). \[m_{i}^{o}=\sum_{j=1}^{Q}G_{j}\cdot\delta\big{(}v_{i}\in\Omega_{j}\big{)}, \tag{17}\]  
where \(Q\) is the number of bounding boxes \(\Omega_{j}\), \(G_{j}\) is the score of the bounding box \(\Omega_{j}\), and \(\delta(v_{i}\in\Omega_{j})\) is the indicator function, \(v_{i}\in\Omega_{j}\) is 1, otherwise is 0.