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3D Trajectories from a Single Viewpoint using Shadows

We consider the problem of obtaining the 3D trajectory of a ball from a sequence of images taken with a camera which is possibly rotating and zooming (but not translating). Techniques are developed to compute the component of image motion of the ball due to camera rotation and zoom, using optic flow. The 3D location of the ball in each frame of the sequence is then determined using a novel geometric construction which makes use of shadows on the known ground plane in order to compute the vertical projection of the ball onto the ground, and the height of the ball above the ground.