On the Use of Shadows in Stance Recovery

The image of an object and of the shadow it casts on a planar surface provide important cues for 3D stance recovery. We assume that the position of the plane on which the shadow lies with respect to a pinhole camera is known, and that the position of the light source is unknown. If the light source is sufficiently far away that parallel projection may be assumed, then knowledge of two point correspondences between images of feature points and images of their shadows is enough to determine the position of the object and the direction of the light source. If the light source is close enough that the shadow points are obtained via perspective projection, then there is a one-parameter infinite family of solutions for the position of the object and the light source. Determining the stance of an object in these manners is highly sensitive to noise, so we provide algorithms for stance recovery that take into account known information about the object. In our experiments, the errors for the location of the 3D feature points obtained by these algorithms are generally less then 0.2% times the error in pixels in the image points, and the errors for the 3D directions of the links is roughly 0.04C times the error in pixels, normalized by the distance to the object from the camera and the length of the link.