3d Pose from 3 Corresponding Points under Weak-perspective Projection

Model-based object recognition commonly involves using a minimal set of matched model and image points to compute the pose of the model in image coordinates. Furthermore, recognition systems often rely on the \weak-perspective" imaging model in place of the perspective imaging model. This paper discusses computing the pose of a model from three corresponding points under weak-perspective projection. A new solution to the problem is proposed which, like previous solutions, involves solving a biquadratic equation. Here the biquadratic is motivated geometrically and its solutions, comprised of an actual and a false solution, are interpreted graphically. The nal equations take a new form, which lead to a simple expression for the image position of any unmatched model point.