Plane Detection Using Particle Swarm Optimization and Conformal Geometric Algebra Carlos L´ opez-Franco 1,⋆ , Jes´ us Hern´ andez-Barrag´ an 1 , Michel L´opez-Franco 2 , Nancy Arana-Daniel 1 , and Alma Y. Alan´ ıs 1 1 Computer Science Department, CUCEI, University of Guadalajara, Mexico 2 CINVESTAV Guadalajara, Mexico Abstract. The detection of planes is a useful capability for a safe nav- igation algorithm, which is a crucial task for robots working in indoor environments. In this paper, the authors present an approach for plane detection based on Conformal Geometric Algebra, and Particle Swarm Optimization, with data obtained from an RGB-D sensor. The simu- lation and experimental results show the effectiveness of the proposed approach. Keywords: Plane detection, Conformal Geometric Algebra, Particle Swarm Optimization (PSO). 1 Introduction An essential task for mobile robots is to move safely in its environment. In human-made indoor environments, the detection of planes is a key problem. One interesting and promising framework for representing geometric objects and its operations is the Conformal Geometric Algebra (CGA) [8]. It also has been used for many different robotics task and computer vision problems. In this work we use CGA to represent the planes, since it will allow us to extend it to different geometric objects and robotics applications. In the last years, stochastic optimization methods have become very popu- lar, they have been successfully applied in many research and applications ar- eas. In general there five popular algorithms: Genetic Algorithms [6], Memetic algorithms [9], Particle Swarm Optimization (PSO) is is an population based optimization[7], Ant-Colony optimization [1] and Shuffled frog leaping algorithm [3]. In [2], the authors present a comparison study of these five EA, they conclude that the PSO algorithm performs better in general, with respect to the quality of the solution and the success rate. For these reasons, we decided to choose the PSO algorithm among the others. To detect the planes we propose the use of PSO in conjunction with CGA. Recently, the RGB-D sensors have gained the attention of researchers,sensors like the Primesense sensor or the Kinect camera, acquire RGB data as normal ⋆ This work has been partially supported by the CONACYT projects CB-156567, CB-103191, CB-106838, and INFR-229696. E. Bayro-Corrochano and E. Hancock (Eds.): CIARP 2014, LNCS 8827, pp. 852–859, 2014. c  Springer International Publishing Switzerland 2014