On The Uniqueness of Correspondence Under Orthographic and Perspective Projections

The task of shape recovery from a motion sequence requires the establishment of correspondence between image points. The two processes, the matching process and the shape recovery one, are traditionally viewed as independent. Yet, information obtained during the process of shape recovery can be used to guide the matching process. This paper discusses the mutual relationship between the two processes. The paper is divided into two parts. In the first part we review the constraints imposed on the correspondence by rigid transformations and extend them to objects that undergo general affine (non rigid) transformation (including stretch and shear), as well as to rigid objects with smooth surfaces. In all these cases corresponding points lie along epipolar lines, and these lines can be recovered from a small set of corresponding points. In the second part of the paper we discuss the potential use of epipolar lines in the matching process. We present an algorithm that recovers the correspondence from three contour images. The algorithm was implemented and used to construct object models for recognition. In addition we discuss how epipolar lines can be used to solve the aperture problem.

Intellectual Property in Computing: (How) Should Software Be Protected? An Industry Perspective

The future of the software industry is today being shaped in the courtroom. Most discussions of intellectual property to date, however, have been frames as debates about how the existing law --- promulgated long before the computer revolution --- should be applied to software. This memo is a transcript of a panel discussion on what forms of legal protection should apply to software to best serve both the industry and society in general. After addressing that question we can consider what laws would bring this about.

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.

Recovery of Three-Dimensional Objects from Single Perspective Images

Any three-dimensional wire-frame object constructed out of parallelograms can be recovered from a single perspective two-dimensional image. A procedure for performing the recovery is given.