In this paper, we introduce a statistical learning method for the visual navigation of the mobile robot. For the visual bavigation of an autonomous robot, the detection of the collision avoidance navigation direction from an image/image sequence captured by imaging systems mounted on the robot is a fundamental task. The robot detects the free space for the navigation and computes the collision-free direction. For the extraction of the free space, the robot separates the dominant plane and obstacle area using independent component analysis. For the computation of the collision avoidance direction, our robot computes the principal component of the gradient of the visual potential field which describes the obstacle area. Some experimental results of navigating the mobile robot in synthetic and real environments are presented.