Assume that we have two perspective images with known intrinsic parameters except for an unknown common focal length. It is a minimally constrained problem to find the relative orientation between the two images given six corresponding points. We present an efficient solution to the problem and show that there are 15 solutions in general (including complex solutions). To the best of our knowledge this was a previously unsolved problem. The solutions are found through eigen-decomposition of a 15/spl times/15 matrix. The matrix itself is generated in closed form. We demonstrate through practical experiments that the algorithm is correct and numerically stable.

We present a solution for optimal triangulation in three views. The solution is guaranteed to find the optimal solution because it computes all the stationary points of the (maximum likelihood) objective function. Internally, the solution is found by computing roots of multivariate polynomial equations, directly solving the conditions for stationarity. The solver makes use of standard methods from computational commutative algebra to convert the root-finding problem into a 47 /spl times/ 47 nonsymmetric eigenproblem. Although there are in general 47 roots, counting both real and complex ones, the number of real roots is usually much smaller. We also show experimentally that the number of stationary points that are local minima and lie in front of each camera is small but does depend on the scene geometry.

This paper reviews two research themes. The first is wide baseline matching - establishing correspondences and cameras for images acquired from very different viewpoints. The second is automated surface reconstruction of a 3D scene from close-range images. These two themes are linked in an example application of automated architectural reconstruction from images. We demonstrate reconstructions of several university buildings from multiple photographs.

We describe and demonstrate a texture region descriptor which is invariant to affine geometric and photometric transformations, and insensitive to the shape of the texture region. It is applicable to texture patches which are locally planar and have stationary statistics. The novelty of the descriptor is that it is based on statistics aggregated over the region, resulting in richer and more stable descriptors than those computed at a point. Two texture matching applications of this descriptor are demonstrated: (1) it is used to automatically identify, regions of the same type of texture, but with varying surface pose, within a single image; (2) it is used to support wide baseline stereo, i.e. to enable the automatic computation of the epipolar geometry between two images acquired from quite separated viewpoints. Results are presented on several sets of real images.

The objective of this work is the automatic detection and grouping of imaged elements which repeat in a scene. We show that structures that repeat in the world (for example wall paper patterns) are related by particular parametrized transformations in perspective images. These image transformations provide powerful grouping constraints, and can be used at the heart of hypothesize and verify grouping algorithms. Parametrized transformations are given for some classes of repeating op-eration in the world as well as some groupers based on these. These groupers are demonstrated on a number of real images, where both the elements and the grouping are determined automatically. It is also shown that the repeating element can be learnt from the image, and hence provides an image descrip-tor. 1