## 1 Introduction  
Borehole camera technology (BCT) is an important optical signal acquisition and processing technology to image the interior structure of boreholes. It has been widely used in geological detection [1], investigating the structure of glaciers [2] and hydrogeological investigation [3]. Among BCT techniques, the digital panoramic borehole camera system (DPBCS) [4] and axial view borehole camera system (AVBCS) [5] are the two most widely used methods. The principle of a DPBCS device is a conic mirror installed on a probe to map the 3D borehole-wall image to a 2D plane image and thus a borehole-wall cylindrical panorama can be produced by image mosaic technology. However, this complex and expensive equipment can only be applied to vertical drilling and the diameter for the test borehole should be in the range from 48 to 180 mm. In comparison, the AVBCS device is relatively simple and cheap. Significantly, it can be applied to the vertical, horizontal and oblique holes and can also be applied in wider drilled holes whose diameters range from 28 mm to 250 mm. The operation principle of an AVBCS is that it takes forward-looking video while the probe moves along the pre-drilled borehole in an axial motion; engineers, by studying the playback or screenshot of the borehole video, can obtain data on the geological structure. However, AVBCS only allows qualitative analysis from the videos. Quantitative data, which will be applied in the analysis of the fracture, joint, structural plane, etc., are not available. Therefore, it is of great practical significance to create a method to generate a panoramic cylindrical image from the borehole video obtained by AVBCS. In addition, some experts use an introscopic camera to take photographs to analyze the rock mass characteristics in boreholes. Table 1 shows the main parameters of the AVBCS used in this study, DPBCS and the introscopic camera used in the literature [6]. Although the video mosaic technique has been deeply investigated for several years, it is still challenging in the field of machine vision. Videos are generally taken in two ways: One is by rotating a camera around its optical axis in a fixed position and the other is to take videos with a moving camera [7]. The process of obtaining a borehole video with AVBCS should be classified as a monocular moving camera. To be more specific, a single CCD (charge-coupled device) camera is installed on the top of the probe, and, accompanied with slight rotation and vibration, the probe moves forward along the central axis of a drilled hole. A literature review shows that there are few studies on borehole video processing with AVBCS, and even fewer on generating cylindrical panoramas from these videos. However, there is some research on similar techniques. On pipeline inspection with mobile cameras [8; 9], to which borehole video-taking is similar, there are some studies: [PERSON] et al. [10] proposed a manifold projection algorithm which transforms a video sequence into a parallel image sequence and thus a video mosaic can be obtained for the most challenging cases of forward motion and zoom. In [11], a method of cylindrical panoramic mosaic from a pipeline video was proposed. A series of standard circles were extracted from video sequences and converted into corresponding strips to construct a panoramic image. These studies shed light on problems in the concerned fields, but in the method proposed by [PERSON], precise camera parameters have to be known beforehand and are hard to achieve with AVBCS devices; and the second study mentioned above assumes that there is no probe jitter; however, it is known that jitter exists and if the camera trajectory is not moving along the central axis of a cylinder, distortion will appear in the panorama. The current method is proposed to solve these problems. Camera movement in a borehole is non-uniform, image distortion will arise if traditional video mosaic methods are employed, and this distortion will be more severe when probe jitter exists.