Inverse Perspective Of A Triangle: New Exact And Approximate Solutions

One of the techniques in m0del-based pose estimation of 3D objects consists of locating "interest points" on models of the objects, detecting these point s in the image, and matching subsets of these image points against subsets of the interest points of the models. Valid matches determine a similar object pose, which can be found by clustering techniques. Solving for the position and orientation of an object knowing the images of n points at known locations on the object is called the n-point perspective problem (see [5] for a review and a four points solution), The three-point problem, also called the triangle pose problem [9], has been solved in various ways. A review of the major direct solutions for three points under exact perspective is provided in [4]. Another direct solution is described in this paper. Computation speed is important when many or all possible combinations of triples of image feature points and triples of model interest points are considered. Direct methods require quite a fe w floating point operations. Some researchers have proposed faster methods based on scaled orthographic projection [8,6,10]. We introduce an alternative approximation which we call orthoperspective, a local scaled orthographic projection using a plane normal to one of the rays, which causes smaller errors for off-center images. The angular terms of the pose of a given triangle depend then only on two parameters of the image triangle, and these can be precomputed in a two dimensional lookup table resulting in a very fast pose estimation algorithm.