3D Pose from Three 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 solutins, involves solving a biquadratic equation. Here the biquadratic is motivate geometrically and its solutions, comprised of an actual and a false solution, are interpreted graphically. The final equations take a new form, which lead to a simple expression for the image position of any unmatched model point.

Trajectory Mapping ("TM''): A New Non-Metric Scaling Technique

Trajectory Mapping "TM'' is a new scaling technique designed to recover the parameterizations, axes, and paths used to traverse a feature space. Unlike Multidimensional Scaling (MDS), there is no assumption that the space is homogenous or metric. Although some metric ordering information is obtained with TM, the main output is the feature parameterizations that partition the given domain of object samples into different categories. Following an introductory example, the technique is further illustrated using first a set of colors and then a collection of textures taken from Brodatz (1966).