# Rectification for Stitched Images with Deformable Meshes and Residual Networks
## 2 Related Work  
Faced with the problems of image rectangles, researchers have conducted some related work and research, including feature matching-based methods, optimization algorithm-based methods, and deep learning methods. However, each method has its own limitations; for example, the feature matching-based method is easily affected by the mismatch and instability of the feature points in the image, resulting in discontinuous or irregularly shaped edges of the spliced image. While the class uses optimization algorithms to adjust the image, it usually needs to define the global or local loss function of the spliced image and use optimization algorithms to minimize the loss function so as to obtain smoother and more regular image edges. However, since these methods require complex optimization calculations on the image and may be affected by local optimal solutions, their effectiveness may be limited when dealing with large-scale images or complex scenes.  
For example, in terms of feature matching, [PERSON] et al. [22] proposed adjusting the stitched image by computing a perspective transformation matrix to make it closer to a rectangular shape. However, this method often relies on the estimation of the geometric structures in specific regions of the image, such as lines or corners. Some approaches suggest transforming local quadrilateral mesh regions on the stitched image to make the overall image more rectangular [23; 24; 25]. Building upon the aforementioned research, [PERSON] et al. [26] proposed optimizing the preservation of line meshes and deforming the rigid structures within the mesh. [PERSON] et al. [27] improved the preservation term from line meshes to geodesic lines. However, the applicability of this method is restricted due to the common occurrence of curved ground lines in panoramic images. Some researchers introduced Seam Carving, an algorithmic approach that alters the size of an image by carving or inserting pixels in different parts of the image, thereby transforming irregular images into rectangular forms [28; 29; 30; 31; 32]. Meanwhile, [PERSON] et al. [21] proposed DRIS (Deep Rectangling for Image Stitching), employing a residual progressive regression strategy for fully convolutional network prediction of mesh deformations. Based on the predicted mesh, irregular images are corrected. This method partially addresses the challenges of flexible structural distortions for image rectification and computational acceleration. Moreover, the approach utilizes a residual progressive regression strategy for fully convolutional network prediction of mesh deformations and subsequent correction of irregular images. However, DRIS still faces certain challenges. For instance, its loss function focuses solely on the situation within the initial mesh, without considering global information for further adjustments. This limitation results in deformation errors in panoramic information. Additionally, the method concentrates on horizontal and vertical objectives within the mesh, making it prone to deformation errors when correcting targets in other scale directions [33; 34]. Currently, there is relatively limited research on image rectification, and achieving image rectification while ensuring minimal loss of information remains a challenging task [35; 36; 37; 38].