Generalization of Desargues Theorem for Sparse 3-D Reconstruction

Visual perception for walking machines needs to handle more degrees of freedom than for wheeled robots. For humanoids, four or six legged robots, camera motion is a 6D one instead of 3-D or planar motions. Classical 3-D reconstruction methods cannot be applied directly because explicit sensor motion is needed. In this paper, we propose an algorithm for 3-D reconstruction of an unstructured environment using a motionfree uncalibrated single camera. Computer vision techniques are employed to obtain an incremental geometrical reconstruction of the environment and therefore using vision as a sensor for robots control tasks like navigation, obstacle avoidance, manipulation, tracking, etc. and 3-D model acquisition. The main contribution is that the off-line 3-D reconstruction problem is considered as a points trajectories search through the video stream. The algorithm takes into account the temporal aspect of the sequence of images in order to have an analytical expression of the geometrical locus of the points trajectories through the sequence of images. The approach is a generalization of the Desargues Theorem applied to multiple views taken from nearby viewpoints. Experiments on both synthetic and real image sequences show the simplicity and the efficiency of the proposed method. The method presented is that paper provides an alternative technical solution, easy to use, flexible in the context of robotic applications and can significantly improve the 3-D estimation accuracy.