# Optical Flow Odometry with Panoramic Image Based on Spherical Congruence Projection
## 2 Related Work  
### Panoramic Image-Based Feature Tracking  
In response to the varying distortion ratios across the panoramic images, researchers have proposed various strategies to mitigate its impact on feature tracking, as well as the SLAM system. The most straightforward approach is employing feature tracking algorithms designed for planar perspective images on untreated panoramic images directly [9]. However, the extracted feature point and its associated neighborhoods required for optical flow calculations undergo varying degrees of distortion, adversely affecting matching accuracy. [PERSON] et al. [10] addressed the distortion issue by performing feature tracking in areas with slight distortion, although this approach sacrifices the advantage of the panoramic image, which is the broad field of view. One commonly used approach to distortion correction involves projecting the original panoramic image into different formats and eliminating the distortion during the projection process. [PERSON] et al. [11] represented the panoramic image as a subdivided icosahedron and proposed a framework to reconstruct a low-resolution 360\({}^{\circ}\) image to a high-resolution image. To apply the convolutional neural network to spherical images, [PERSON] et al. [12] proposed an approach by utilizing the spherical polyhedron to represent omnidirectional images. [PERSON] et al. [13] presented an optimized content-aware projection method to alleviate the distortion problem during depth estimation of 360\({}^{\circ}\) images. [PERSON] et al. [14] utilized the Scaramuzza model to rectify the panoramic image into the planar perspective image to eliminate image distortion. [PERSON] et al. [8] suggested projecting the panoramic image onto a cube by treating each cube face as an image plane of a virtual pinhole camera with 90\({}^{\circ}\) FoV. [PERSON] et al. [15] extended this approach by combining the Enhanced Unified Camera Mode during the cube map. Besides the cube shape, some researchers tried to project the panoramic image onto a polyhedron to mitigate pixel distortion [16]. While the image is corrected for individual planes, noticeable pixel stretching or compressing near the corners and edges is inevitable for the cube and polyhedron images, and the continuous flow of information in panoramic images is disrupted as well. Another widely used projection method is ERP, which maps the spherical image onto the 2D plane based on the longitude and latitude coordinates of pixels [17]. However, ERP images suffer from poor pixel uniformity, resulting in significant information loss when projecting content near the poles. Therefore, even though ERP-based feature tracking offers computational efficiency, it is suboptimal in terms of matching accuracy. To address the issue of uneven pixel distribution in ERP images, [PERSON] et al. [18] adopted the geodesic grid-based spherical data structure for panoramic images, which was developed by [PERSON] [19], and proposed an FAST corner feature extraction method utilizing this structure. This approach achieved better pixel uniformity compared to longitude-latitude-based segmentation. [PERSON] et al. [20] introduced the SPHORB algorithm for panoramic images based on a similar geodesic grid segmentation approach, which outperformed the traditional ORB algorithm for panoramic images in tasks of feature tracking. [PERSON] et al. [21] proposed the BRISKS feature for spherical images on a geodesic grid. Compared to SPHORB, the statistical-based feature extraction approach makes it more adaptable to varying pixel structures, albeit with a tradeoff in extraction efficiency. Studies in [22; 23] attempted to represent the distortion information using an attitude matrix and built a distorted Binary Robust Independent Elementary Feature (BRIEF) descriptor for the fisheye camera. [PERSON] et al. [24] and [PERSON] et al. [25] proposed methods involving projecting the spherical pixel and its surroundings onto the tangent plane and constructing the descriptor accordingly.