The octopus uses the arm-swimming behavior primarily for escape, defense, or foraging. This mode of locomotion is comprised of two strokes, with the arms opening slowly and closing rapidly, and generally results in considerable propulsive acceleration. In light of the recent development by our group of an octopus-like eight-arm underwater robot, we are interested to analyze the details of the biological arm swimming motion, in order to understand its kinematics. In this paper, we address methodological aspects of the 3D reconstruction process of octopus arm trajectories, based on computer vision, and present the resulting arm swimming movement of a benthic common octopus. The 3D trajectories of all eight octopus arms were tracked and analyzed, providing information about speed, acceleration and arm elongation. The animal's performance is then used for a direct comparison with our 8-arm robotic swimmer. The data obtained provide new kinematic information about this, relatively unknown, propulsive mode, which can be exploited for multi-functional underwater robots.