Determining 3-D Motion and Structure of a Rigid Body Using the Spherical Projection

摘要

Projection on the unit sphere is proposed as a fundamental analytical operation in determining three-dimensional motion and structure of a rigid body from an image sequence. Points on the image plane are represented by their central projections on the unit sphere, using a homogeneous coordinate parameterization. Based on the simple geometry of corresponding points on the unit sphere, methods for the determination of three-dimensional rigid body motion from an image sequence are described. For the pure translation case, two new methods are shown for determining object structure. For a general rigid motion consisting of rotation plus translation, the equations used in existing methods for objects with curved surfaces are derived. Object structure can be determined by the method for the pure translation case. A method is shown for computing the pure parameters for planar surfaced objects.