This paper proposes a new method for recovery of epipolar geometry and feature correspondence between images which have undergone a significant deformation, either due to large rotation or wide baseline of the cameras. The method also encodes the uncertainty by providing an arbitrarily close approximation to the posterior distribution of the two view relation. The method operates on a pyramid from coarse to fine resolution, thus raising the problem of how to propagate information from one level to another in a statistically consistent way. The distribution of the parameters at each resolution is encoded nonparametrically as a set of particles. At the coarsest level, a random sample consensus Monte Carlo Markov chain (RANSAC-MCMC) estimator is used to initialize this set of particles, the posterior can then be approximated as a mixture of Gaussians fitted to these particles. The distribution at a coarser level influences the distribution at a finer level using the technique of sampling-importance-resampling (SIR) and MCMC, which allows for asymptotically correct approximations of the posterior distribution. The estimate of the posterior distribution at the level above is being used as the importance sampling function to generate a new set of particles, which can be further improved by MCMC. It is shown that the method is superior to previous single resolution RANSAC-style feature matchers.

This paper describes an efficient method to calculate, from an image of an object, configurations of a two-fingered robot gripper that form a "cage" to contain that object. Closing the fingers on the object from these configurations is guaranteed to reach a given desired grasp. This builds on the visual grasping theory of A. Blake et al. (1993), which describes how to find optimal grasps. It extends the results of E. Rimon and A. Blake (1996) which show how to construct such cages, in two ways. First, a more efficient algorithm for computing the cage is described. Second, a further development deals with occlusion by solving the caging problem within a restricted image window. The new methods greatly reduce the complexity of the visual caging problem, making it feasible in a real time computer vision system.

This paper extends the caging theory of Rimon and Blake (1996) for one-parameter two-finger grippers to one-parameter three-finger grippers. The caging theory describes how the fingers of a robot gripper can be placed around an object so that it cannot escape. As the fingers close from such a configuration, the freedom of the object to move is gradually restricted, until, in the absence of friction, it is completely immobilized by the fingers at an immobilizing grasp. The extension of the caging theory to three-fingered grippers is important because convex objects cannot be caged by two-finger grippers. The computation of the set of caging formations requires the identification of both the two- and three-finger frictionless grasps. These grasps correspond to critical points of the opening parameter in the gripper's configuration space. There are two main problems here. Firstly, a method is needed to compute the critical points of the opening parameter in the three-finger contact space. This is complicated by the fact that this space may have more that one connected component. The second problem is how to associate the immobilizing grasps with punctures. In this paper we solve both these problems, presenting efficient algorithmic solutions.