# Target Image Mask Correction Based on Skeleton Divergence
## 2 Materials and Methods
### Decision-Based Sparse RGB-Depth Regularization Verification  
Decisions based on TOPSIS [15] are used in this study. When it is difficult to find the optimal splicing strategy, or the minimum merge cost of the splicing strategy is always greater than the preset merge cost error threshold, decisions are made using the sparse point-cloud regularization constraint. Because of the large amount of depth image point-cloud information data in the system, the global regularization constraint inevitably leads to high computational cost, and redundant data limit the effectiveness of the system. Considering the need to centrally sample the high curvature region while simplifying the point cloud, in order to reduce the computational complexity and improve the accuracy of the detail mask correction, this study refers to the method and application scenario of [17]. Cloud information is refined and pre-processed with the help of incremental and hierarchical clustering, iterative simplification concentrates the point-cloud sampling in the high-curvature region. At the same time, because the adopted skeleton-extraction process causes the point cloud to be partitioned by the local structure, the scope of the search is further reduced, and the calculation expenditure is reduced. A surface deformation model may then be established [18]. When the edge-guided discrete pixel regions are merged, there is an area deformation error related to the discrete pixel region, and the optimal stitching strategy is screened using the size of the edge stitching error.  
The TOPSIS [15] process is summarized as follows.  
Suppose that the set of strategy to be determined is \(\mathrm{D}=\{d_{1},d_{2},\cdots,d_{n}\}\). If the m attributes of the measure \(d_{i}\) are \(a_{i1},a_{i2},\cdots,a_{im}\), then the decision matrix can be set to \(\mathrm{A}=\left(a_{ij}\right)_{n\times m}\), and thus the normalized matrix \(\mathrm{B}=\left(b_{ij}\right)_{n\times m}\) can be obtained, among it,  
\[b_{ij}=\frac{a_{ij}}{\sqrt{\sum\limits_{i=1}^{n}{a_{ij}}^{2}}},i=1,2,\ldots,n ;j=1,2,\ldots,m. \tag{16}\]  
The weighted canonical matrix is \(\mathrm{C}=\left(c_{ij}\right)_{n\times m}\). The manually set weight vector is \(\mathrm{W}=[w_{1},w_{2},\cdots,w_{m}]\), then,  
\[c_{ij}=w_{j}\cdot b_{ij},i=1,2,\ldots,n;j=1,2,\ldots,m. \tag{17}\]Determine positive ideal solution C\({}^{*}\) and negative ideal solution \(C_{0}\),  
\[c_{j}^{\,*}=\left\{\begin{array}{l}\max\!c_{ij}\\ \min\!c_{ij}\end{array},c_{j}^{\,0}=\left\{\begin{array}{l}\max\!c_{ij}\\ \min\!c_{ij}\end{array}\right.. \tag{18}\]  
Calculate the distance from each solution to the positive and negative ideal solutions, as follows.  
\[s_{i}^{\,*} = \sqrt{\sum\limits_{j=1}^{n}{(c_{ij}-c_{j}^{\,*})}},i=1,2,\ldots,m\] \[s_{i}^{\,0} = \sqrt{\sum\limits_{j=1}^{n}{(c_{ij}-c_{j}^{\,0})}},i=1,2,\ldots,m \tag{19}\]  
Calculate the comprehensive evaluation value and select the strategy with the highest value of \(f_{i}^{\,*}\) as the optimal merge strategy.  
\[f_{i}^{\,*}=\frac{s_{i}^{\,0}}{s_{i}^{\,0}+s_{i}^{\,*}},i=1,2,\ldots,m. \tag{20}\]  
In this study, when it is easy to screen out the optimal strategy, four evaluation indicators are selected, namely the minimum combined cost error and the overall minimum cost error of the three channels, i.e., m = 4. When it is difficult to select the optimal strategy, five evaluation indicators are selected, namely the minimum combined cost error, the overall minimum cost error of the three channels, and the matching ratio of the combined result of each combining strategy under the minimum regularization constraint, i.e., m = 5. The value of the weight vector is derived empirically, when m = 4, W = [0.4, 0.2, 0.2, 0.2]. Moreover, when m = 5, W = [0.2, 0.2, 0.2, 0.2, 0.2].