# A Segmentation-Based Optimal Seamline Generation Method for SAR Image Mosaic
## 2 Materials and Methods
### Segmentation-Based Optimal Seamline Generation Model  
#### 2.3.1 Joint Segmentation  
During the processing of remote sensing image mosaicking, the geometric and radiometric differences between ortho-rectificated images make selecting the optimal seamline a challenge. The goal is to circumvent areas with significant discrepancies, thus ensuring the visual effect and the integrity of geographic targets in the mosaic images. Furthermore, the selection and optimization of the seamline are not only critical steps in the mosaicking procedure but are also complicated. Traditional methods mainly rely on pixels or blocks as the basic processing units, employing a pixel-by-pixel path search strategy across the entire overlap area. To achieve optimal mosaicking, a segmentation-based method is employed to partition the overlap areas to extract consistency parcels. This ensures the radiometric and geometric consistency of signification features across overlap areas.  
Figure 1: Framework diagram of the proposed method.  
Unlike traditional segmentation-based seamline extraction techniques, this paper employs joint segmentation of SAR images to process the overlapping areas. For individual image segmentation, the fractal net evolution approach (FNEA) is used to generate superpixels [35]. FNEA is a bottom-up area-merging algorithm that uses spectral and shape features to describe each parcel. The essence of FNEA lies in its merging rule, which prioritizes the combination of adjacent parcel pairs that minimizes the heterogeneity increment upon merging. The merging criterion is described as follows:  
\[\begin{cases}h=\omega_{spectral}\times h_{spectral}+\omega_{shape}\times h_{ shape}<T\\ \omega_{spectral}+\omega_{shape}=1\end{cases}, \tag{1}\]  
where \(h\) indicates the heterogeneity increment, which is calculated as the weighted sum of spectral heterogeneity, \(h_{spectral}\), and shape heterogeneity, \(h_{shape}\). \(h_{spectral}\) is derived from the weighted standard deviation of each of the channels, while \(h_{shape}\) consists of the compactness and smoothness of the parcels, with detailed calculations found in reference [35]. \(T\) represents a predefined threshold.  
Image mosaicking involves processing multiple images, which requires ensuring that the segmentation results remain consistent across overlap images. To achieve this, a joint segmentation strategy is introduced to establish an interaction between each individual image segmentation procedure and produce a common segmentation result. Consider two images denoted as \(I_{A}\) and \(I_{B}\), with segmentation procedures employing thresholds \(T_{A}\) and \(T_{B}\), respectively. The FNEA is then executed according to the following joint strategy:  
\[\begin{cases}h_{A}=\omega_{spectral}\times h_{spectral}+\omega_{shape}\times h _{shape}<T_{A}\\ h_{B}=\omega_{spectral}\times h_{spectral}+\omega_{shape}\times h_{shape}<T_{B} \\ h_{A}<T_{A}\;\;and\;\;h_{B}<T_{B}\end{cases}, \tag{2}\]  
where \(h_{A}\) and \(h_{B}\) denote the heterogeneity increment calculated from \(I_{A}\) and \(I_{B}\), respectively. The joint strategy describes the implication that the parcel pairs can only be merged if the merging conditions in both \(I_{A}\) and \(I_{B}\) are simultaneously met. The benefit of the joint segmentation method is that the radiometric consistency and geometric integrity of segmented parcels in single images can be improved. Meanwhile, the geographic target's consistency across overlap images can be maintained. Moreover, this method can be easily extended to more images. Figure 2 illustrates the comparison between the traditional segmentation and joint segmentation frameworks.  
Figure 2: Schematic of parcels extraction. (**a**) Traditional segmentation-based parcel extraction technique. (**b**) Joint segmentation-based parcel extraction framework.