The Effect of Indexing on the Complexity of Object Recognition

Many current recognition systems use constrained search to locate objects in cluttered environments. Previous formal analysis has shown that the expected amount of search is quadratic in the number of model and data features, if all the data is known to come from a sinlge object, but is exponential when spurious data is included. If one can group the data into subsets likely to have come from a single object, then terminating the search once a "good enough" interpretation is found reduces the expected search to cubic. Without successful grouping, terminated search is still exponential. These results apply to finding instances of a known object in the data. In this paper, we turn to the problem of selecting models from a library, and examine the combinatorics of determining that a candidate object is not present in the data. We show that the expected search is again exponential, implying that naﶥ approaches to indexing are likely to carry an expensive overhead, since an exponential amount of work is needed to week out each of the incorrect models. The analytic results are shown to be in agreement with empirical data for cluttered object recognition.

Motivated Action Theory: A Formal Theory of Causal Reasoning

When we reason about change over time, causation provides an implicit preference: we prefer sequences of situations in which one situation leads causally to the next, rather than sequences in which one situation follows another at random and without causal connections. In this paper, we explore the problem of temporal reasoning --- reasoning about change over time --- and the crucial role that causation plays in our intuitions. We examine previous approaches to temporal reasoning, and their shortcomings, in light of this analysis. We propose a new system for causal reasoning, motivated action theory, which builds upon causation as a crucial preference creterion. Motivated action theory solves the traditional problems of both forward and backward reasoning, and additionally provides a basis for a new theory of explanation.

Qualitative Analysis of MOS Circuits

With the push towards sub-micron technology, transistor models have become increasingly complex. The number of components in integrated circuits has forced designer's efforts and skills towards higher levels of design. This has created a gap between design expertise and the performance demands increasingly imposed by the technology. To alleviate this problem, software tools must be developed that provide the designer with expert advice on circuit performance and design. This requires a theory that links the intuitions of an expert circuit analyst with the corresponding principles of formal theory (i.e. algebra, calculus, feedback analysis, network theory, and electrodynamics), and that makes each underlying assumption explicit.