# Rectification for Stitched Images with Deformable Meshes and Residual Networks
## 5 Conclusions and Future Work  
This paper proposes a method for rectifying irregularly stitched images using deformable meshes and residual networks. The approach involves predicting initial mesh models for irregular images using three types of shapes: triangles, rectangles, and regular hexagons. The selection of different meshes can be dynamically adjusted based on the requirements of predicting rigid structures or actual image content. The predicted mesh model, predefined mesh model, and irregular input image are jointly input into a width residual network for rectification regression. The loss function comprises local and global loss terms, ensuring that the loss of image information within the mesh and global contextual information is minimized. The final output rectifies the irregularly stitched image into a rectangularized image. The generated rectangularized image not only reduces the information loss in image deformation, but can also be adapted according to different actual input image structures, which further improves the effect of image rectangularization. The image rectangularization has significant advantages in the practical application of image stitching, including simplifying the processing flow, increasing accuracy and stability, and improving the accuracy of stitching results. This enables it to have a wide range of applications in fields such as geographic information systems and medical image processing.  
There is still room for further improvement and optimization of the algorithms in this paper. When constructing non-traditional rectangular grids such as triangles or hexagons, the complex calculations require further optimization. For example, calculating the relative positions or distances between neighboring cells may involve more complex geometric operations. Compared to rectangular grids, triangle and hexagonal grids have more complex vertex coordinates and connectivity, and they typically require more storage to represent the same regions. In addition, using neural network structures in deep learning networks for non-rectangular meshes may require more parameters and more complex processing layers, which may lead to slower training and inference. In the future, we will continue to investigate and improve the efficiency of these areas.  
Conceptualization, Y.F. and S.M.; Data curation, Y.F.; Formal analysis, Z.W. and B.L.; Funding acquisition, S.M.; Methodology, Y.F.; Project administration, S.M.; Resources, Y.F.; Software, Y.F.; Supervision, S.M.; Validation, Y.F., M.L. and J.K.; Visualization, S.M.; Writing--original draft, Y.F.; Writing--review and editing, Y.F. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program for the 14 th Five-Year Plan (Prevention and Control of Major Natural Disasters and Public Security, [PERSON] et al.), grant number SQ2022 YFC3000083.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
We would like to express our gratitude to many colleagues at Beijing LongRuan Technology Co., Ltd., for their extensive assistance in providing data and hardware support for this experiment.  
The authors declare no conflicts of interest.