Stereovision with a Single Camera and Multiple Mirrors El Mustapha Mouaddib CREA-University of Picardie Jules Verne 7, Rue du Moulin Neuf, 80000, Amiens, France mouaddib@u-picardie.fr Ryusuke Sagawa, Tomio Echigo, Yasushi Yagi Department of Intelligent Media, ISIR Osaka University, 8-1 Mihogaoka, Ibaraki Osaka, 567-0047, Japan (sagawa,echigo,yagi)@am.sanken.osaka-u.ac.jp Abstract— You can create catadioptric omnidirectional stereovision using several mirrors with a single camera. These systems have interesting advantages, for instance in the case of mobile robot navigation and environment reconstruction. Our paper aims at estimating the ”quality” of such stereovision system. What happens when the number of mirrors increases? Is it better to increase the base-line or to increase the number of mirrors? We propose some criteria and a methodology to compare different significant categories (seven): three already existing systems and four new designs that we propose. We also study and propose a global comparison between the best configurations. Index Terms— Stereovision, Omnidirectional Vision, Cata- dioptric, Multi Mirrors, Evaluation. I. I NTRODUCTION Omnidirectional catadioptric computer vision is achieved using convex mirrors and a conventional camera. It offers the robustness of 3D calculations, and its image acquisition speed remains similar to that of conventional cameras. The increased interest of researchers in problems related to these systems have brought notable improvements in their design, geometry, calibration and image processing. So, these sensors have become more popular with many applications such as in mobiles, robots navigation, art, architecture and for tourism. To carry out omnidirectional stereovision, recourse is often made either to the rotation of a pair of cameras[2], or the use of two omnidirectional catadioptric cameras [21]. The first solution is better to obtain very good resolution, but it requires the rotation of the cameras and this prevents treating scenes with moving objects. The second approach avoids this problem, but it needs two cameras and two mirrors, thus increasing the weight and size of the sensor. It also has all the conventional stereovision disadvantages: synchronization problems between the cameras and their calibration, optical response differences between cameras, and so on. Another way to recover stereovision is to exploit only one camera that observes several mirrors. This makes it possible to design sensors having many advantages compared to the systems based on the use of several cameras; they are: single calibration, no synchronization problem, similar op- tical response, large view field, rigid link between mirrors, and finally, cost. Several reports have dealt with a single camera associated to planar mirrors [3][11] [4] [13][12]. We restrict our overview to the stereo system based on a single camera and convex mirrors. Nayar [7] was proba- bly first to use a stereo vision system based on convex mirrors (specular curved surfaces) and a single camera. In his report, Nayar proposed a system based on a single conventional camera (one lens) and two specular spheres. That is why he named it ”SPHEREO”, like SPHeres when stereo is like stEREOpsis. His paper dealt with calibration by using four LEDs, explained how to recover depth by using a classic triangulation, studied the characteristics of its accuracy and briefly proposed a procedure to solve the matching problem by using epipolar constraints. Southwell et al. [14], proposed a stereo vision system that used two vertically aligned mirrors with different curvatures (”two- biconvex lobes”). This approach is not suitable for small sensors; so, more recently, Sagawa et al. [10], proposed a single camera with nine spherical (they are easier to make) mirrors: a principal one surrounded by eight mirrors. Since the compound spherical mirrors they proposed are very small, the accuracy of distance measurements is lower than that of a wide-baseline stereo system. Therefore, the multi-mirror system increases the robustness of computing corresponding points. Our paper aims at estimating a global quality for a stere- ovision system using a single camera and multi-mirrors. What happens when we increase the number of mirrors, and is it better to increase the base-line or to increase the number of mirrors ? In this paper, we propose some criteria and a methodology to make comparisons between different significant categories (seven): three already existing sys- tems and four new designs that we propose. Each category has been studied and a global comparison between the best proposed configurations. In each work regarding such proposed system, we find discussion about quality, depth accuracy, resolution, view field, etc; however, there are only few works dedicated to a global analysis, optimization and a formalization of the criteria. You can, for example, refer to [17] [16]. II. CAMERA AND MIRRORS GEOMETRY As we noted above, we want to deal with one single camera and multi-mirrors systems. In this case, stereovision is possible if the same point has at least two different images in the image plane. This is feasible in two ways: different centers of projection and/or different shapes of the mirrors (reflective surfaces). Several parameters intervene in this design. We note the following most important ones: • Number (at least 2) Proceedings of the 2005 IEEE International Conference on Robotics and Automation Barcelona, Spain, April 2005 0-7803-8914-X/05/$20.00 ©2005 IEEE. 800