Fusion of 3D laser radar (LIDAR) imagery and aerial optical imagery is an efficient method for constructing 3D virtual reality models. One difficult aspect of creating such models is registering the optical image with the LIDAR point cloud, which is characterized as a camera pose estimation problem. We propose a novel application of mutual information registration methods, which exploits the statistical dependency in urban scenes of optical apperance with measured LIDAR elevation. We utilize the well known downhill simplex optimization to infer camera pose parameters. We discuss three methods for measuring mutual information between LIDAR imagery and optical imagery. Utilization of OpenGL and graphics hardware in the optimization process yields registration times dramatically lower than previous methods. Using an initial registration comparable to GPS/INS accuracy, we demonstrate the utility of our algorithm with a collection of urban images and present 3D models created with the fused imagery.

The minmax regret problem for combinatorial optimization under uncertainty can be viewed as a zero-sum game played between an optimizing player and an adversary, where the optimizing player selects a solution and the adversary selects costs with the intention of maximizing the regret of the player. The existing minmax regret model considers only deterministic solutions/strategies, and minmax regret versions of most polynomial solvable problems are NP-hard. In this paper, we consider a randomized model where the optimizing player selects a probability distribution (corresponding to a mixed strategy) over solutions and the adversary selects costs with knowledge of the player's distribution, but not its realization. We show that under this randomized model, the minmax regret version of any polynomial solvable combinatorial problem becomes polynomial solvable. This holds true for both the interval and discrete scenario representations of uncertainty. Using the randomized model, we show new proofs of existing approximation algorithms for the deterministic model based on primal-dual approaches. Finally, we prove that minmax regret problems are NP-hard under general convex uncertainty.

Abstract-We analyze losses resulting from uncertain transition probabilities in Markov decision processes with bounded nonnegative rewards. We assume that policies are precomputed using exact dynamic programming with the estimated transition probabilities, but the system evolves according to different, true transition probabilities. Given a bound on the total variation error of estimated transition probability distributions, we derive upper bounds on the loss of expected total reward. The approach analyzes the growth of errors incurred by stepping backwards in time while precomputing value functions, which requires bounding a multilinear program. Loss bounds are given for the finite horizon undiscounted, finite horizon discounted, and infinite horizon discounted cases, and a tight example is shown.

Rollout algorithms have demonstrated excellent performance on a variety of dynamic and discrete optimization problems. Interpreted as an approximate dynamic programming algorithm, a rollout algorithm estimates the value-to-go at each decision stage by simulating future events while following a greedy policy, referred to as the base policy. While in many cases rollout algorithms are guaranteed to perform as well as their base policies, there have been few theoretical results showing additional improvement in performance. In this paper we perform a probabilistic analysis of the subset sum problem and knapsack problem, giving theoretical evidence that rollout algorithms perform strictly better than their base policies. Using a stochastic model from the existing literature, we analyze two rollout methods that we refer to as the consecutive rollout and exhaustive rollout, both of which employ a simple greedy base policy. For the subset sum problem, we prove that after only a single iteration of the rollout algorithm, both methods yield at least a 30% reduction in the expected gap between the solution value and capacity, relative to the base policy. Analogous results are shown for the knapsack problem.