In this paper, we propose the use of mirrors and a single camera for computational stereo. When compared to conventional stereo systems that use two cameras, our method has a number of significant advantages such as wide field of view, single viewpoint projection, identical camera parameters and ease of calibration. We propose four stereo systems that use a single camera pointed towards planar, ellipsoidal, hyperboloidal, and paraboloidal mirrors. In each case, we present a derivation of the epipolar constraints. Next, we attempt to understand what can be seen by each system, and formalize the notion of field of view. We conclude with two experiments to obtain 3-D structure. In the first we use a pair of planar mirrors, and in the second a pair of paraboloidal mirrors. The results of our experiments demonstrate the viability of stereo using mirrors.

The problem of finding the closest point in high-dimensional spaces is common in computational vision. Unfortunately, the complexity of most existing search algorithms, such as k-d tree and R-tree, grows exponentially with dimension, making them impractical for dimensionality above 15. In nearly all applications, the closest point is of interest only if it lies within a user specified distance /spl epsiv/. We present a simple and practical algorithm to efficiently search for the nearest neighbor within Euclidean distance /spl epsiv/. Our algorithm uses a projection search technique along with a novel data structure to dramatically improve performance in high dimensions. A complexity analysis is presented which can help determine /spl epsiv/ in structured problems. Benchmarks clearly show the superiority of the proposed algorithm for high dimensional search problems frequently encountered in machine vision, such as real-time object recognition.

A real-time vision system is described that can recognize 100 complex three-dimensional objects. In contrast to traditional strategies that rely on object geometry and local image features, the present system is founded on the concept of appearance matching. Appearance manifolds of the 100 objects were automatically learned using a computer-controlled turntable. The entire learning process was completed in 1 day. A recognition loop has been implemented that performs scene change detection, image segmentation, region normalizations, and appearance matching, in less than 1 second. The hardware used by the recognition system includes no more than a CCD color camera and a workstation. The real-time capability and interactive nature of the system have allowed numerous observers to test its performance. To quantify performance, we have conducted controlled experiments on recognition and pose estimation. The recognition rate was found to be 100% and object pose was estimated with a mean absolute error of 2.02 degrees and standard deviation of 1.67 degrees.

In contrast to the traditional approach, visual recognition is formulated as one of matching appearance rather than shape. For any given robot vision task, all possible appearance variations define its visual workspace. A set of images is obtained by coarsely sampling the workspace. The image set is compressed to obtain a low-dimensional subspace, called the eigenspace, in which the visual workspace is represented as a continuous appearance manifold. Given an unknown input image, the recognition system first projects the image to eigenspace. The parameters of the vision task are recognized based on the exact location of the projection on the appearance manifold. An efficient algorithm for finding the closest manifold point is described. The proposed appearance representation has several applications in robot vision. As examples, a precise visual positioning system, a real-time visual tracking system, and a real-time temporal inspection system are described.

The problem of vision-based robot positioning and tracking is addressed. A general learning algorithm is presented for determining the mapping between robot position and object appearance. The robot is first moved through several displacements with respect to its desired position, and a large set of object images is acquired. This image set is compressed using principal component analysis to obtain a four-dimensional subspace. Variations in object images due to robot displacements are represented as a compact parametrized manifold in the subspace. While positioning or tracking, errors in end-effector coordinates are efficiently computed from a single brightness image using the parametric manifold representation. The learning component enables accurate visual control without any prior hand-eye calibration. Several experiments have been conducted to demonstrate the practical feasibility of the proposed positioning/tracking approach and its relevance to industrial applications.>