Navigation by Tracking Vanishing Points

4 Captions Table 1. Angular displacements of a camera which is rotated of a xed amount around an axis orthogonal to the image plane between consecutive frames: the rst row reports angular displacements as measured with a goniome-ter, whilst the second row refers to computed values from vanishing points. Fig. 1. Extraction of vanishing points. a) A corridor at IRST; b) edges approximated by straight lines longer than 30 pixels; c) pairwise intersections of all the lines which go through the edges in b) apart from the lines whose angle with the vertical directions is less than 5 degrees; d) the cross marks the estimated location of the vanishing point. Fig. 2. Vanishing points can be detected even in the presence of many curved lines. a) the same corridor of g. 1a but with people around; b) estimated location of the vanishing point. Fig. 3. a) A sequence of images (second, fourth, sixth and eighth frame are shown of a sequence of ten images) taken while the viewing camera is rotating at the intersection between two corridors at IRST; b) the extracted segements of straight edges and the estimated localization of the vanishing points. 3 where V T is the transpose of V, V(t) is the 33 matrix whose columns are the coordinates of the vanishing points at time t in an orthogonal system of coordinates associated with the viewing camera, and t the time interval between frames. Fig. 3 shows some frames of an image sequence in which the vanishing points have been extracted according to the procedure described above. The tracking procedure is trivial due to the distance between the vanishing points. The estimated rotational component of motion was within the accuracy of the goniometer used to rotate the viewing camera (:2 o), as reported in table 1. Concluding, in many indoor scenes, the recovery of the rotational component of egomotion of a navigating robot can be obtained by tracking vanishing points.