Direct Computation of 3D Shape Invariants and the Focus of Expansion

Structure from motion often refers to the computation of 3D structure from a matched sequence of images. However, a depth map of a surface is difficult to compute and may not be a good representation for storage and recognition. Given matched images, I will first show that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line-segments in one image. Using this result, local surface patches can be classified as convex, concave, parabolic (cylindrical), hyperbolic (saddle point) or planar. At the same time the translational component of the optical flow is obtained, from which the focus of expansion can be computed.

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.

Robust and Efficient 3D Recognition by Alignment

Alignment is a prevalent approach for recognizing 3D objects in 2D images. A major problem with current implementations is how to robustly handle errors that propagate from uncertainties in the locations of image features. This thesis gives a technique for bounding these errors. The technique makes use of a new solution to the problem of recovering 3D pose from three matching point pairs under weak-perspective projection. Furthermore, the error bounds are used to demonstrate that using line segments for features instead of points significantly reduces the false positive rate, to the extent that alignment can remain reliable even in cluttered scenes.

Stereo-Based Head Pose Tracking Using Iterative Closest Point and Normal Flow Constraint

In this text, we present two stereo-based head tracking techniques along with a fast 3D model acquisition system. The first tracking technique is a robust implementation of stereo-based head tracking designed for interactive environments with uncontrolled lighting. We integrate fast face detection and drift reduction algorithms with a gradient-based stereo rigid motion tracking technique. Our system can automatically segment and track a user's head under large rotation and illumination variations. Precision and usability of this approach are compared with previous tracking methods for cursor control and target selection in both desktop and interactive room environments. The second tracking technique is designed to improve the robustness of head pose tracking for fast movements. Our iterative hybrid tracker combines constraints from the ICP (Iterative Closest Point) algorithm and normal flow constraint. This new technique is more precise for small movements and noisy depth than ICP alone, and more robust for large movements than the normal flow constraint alone. We present experiments which test the accuracy of our approach on sequences of real and synthetic stereo images. The 3D model acquisition system we present quickly aligns intensity and depth images, and reconstructs a textured 3D mesh. 3D views are registered with shape alignment based on our iterative hybrid tracker. We reconstruct the 3D model using a new Cubic Ray Projection merging algorithm which takes advantage of a novel data structure: the linked voxel space. We present experiments to test the accuracy of our approach on 3D face modelling using real-time stereo images.