## 1 Introduction  
Conventional stereoscopic reconstruction systems based on perspective cameras have a limited field-of-view that restricts them in applications that involve wide areas such as large-scale reconstruction or self-driving cars. To compensate for the narrow field-of-view, these systems acquire multiple images and combine them to cover the desired scene [1]. A different way to increase the field-of-view is to use fish-eye lenses [2] or mirrors in conjunction with lenses to constitute a panoramic catadioptric system [34]. Catadioptric omnidirectional stereo vision can be achieved using one camera with multiple mirrors [5, 6]; two cameras and a single mirror [7] or two cameras and two mirrors [8]. The common types of mirrors used are hyperbolic double mirrors [9], multiple conic mirrors [10, 11], multiple parabolic mirrors [12], concave lens with a convex mirrors [13, 14], multi-planar mirrors [15], and mirror pyramids [16]. The large field-of-view of these systems makes them useful in applications such as driver assistance tasks [17, 18], unmanned vehicle aerial navigation [19, 20, 21], visual odometry [22], and 3D reconstruction for metrology applications [23, 24]. To perform 3D reconstruction with a stereo system, we need to find matching points on the set of cameras. Typically, there are two methods for matching image pairs in passive stereo systems: dense methods based on finding a disparity map by pixel-wise comparison of rectified images along the image rows, and sparse methods using matching features based on pixel region descriptors. One challenge of the dense methods with panoramic images is that the rectified images are heavily distorted, and their appearance depends on the relative configuration of the two cameras. Therefore, many pixels are interpolated in some image regions, influencing pixel mapping precision and 3D reconstruction. A limitation of dense omnidirectional stereo matching is the running time making it not suitable for real-time applications [25]. On the other hand, sparse methods with panoramic images provide a confined number of matching features for triangulation [26; 27] due to the reduced spatial resolution, wasted image-plane pixels, and exposure control [28]. Due to this, it is a common practice to manually select matching points for calibration or to validate the measurements [5; 29]. Another prevalent limitation of these systems is the validation in indoor environments only. For example, [PERSON] et al. [26] present a reconstruction algorithm for multiple spherical images; they use a combination of manually selected points and SIFT matching to estimate the fundamental matrix for each image pairs and present sparse reconstruction results in indoor environments. [PERSON] et al. [5], present a bi-lobed panoramic sensor with the matching features detected using the Panoramic Hough Transform. The results show sparse points of scene polygons in indoor environments. The work presented by [29] similar to our research proposal, shows a sensor with the same amount of components but with the use of hyperbolic mirrors. The 3D reconstruction was done on manually selected points to avoid possible errors due to an automatic matching. To validate the method, they selected four corners of the ceiling to compute the size of the room with an estimated error between 1 and 6 cm. [PERSON] et al. [30] propose an omnidirectional stereo vision sensor composed of one CCD camera and two pyramid mirrors. To evaluate the performance of the proposed sensor, they tested a calibration plane. Although this sensor cannot accomplish a whole panoramic view, it nevertheless provides a useful vision measurement approach for indoor scenes. [PERSON] et al. [31] propose a catadioptric stereo camera system that uses a single camera and a single lens with conic mirrors. Stereo matching was conducted with a window-based correlation search.