Tham khảo tài liệu 'active visual inference of surface shape - roberto cipolla part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Ego-motion from the image motion of curves 111 Knowledge of the normal component of image velocity alone is insufficient to solve for the ego-motion of the viewer. By assuming no or knowledge of rotational velocity qualitative constraints can be recovered 106 186 . By making certain assumptions about the surface being viewed a solution may sometimes be possible. Murray and Buxton 158 show for example how to recover egomotion and structure from a minimum of eight vernier velocities from the same planar patch. In the following we show that it is also possible to recover ego-motion without segmentation or making any assumption about surface shape. The only assumption made is that of a static scene. The only information used is derived from the spatio-temporal image of an image curve under viewer motion. This is achieved by deriving an additional constraint from image accelerations. This approach was motivated by the work of Faugcras 71 which investigated the relationship between optical flow and the geometry of the spatio-temporal image. In the following analysis a similar result is derived independently. Unlike Faugeras s approach the techniques of differential geometry are not applied to the spatiotemporal image surface. Instead the result is derived directly from the equations of the image velocity and acceleration of a point on a curve by expressing these in terms of quantities which can be measured from the spatio-temporal image. The derivation follows. The image velocity of a point on a fixed space curve is related to the viewer motion and depth of the point by U A q A q . q 5----V2 - - ÍÌ A q. A By differentiating with respect to time and substituting the rigidity constraint 7 xt 0 the normal component of acceleration can be expressed in terms of the viewer s motion U Ut ÍỈ Fit and the 3D geometry of the space curve A 8 q -np A A A 2 A Note that because of the aperture problem neither the .
