Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

Actors and Continuous Functionals

This paper presents precise versions of some "laws" that must be satisfied by computations involving communicating parallel processes. The laws take the form of stating plausible restrictions on the histories of computations that are physically realizable. The laws are very general in that they are obeyed by parallel processes executing on a time varying number of distributed physical processors.

The Essential Dynamics Algorithm: Essential Results

This paper presents a novel algorithm for learning in a class of stochastic Markov decision processes (MDPs) with continuous state and action spaces that trades speed for accuracy. A transform of the stochastic MDP into a deterministic one is presented which captures the essence of the original dynamics, in a sense made precise. In this transformed MDP, the calculation of values is greatly simplified. The online algorithm estimates the model of the transformed MDP and simultaneously does policy search against it. Bounds on the error of this approximation are proven, and experimental results in a bicycle riding domain are presented. The algorithm learns near optimal policies in orders of magnitude fewer interactions with the stochastic MDP, using less domain knowledge. All code used in the experiments is available on the project's web site.

Planning for Conjunctive Goals

The problem of achieving conjunctive goals has been central to domain independent planning research; the nonlinear constraint-posting approach has been most successful. Previous planners of this type have been comlicated, heuristic, and ill-defined. I have combined and distilled the state of the art into a simple, precise, implemented algorithm (TWEAK) which I have proved correct and complete. I analyze previous work on domain-independent conjunctive planning; in retrospect it becomes clear that all conjunctive planners, linear and nonlinear, work the same way. The efficiency of these planners depends on the traditional add/delete-list representation for actions, which drastically limits their usefulness. I present theorems that suggest that efficient general purpose planning with more expressive action representations is impossible, and suggest ways to avoid this problem.